Helmholtz test, sod shock tube

Components/Pipe1D.cs

@@ -3,33 +3,71 @@ using FluidSim.Interfaces;
 
 namespace FluidSim.Components
 {
+    public enum BoundaryType
+    {
+        VolumeCoupling,
+        OpenEnd,
+        ClosedEnd
+    }
+
     public class Pipe1D
     {
         public Port PortA { get; }
         public Port PortB { get; }
         public double Area => _area;
+        public double DampingMultiplier { get; set; } = 1.0;
 
         private int _n;
-        private double _dx, _dt, _gamma = 1.4, _area;
+        private double _dx, _dt, _gamma, _area, _diameter;
         private double[] _rho, _rhou, _E;
 
-        // Volume states at boundaries
+        // Volume‑coupling ghost states for boundaries A and B
-        private double _rhoLeft, _pLeft, _rhoRight, _pRight;
+        private double _rhoA, _pA;
-        private bool _leftBCSet, _rightBCSet;
+        private double _rhoB, _pB;
+        private bool _aBCSet, _bBCSet;
 
-        public double FrictionFactor { get; set; } = 0.02;
+        private BoundaryType _aBCType = BoundaryType.VolumeCoupling;
+        private BoundaryType _bBCType = BoundaryType.VolumeCoupling;
+
+        private double _aAmbientPressure = 101325.0;
+        private double _bAmbientPressure = 101325.0;
+
+        private const double CflTarget = 0.8;
+        private const double ReferenceSoundSpeed = 340.0;
 
         public int GetCellCount() => _n;
         public double GetCellDensity(int i) => _rho[i];
         public double GetCellPressure(int i) => Pressure(i);
         public double GetCellVelocity(int i) => _rhou[i] / Math.Max(_rho[i], 1e-12);
 
-        public Pipe1D(double length, double area, int nCells, int sampleRate)
+        public BoundaryType ABCType => _aBCType;
+        public BoundaryType BBCType => _bBCType;
+
+        public Pipe1D(double length, double area, int sampleRate, int forcedCellCount = 0)
         {
+            double dtGlobal = 1.0 / sampleRate;
+            int nCells;
+
+            if (forcedCellCount > 1)
+            {
+                nCells = forcedCellCount;
+            }
+            else
+            {
+                double dxTarget = ReferenceSoundSpeed * dtGlobal * CflTarget;
+                nCells = Math.Max(2, (int)Math.Round(length / dxTarget, MidpointRounding.AwayFromZero));
+                while (length / nCells > dxTarget * 1.01 && nCells < int.MaxValue - 1)
+                    nCells++;
+            }
+
             _n = nCells;
-            _dx = length / nCells;
+            _dx = length / _n;
-            _dt = 1.0 / sampleRate;
+            _dt = dtGlobal;
             _area = area;
+            _gamma = 1.4;
+
+            // Hydraulic diameter for a circular pipe
+            _diameter = 2.0 * Math.Sqrt(area / Math.PI);
 
             _rho = new double[_n];
             _rhou = new double[_n];
@@ -39,6 +77,11 @@ namespace FluidSim.Components
             PortB = new Port();
         }
 
+        public void SetABoundaryType(BoundaryType type) => _aBCType = type;
+        public void SetBBoundaryType(BoundaryType type) => _bBCType = type;
+        public void SetAAmbientPressure(double p) => _aAmbientPressure = p;
+        public void SetBAmbientPressure(double p) => _bAmbientPressure = p;
+
         public void SetUniformState(double rho, double u, double p)
         {
             double e = p / ((_gamma - 1) * rho);
@@ -51,24 +94,181 @@ namespace FluidSim.Components
             }
         }
 
-        public double GetLeftPressure() => Pressure(0);
+        public void SetCellState(int i, double rho, double u, double p)
-        public double GetRightPressure() => Pressure(_n - 1);
-        public double GetLeftDensity() => _rho[0];
-        public double GetRightDensity() => _rho[_n - 1];
-
-        // ★ New: pass both density and pressure from the volume
-        public void SetLeftVolumeState(double rhoVol, double pVol)
         {
-            _rhoLeft = rhoVol;
+            if (i < 0 || i >= _n) return;
-            _pLeft = pVol;
+            _rho[i] = rho;
-            _leftBCSet = true;
+            _rhou[i] = rho * u;
+            double e = p / ((_gamma - 1) * rho);
+            _E[i] = rho * e + 0.5 * rho * u * u;
         }
 
-        public void SetRightVolumeState(double rhoVol, double pVol)
+        public void SetAVolumeState(double rhoVol, double pVol)
         {
-            _rhoRight = rhoVol;
+            _rhoA = rhoVol;
-            _pRight = pVol;
+            _pA = pVol;
-            _rightBCSet = true;
+            _aBCSet = true;
+        }
+
+        public void SetBVolumeState(double rhoVol, double pVol)
+        {
+            _rhoB = rhoVol;
+            _pB = pVol;
+            _bBCSet = true;
+        }
+
+        public void ClearBC() => _aBCSet = _bBCSet = false;
+
+        public int GetRequiredSubSteps(double dtGlobal, double cflTarget = 0.8)
+        {
+            double maxW = 0.0;
+            for (int i = 0; i < _n; i++)
+            {
+                double rho = _rho[i];
+                double u = Math.Abs(_rhou[i] / Math.Max(rho, 1e-12));
+                double c = Math.Sqrt(_gamma * Pressure(i) / Math.Max(rho, 1e-12));
+                double local = u + c;
+                if (local > maxW) maxW = local;
+            }
+            maxW = Math.Max(maxW, 1e-8);
+            return Math.Max(1, (int)Math.Ceiling(dtGlobal * maxW / (cflTarget * _dx)));
+        }
+
+        public void SimulateSingleStep(double dtSub)
+        {
+            int n = _n;
+            double[] Fm = new double[n + 1];
+            double[] Fp = new double[n + 1];
+            double[] Fe = new double[n + 1];
+
+            // ---------- Boundary A (face 0, left) ----------
+            double rhoIntA = _rho[0];
+            double uIntA = _rhou[0] / Math.Max(rhoIntA, 1e-12);
+            double pIntA = Pressure(0);
+
+            switch (_aBCType)
+            {
+                case BoundaryType.VolumeCoupling:
+                    if (_aBCSet)
+                    {
+                        HLLCFlux(_rhoA, 0.0, _pA,
+                                 rhoIntA, uIntA, pIntA,
+                                 out Fm[0], out Fp[0], out Fe[0]);
+                    }
+                    else
+                    {
+                        Fm[0] = 0; Fp[0] = pIntA; Fe[0] = 0;
+                    }
+                    break;
+
+                case BoundaryType.OpenEnd:
+                    OpenEndFluxA(rhoIntA, uIntA, pIntA, _aAmbientPressure,
+                                 out Fm[0], out Fp[0], out Fe[0]);
+                    break;
+
+                case BoundaryType.ClosedEnd:
+                    ClosedEndFlux(rhoIntA, uIntA, pIntA, isRightBoundary: false,
+                                  out Fm[0], out Fp[0], out Fe[0]);
+                    break;
+            }
+
+            // ---------- Internal faces ----------
+            for (int i = 0; i < n - 1; i++)
+            {
+                double rhoL = _rho[i];
+                double uL = _rhou[i] / Math.Max(rhoL, 1e-12);
+                double pL = Pressure(i);
+
+                double rhoR = _rho[i + 1];
+                double uR = _rhou[i + 1] / Math.Max(rhoR, 1e-12);
+                double pR = Pressure(i + 1);
+
+                HLLCFlux(rhoL, uL, pL, rhoR, uR, pR,
+                         out Fm[i + 1], out Fp[i + 1], out Fe[i + 1]);
+            }
+
+            // ---------- Boundary B (face n, right) ----------
+            double rhoIntB = _rho[n - 1];
+            double uIntB = _rhou[n - 1] / Math.Max(rhoIntB, 1e-12);
+            double pIntB = Pressure(n - 1);
+
+            switch (_bBCType)
+            {
+                case BoundaryType.VolumeCoupling:
+                    if (_bBCSet)
+                    {
+                        HLLCFlux(rhoIntB, uIntB, pIntB,
+                                 _rhoB, 0.0, _pB,
+                                 out Fm[n], out Fp[n], out Fe[n]);
+                    }
+                    else
+                    {
+                        Fm[n] = 0; Fp[n] = pIntB; Fe[n] = 0;
+                    }
+                    break;
+
+                case BoundaryType.OpenEnd:
+                    OpenEndFluxB(rhoIntB, uIntB, pIntB, _bAmbientPressure,
+                                 out Fm[n], out Fp[n], out Fe[n]);
+                    break;
+
+                case BoundaryType.ClosedEnd:
+                    ClosedEndFlux(rhoIntB, uIntB, pIntB, isRightBoundary: true,
+                                  out Fm[n], out Fp[n], out Fe[n]);
+                    break;
+            }
+
+            // ---- Cell update with linear laminar damping ----
+            double radius = _diameter / 2.0;
+            double mu_air = 1.8e-5;
+            double laminarCoeff = DampingMultiplier * 8.0 * mu_air / (radius * radius);
+
+            for (int i = 0; i < n; i++)
+            {
+                double dM = (Fm[i + 1] - Fm[i]) / _dx;
+                double dP = (Fp[i + 1] - Fp[i]) / _dx;
+                double dE = (Fe[i + 1] - Fe[i]) / _dx;
+
+                _rho[i] -= dtSub * dM;
+                _rhou[i] -= dtSub * dP;
+                _E[i] -= dtSub * dE;
+
+                double rho = Math.Max(_rho[i], 1e-12);
+                double dampingRate = laminarCoeff / rho;
+                double dampingFactor = Math.Exp(-dampingRate * dtSub);
+                _rhou[i] *= dampingFactor;
+
+                if (_rho[i] < 1e-12) _rho[i] = 1e-12;
+                double kinetic = 0.5 * _rhou[i] * _rhou[i] / _rho[i];
+                double pMin = 100.0;
+                double eMin = pMin / ((_gamma - 1) * _rho[i]) + kinetic;
+                if (_E[i] < eMin) _E[i] = eMin;
+            }
+
+            // ---------- Port quantities ----------
+            double mdotA_sub = _aBCType == BoundaryType.VolumeCoupling && _aBCSet ? Fm[0] * _area : 0.0;
+            double mdotB_sub = _bBCType == BoundaryType.VolumeCoupling && _bBCSet ? -Fm[n] * _area : 0.0;
+
+            PortA.MassFlowRate = mdotA_sub;
+            PortB.MassFlowRate = mdotB_sub;
+            PortA.Pressure = pIntA;
+            PortB.Pressure = pIntB;
+            PortA.Density = _rho[0];
+            PortB.Density = _rho[n - 1];
+
+            // Corrected enthalpy for both directions
+            if (_aBCType == BoundaryType.VolumeCoupling && _aBCSet)
+            {
+                PortA.SpecificEnthalpy = mdotA_sub < 0
+                    ? GetCellTotalSpecificEnthalpy(0)
+                    : (_gamma / (_gamma - 1.0)) * _pA / Math.Max(_rhoA, 1e-12);
+            }
+            if (_bBCType == BoundaryType.VolumeCoupling && _bBCSet)
+            {
+                PortB.SpecificEnthalpy = mdotB_sub < 0
+                    ? GetCellTotalSpecificEnthalpy(_n - 1)
+                    : (_gamma / (_gamma - 1.0)) * _pB / Math.Max(_rhoB, 1e-12);
+            }
         }
 
         private double GetCellTotalSpecificEnthalpy(int i)
@@ -80,94 +280,103 @@ namespace FluidSim.Components
             return h + 0.5 * u * u;
         }
 
-        public void Simulate()
+        private double Pressure(int i) =>
-        {
-            int n = _n;
-            double[] Fm = new double[n + 1], Fp = new double[n + 1], Fe = new double[n + 1];
-
-            // --- Left boundary (face 0) ---
-            if (_leftBCSet)
-            {
-                // Ghost = actual volume state (ρ_vol, u=0, p_vol)
-                double rhoL = _rhoLeft;
-                double uL = 0.0;
-                double pL = _pLeft;
-
-                double rhoR = _rho[0];
-                double uR = _rhou[0] / Math.Max(rhoR, 1e-12);
-                double pR = Pressure(0);
-
-                HLLCFlux(rhoL, uL, pL, rhoR, uR, pR, out Fm[0], out Fp[0], out Fe[0]);
-            }
-            else
-            {
-                Fm[0] = 0;
-                Fp[0] = Pressure(0);
-                Fe[0] = 0;
-            }
-
-            // --- Internal faces ---
-            for (int i = 0; i < n - 1; i++)
-            {
-                double uL = _rhou[i] / Math.Max(_rho[i], 1e-12);
-                double uR = _rhou[i + 1] / Math.Max(_rho[i + 1], 1e-12);
-                HLLCFlux(_rho[i], uL, Pressure(i), _rho[i + 1], uR, Pressure(i + 1),
-                         out Fm[i + 1], out Fp[i + 1], out Fe[i + 1]);
-            }
-
-            // --- Right boundary (face n) ---
-            if (_rightBCSet)
-            {
-                double rhoL = _rho[n - 1];
-                double uL = _rhou[n - 1] / Math.Max(rhoL, 1e-12);
-                double pL = Pressure(n - 1);
-
-                // Ghost = actual volume state (ρ_vol, u=0, p_vol)
-                double rhoR = _rhoRight;
-                double uR = 0.0;
-                double pR = _pRight;
-
-                HLLCFlux(rhoL, uL, pL, rhoR, uR, pR, out Fm[n], out Fp[n], out Fe[n]);
-            }
-            else
-            {
-                Fm[n] = 0;
-                Fp[n] = Pressure(n - 1);
-                Fe[n] = 0;
-            }
-
-            // --- Cell update ---
-            for (int i = 0; i < n; i++)
-            {
-                double dM = (Fm[i + 1] - Fm[i]) / _dx;
-                double dP = (Fp[i + 1] - Fp[i]) / _dx;
-                double dE = (Fe[i + 1] - Fe[i]) / _dx;
-                _rho[i] -= _dt * dM;
-                _rhou[i] -= _dt * dP;
-                _E[i] -= _dt * dE;
-
-                if (_rho[i] < 1e-12) _rho[i] = 1e-12;
-                double kinetic = 0.5 * _rhou[i] * _rhou[i] / _rho[i];
-                if (_E[i] < kinetic) _E[i] = kinetic;
-            }
-
-            // --- Friction disabled ---
-            // if (FrictionFactor > 0) { … }
-
-            // --- Port flows ---
-            PortA.MassFlowRate = _leftBCSet ? Fm[0] * _area : 0.0;
-            PortB.MassFlowRate = _rightBCSet ? -Fm[n] * _area : 0.0;
-
-            PortA.SpecificEnthalpy = GetCellTotalSpecificEnthalpy(0);
-            PortB.SpecificEnthalpy = GetCellTotalSpecificEnthalpy(_n - 1);
-
-            _leftBCSet = _rightBCSet = false;
-        }
-
-        double Pressure(int i) =>
             (_gamma - 1.0) * (_E[i] - 0.5 * _rhou[i] * _rhou[i] / Math.Max(_rho[i], 1e-12));
 
-        void HLLCFlux(double rL, double uL, double pL, double rR, double uR, double pR,
+        // ========== Characteristic‑based Open End ==========
+        private void OpenEndFluxA(double rhoInt, double uInt, double pInt, double pAmb,
+                                  out double fm, out double fp, out double fe)
+        {
+            double cInt = Math.Sqrt(_gamma * pInt / Math.Max(rhoInt, 1e-12));
+
+            // Subsonic inflow (uInt ≤ 0, so flow inside pipe ←)
+            if (uInt <= -cInt)   // supersonic inflow – use interior state as ghost
+            {
+                fm = rhoInt * uInt;
+                fp = rhoInt * uInt * uInt + pInt;
+                fe = (rhoInt * (pInt / ((_gamma - 1) * rhoInt) + 0.5 * uInt * uInt) + pInt) * uInt;
+                return;
+            }
+            else if (uInt <= 0)   // subsonic inflow
+            {
+                // Reservoir condition: p = pAmb, T = 300K, u = 0
+                double T0 = 300.0;
+                double R = 287.0;
+                double rhoGhost = pAmb / (R * T0);
+                HLLCFlux(rhoGhost, 0.0, pAmb, rhoInt, uInt, pInt, out fm, out fp, out fe);
+                return;
+            }
+            else   // subsonic outflow (uInt > 0)
+            {
+                // Ghost pressure forced to pAmb
+                double s = pInt / Math.Pow(rhoInt, _gamma);
+                double rhoGhost = Math.Pow(pAmb / s, 1.0 / _gamma);
+                double cGhost = Math.Sqrt(_gamma * pAmb / rhoGhost);
+
+                // Outgoing Riemann invariant J⁻ = uInt - 2*cInt/(γ-1) (for left boundary)
+                double J_minus = uInt - 2.0 * cInt / (_gamma - 1.0);
+                double uGhost = J_minus + 2.0 * cGhost / (_gamma - 1.0);
+
+                // Prevent spurious inflow by clipping to zero
+                if (uGhost < 0) uGhost = 0;
+
+                HLLCFlux(rhoGhost, uGhost, pAmb, rhoInt, uInt, pInt, out fm, out fp, out fe);
+            }
+        }
+
+        private void OpenEndFluxB(double rhoInt, double uInt, double pInt, double pAmb,
+                                  out double fm, out double fp, out double fe)
+        {
+            double cInt = Math.Sqrt(_gamma * pInt / Math.Max(rhoInt, 1e-12));
+
+            if (uInt >= cInt)   // supersonic outflow (extrapolation)
+            {
+                fm = rhoInt * uInt;
+                fp = rhoInt * uInt * uInt + pInt;
+                fe = (rhoInt * (pInt / ((_gamma - 1) * rhoInt) + 0.5 * uInt * uInt) + pInt) * uInt;
+                return;
+            }
+            else if (uInt >= 0)   // subsonic outflow
+            {
+                double s = pInt / Math.Pow(rhoInt, _gamma);
+                double rhoGhost = Math.Pow(pAmb / s, 1.0 / _gamma);
+                double cGhost = Math.Sqrt(_gamma * pAmb / rhoGhost);
+
+                // Outgoing Riemann invariant J⁺ = uInt + 2*cInt/(γ-1) (for right boundary)
+                double J_plus = uInt + 2.0 * cInt / (_gamma - 1.0);
+                double uGhost = J_plus - 2.0 * cGhost / (_gamma - 1.0);
+
+                // Clip to zero to prevent inflow
+                if (uGhost > 0) uGhost = 0;
+
+                HLLCFlux(rhoInt, uInt, pInt, rhoGhost, uGhost, pAmb, out fm, out fp, out fe);
+            }
+            else   // subsonic inflow
+            {
+                double T0 = 300.0;
+                double R = 287.0;
+                double rhoGhost = pAmb / (R * T0);
+                HLLCFlux(rhoInt, uInt, pInt, rhoGhost, 0.0, pAmb, out fm, out fp, out fe);
+            }
+        }
+
+        // ========== Closed end (mirror) ==========
+        private void ClosedEndFlux(double rhoInt, double uInt, double pInt, bool isRightBoundary,
+                                   out double fm, out double fp, out double fe)
+        {
+            double rhoGhost = rhoInt;
+            double pGhost = pInt;
+            double uGhost = -uInt;   // mirror velocity
+
+            if (isRightBoundary)
+                HLLCFlux(rhoInt, uInt, pInt, rhoGhost, uGhost, pGhost, out fm, out fp, out fe);
+            else
+                HLLCFlux(rhoGhost, uGhost, pGhost, rhoInt, uInt, pInt, out fm, out fp, out fe);
+        }
+
+        // ========== Standard HLLC flux ==========
+        private void HLLCFlux(double rL, double uL, double pL,
+                              double rR, double uR, double pR,
                               out double fm, out double fp, out double fe)
         {
             double cL = Math.Sqrt(_gamma * pL / Math.Max(rL, 1e-12));
@@ -176,6 +385,7 @@ namespace FluidSim.Components
             double ER = pR / ((_gamma - 1) * rR) + 0.5 * uR * uR;
             double SL = Math.Min(uL - cL, uR - cR);
             double SR = Math.Max(uL + cL, uR + cR);
+
             double Ss = (pR - pL + rL * uL * (SL - uL) - rR * uR * (SR - uR))
                       / (rL * (SL - uL) - rR * (SR - uR));
 
@@ -199,5 +409,12 @@ namespace FluidSim.Components
                 fm = rsR * Ss; fp = rsR * Ss * Ss + ps; fe = (rsR * EsR + ps) * Ss;
             }
         }
+
+        public double GetPressureAtFraction(double fraction)
+        {
+            int i = (int)(fraction * (_n - 1));
+            i = Math.Clamp(i, 0, _n - 1);
+            return Pressure(i);
+        }
     }
 }

Components/Volume0D.cs

@@ -50,13 +50,26 @@ namespace FluidSim.Components
             Port.SpecificEnthalpy = SpecificEnthalpy;
         }
 
+        // Original integrate (uses the constructor’s sample rate)
         public void Integrate()
+        {
+            Integrate(_dt);
+        }
+
+        public void SetPressure(double newPressure)
+        {
+            InternalEnergy = newPressure * Volume / (Gamma - 1.0);
+            // Mass stays the same, so density is unchanged
+        }
+
+        // New overload: integrate with a custom time step (for sub‑steps)
+        public void Integrate(double dtOverride)
         {
             double mdot = Port.MassFlowRate;
             double h_in = Port.SpecificEnthalpy;
 
-            double dm = mdot * _dt;
+            double dm = mdot * dtOverride;
-            double dE = (mdot * h_in) * _dt - Pressure * dVdt * _dt;
+            double dE = (mdot * h_in) * dtOverride - Pressure * dVdt * dtOverride;
 
             Mass += dm;
             InternalEnergy += dE;

Core/OrificeBoundary.cs

@@ -1,5 +1,5 @@
 using System;
-using FluidSim.Components;
+using FluidSim.Interfaces;
 
 namespace FluidSim.Core
 {

Core/Simulation.cs

@@ -1,67 +0,0 @@
-using System;
-using FluidSim.Components;
-using FluidSim.Utils;
-
-namespace FluidSim.Core
-{
-    public static class Simulation
-    {
-        private static Solver solver;
-        private static Volume0D volA, volB;
-        private static Pipe1D pipe;
-        private static Connection connA, connB;
-        private static int stepCount;
-        private static double time;
-        private static double dt;
-
-        public static void Initialize(int sampleRate)
-        {
-            dt = 1.0 / sampleRate;
-
-            double V = 5.0 * Units.L;
-            volA = new Volume0D(V, 1.1 * Units.atm, Units.Celsius(20), sampleRate);
-            volB = new Volume0D(V, 1.0 * Units.atm, Units.Celsius(20), sampleRate);
-
-            double length = 150 * Units.mm;
-            double diameter = 25 * Units.mm;
-            double area = Units.AreaFromDiameter(25, Units.mm);
-            int nCells = 10;
-
-            pipe = new Pipe1D(length, area, nCells, sampleRate);
-            pipe.SetUniformState(volA.Density, 0.0, volA.Pressure);
-            pipe.FrictionFactor = 0.02;
-
-            // Connections with orifice area equal to pipe area (flange joint)
-            connA = new Connection(volA.Port, pipe.PortA) { Area = area, DischargeCoefficient = 1.0, Gamma = 1.4 };
-            connB = new Connection(pipe.PortB, volB.Port) { Area = area, DischargeCoefficient = 1.0, Gamma = 1.4 };
-
-            solver = new Solver();
-            solver.AddVolume(volA);
-            solver.AddVolume(volB);
-            solver.AddPipe(pipe);
-            solver.AddConnection(connA);
-            solver.AddConnection(connB);
-        }
-
-        public static float Process()
-        {
-            solver.Step();
-            time += dt;
-            stepCount++;
-            Log();
-            return 0f;
-        }
-
-        public static void Log()
-        {
-            if (stepCount <= 50 || stepCount % 200 == 0)
-            {
-                Console.WriteLine(
-                    $"t = {time * 1e3:F3} ms  Step {stepCount:D4}: " +
-                    $"PA = {volA.Pressure / 1e5:F6} bar, " +
-                    $"PB = {volB.Pressure / 1e5:F6} bar, " +
-                    $"FlowA = {pipe.PortA.MassFlowRate * 1e3:F2} g/s");
-            }
-        }
-    }
-}

Core/Solver.cs

@@ -1,4 +1,5 @@
-using System.Collections.Generic;
+using System;
+using System.Collections.Generic;
 using FluidSim.Components;
 using FluidSim.Interfaces;
 
@@ -10,70 +11,160 @@ namespace FluidSim.Core
         private readonly List<Pipe1D> _pipes = new();
         private readonly List<Connection> _connections = new();
 
+        private double _dt;
+
         public void AddVolume(Volume0D v) => _volumes.Add(v);
         public void AddPipe(Pipe1D p) => _pipes.Add(p);
         public void AddConnection(Connection c) => _connections.Add(c);
+        public void SetTimeStep(double dt) => _dt = dt;
 
-        public void Step()
+        /// <summary>
+        /// Set boundary type for a pipe end. isA = true for port A (left), false for port B (right).
+        /// </summary>
+        public void SetPipeBoundary(Pipe1D pipe, bool isA, BoundaryType type, double ambientPressure = 101325.0)
         {
-            // 1. Volumes publish state to their ports
+            if (isA)
+            {
+                pipe.SetABoundaryType(type);
+                if (type == BoundaryType.OpenEnd)
+                    pipe.SetAAmbientPressure(ambientPressure);
+            }
+            else
+            {
+                pipe.SetBBoundaryType(type);
+                if (type == BoundaryType.OpenEnd)
+                    pipe.SetBAmbientPressure(ambientPressure);
+            }
+        }
+
+        public float Step()
+        {
+            // 1. Volumes publish state
             foreach (var v in _volumes)
                 v.PushStateToPort();
 
-            // 2. Set volume states as boundary conditions on pipes
+            // 2. Set volume BCs for volume‑coupled ends
             foreach (var conn in _connections)
             {
                 if (IsPipePort(conn.PortA) && IsVolumePort(conn.PortB))
+                {
+                    var pipe = GetPipe(conn.PortA);
+                    bool isA = pipe.PortA == conn.PortA;
+                    if ((isA && pipe.ABCType == BoundaryType.VolumeCoupling) ||
+                        (!isA && pipe.BBCType == BoundaryType.VolumeCoupling))
                         SetVolumeBC(conn.PortA, conn.PortB);
+                }
                 else if (IsVolumePort(conn.PortA) && IsPipePort(conn.PortB))
+                {
+                    var pipe = GetPipe(conn.PortB);
+                    bool isA = pipe.PortB == conn.PortB;
+                    if ((isA && pipe.ABCType == BoundaryType.VolumeCoupling) ||
+                        (!isA && pipe.BBCType == BoundaryType.VolumeCoupling))
                         SetVolumeBC(conn.PortB, conn.PortA);
                 }
+            }
 
-            // 3. Run pipe simulations
+            // 3. Sub‑steps
+            int nSub = 1;
             foreach (var p in _pipes)
-                p.Simulate();
+                nSub = Math.Max(nSub, p.GetRequiredSubSteps(_dt));
+            double dtSub = _dt / nSub;
+
+            for (int sub = 0; sub < nSub; sub++)
+            {
+                foreach (var p in _pipes)
+                    p.SimulateSingleStep(dtSub);
 
-            // 4. Transfer pipe‑port flows to volume ports
                 foreach (var conn in _connections)
                 {
                     if (IsPipePort(conn.PortA) && IsVolumePort(conn.PortB))
-                    TransferPipeToVolume(conn.PortA, conn.PortB);
-                else if (IsVolumePort(conn.PortA) && IsPipePort(conn.PortB))
-                    TransferPipeToVolume(conn.PortB, conn.PortA);
-            }
-
-            // 5. Integrate volumes
-            foreach (var v in _volumes)
-                v.Integrate();
-        }
-
-        bool IsVolumePort(Port p) => _volumes.Exists(v => v.Port == p);
-        bool IsPipePort(Port p) => _pipes.Exists(pp => pp.PortA == p || pp.PortB == p);
-        Pipe1D GetPipe(Port p) => _pipes.Find(pp => pp.PortA == p || pp.PortB == p);
-
-        void SetVolumeBC(Port pipePort, Port volPort)
                     {
-            Pipe1D pipe = GetPipe(pipePort);
+                        var pipe = GetPipe(conn.PortA);
-            if (pipe == null) return;
+                        bool isA = pipe.PortA == conn.PortA;
-            bool isLeft = pipe.PortA == pipePort;
+                        if ((isA && pipe.ABCType == BoundaryType.VolumeCoupling) ||
-
+                            (!isA && pipe.BBCType == BoundaryType.VolumeCoupling))
-            if (isLeft)
+                            TransferAndIntegrate(conn.PortA, conn.PortB, dtSub);
-                pipe.SetLeftVolumeState(volPort.Density, volPort.Pressure);
+                    }
-            else
+                    else if (IsVolumePort(conn.PortA) && IsPipePort(conn.PortB))
-                pipe.SetRightVolumeState(volPort.Density, volPort.Pressure);
+                    {
+                        var pipe = GetPipe(conn.PortB);
+                        bool isA = pipe.PortB == conn.PortB;
+                        if ((isA && pipe.ABCType == BoundaryType.VolumeCoupling) ||
+                            (!isA && pipe.BBCType == BoundaryType.VolumeCoupling))
+                            TransferAndIntegrate(conn.PortB, conn.PortA, dtSub);
+                    }
                 }
 
-        void TransferPipeToVolume(Port pipePort, Port volPort)
+                if (sub < nSub - 1)
+                {
+                    foreach (var v in _volumes)
+                        v.PushStateToPort();
+
+                    foreach (var conn in _connections)
+                    {
+                        if (IsPipePort(conn.PortA) && IsVolumePort(conn.PortB))
+                        {
+                            var pipe = GetPipe(conn.PortA);
+                            bool isA = pipe.PortA == conn.PortA;
+                            if ((isA && pipe.ABCType == BoundaryType.VolumeCoupling) ||
+                                (!isA && pipe.BBCType == BoundaryType.VolumeCoupling))
+                                SetVolumeBC(conn.PortA, conn.PortB);
+                        }
+                        else if (IsVolumePort(conn.PortA) && IsPipePort(conn.PortB))
+                        {
+                            var pipe = GetPipe(conn.PortB);
+                            bool isA = pipe.PortB == conn.PortB;
+                            if ((isA && pipe.ABCType == BoundaryType.VolumeCoupling) ||
+                                (!isA && pipe.BBCType == BoundaryType.VolumeCoupling))
+                                SetVolumeBC(conn.PortB, conn.PortA);
+                        }
+                    }
+                }
+            }
+
+            // 5. Audio samples (none for now, but placeholder)
+            var audioSamples = new List<float>();
+            foreach (var conn in _connections)
+            {
+                if (conn is SoundConnection sc)
+                    audioSamples.Add(sc.GetAudioSample());
+            }
+
+            // 6. Clear BC flags
+            foreach (var p in _pipes)
+                p.ClearBC();
+
+            return SoundProcessor.MixAndClip(audioSamples.ToArray());
+        }
+
+        private bool IsVolumePort(Port p) => _volumes.Exists(v => v.Port == p);
+        private bool IsPipePort(Port p) => _pipes.Exists(pp => pp.PortA == p || pp.PortB == p);
+        private Pipe1D GetPipe(Port p) => _pipes.Find(pp => pp.PortA == p || pp.PortB == p);
+        private Volume0D GetVolume(Port p) => _volumes.Find(v => v.Port == p);
+
+        private void SetVolumeBC(Port pipePort, Port volPort)
+        {
+            var pipe = GetPipe(pipePort);
+            if (pipe == null) return;
+            bool isA = pipe.PortA == pipePort;
+            if (isA)
+                pipe.SetAVolumeState(volPort.Density, volPort.Pressure);
+            else
+                pipe.SetBVolumeState(volPort.Density, volPort.Pressure);
+        }
+
+        private void TransferAndIntegrate(Port pipePort, Port volPort, double dtSub)
         {
             double mdot = pipePort.MassFlowRate;
             volPort.MassFlowRate = -mdot;
 
             if (mdot < 0)  // pipe → volume
             {
-                // pipePort.SpecificEnthalpy is already total (h + ½u²)
                 volPort.SpecificEnthalpy = pipePort.SpecificEnthalpy;
             }
-            // else: volume → pipe, volume’s own static enthalpy is used (already set)
+            // else volume’s own enthalpy (from PushStateToPort) is used
+
+            GetVolume(volPort)?.Integrate(dtSub);
         }
     }
 }

Core/SoundProcessor.cs

@@ -0,0 +1,23 @@
+namespace FluidSim.Core
+{
+    /// <summary>
+    /// Mixes multiple audio samples and applies a soft‑clipping tanh.
+    /// </summary>
+    public static class SoundProcessor
+    {
+        /// <summary>Overall gain applied after mixing (before tanh).</summary>
+        public static float MasterGain { get; set; } = 0.01f;
+
+        /// <summary>
+        /// Mixes an array of raw audio samples and returns a single sample in [‑1, 1].
+        /// </summary>
+        public static float MixAndClip(params float[] samples)
+        {
+            float sum = 0f;
+            foreach (float s in samples)
+                sum += s;
+            sum *= MasterGain;
+            return sum;
+        }
+    }
+}

Interfaces/Connection.cs

@@ -1,6 +1,4 @@
-using FluidSim.Interfaces;
+namespace FluidSim.Interfaces
-
-namespace FluidSim.Components
 {
     /// <summary>Pure data link between two ports, with orifice parameters.</summary>
     public class Connection

Interfaces/SoundConnection.cs

@@ -0,0 +1,25 @@
+namespace FluidSim.Interfaces
+{
+    /// <summary>
+    /// A Connection that also produces an audio sample from the pressure drop across it.
+    /// </summary>
+    public class SoundConnection : Connection
+    {
+        /// <summary>Gain applied to the normalised pressure difference.</summary>
+        public float Gain { get; set; } = 1.0f;
+
+        /// <summary>Reference pressure used for normalisation (Pa). Default: 1 atm.</summary>
+        public double ReferencePressure { get; set; } = 101325.0;
+
+        public SoundConnection(Port a, Port b) : base(a, b) { }
+
+        /// <summary>
+        /// Returns a normalised audio sample proportional to the pressure difference.
+        /// </summary>
+        public float GetAudioSample()
+        {
+            double dp = PortA.Pressure - PortB.Pressure;
+            return (float)(dp / ReferencePressure) * Gain;
+        }
+    }
+}

Program.cs

@@ -9,61 +9,176 @@ namespace FluidSim;
 public class Program
 {
     private const int SampleRate = 44100;
+    private const double DrawFrequency = 60.0;
+    private static Scenario scenario;
+
+    // Speed control
+    //private static double desiredSpeed = 1.0;
+    private static double desiredSpeed = 0.0001;
+    private static double currentSpeed = desiredSpeed;
+    private const double MinSpeed = 0.0001;
+    private const double MaxSpeed = 1.0;
+    private const double ScrollFactor = 1.1;
+
+    // Space‑toggle state
+    private static double lastDesiredSpeed = 0.1;   // remembers the last non‑1.0 scroll speed
+    private static bool isRealTime = true;          // true when desiredSpeed == 1.0
+
     private static volatile bool running = true;
 
     public static void Main()
     {
         var mode = new VideoMode(new Vector2u(1280, 720));
-        var window = new RenderWindow(mode, "Fluid Simulation");
+        var window = new RenderWindow(mode, "Pipe Resonator");
         window.SetVerticalSyncEnabled(true);
         window.Closed += (_, _) => { running = false; window.Close(); };
+        window.MouseWheelScrolled += OnMouseWheel;
+        window.KeyPressed += OnKeyPressed;
 
-        var soundEngine = new SoundEngine(bufferCapacity: 2048);
+        var soundEngine = new SoundEngine(bufferCapacity: 16384);
         soundEngine.Volume = 70;
         soundEngine.Start();
 
-        double lastAudioTime = 0.0;
+        //scenario = new PipeResonatorScenario();
+        //scenario = new HelmholtzResonatorScenario();
+        scenario = new SodShockTubeScenario();
+
+        scenario.Initialize(SampleRate);
+
         var stopwatch = Stopwatch.StartNew();
+        double lastDrawTime = 0.0;
+        double drawInterval = 1.0 / DrawFrequency;
+        double lastSpeedUpdateTime = stopwatch.Elapsed.TotalSeconds;
 
-        int warmupSamples = SampleRate / 2;
+        // Resampling buffer
-        float[] warmup = new float[warmupSamples];
+        List<float> simBuffer = new List<float>(4096);
-        for (int i = 0; i < warmupSamples; i++)
+        double readIndex = 0.0;
-            warmup[i] = 0;
 
-        soundEngine.WriteSamples(warmup, warmupSamples);
+        for (int i = 0; i < 4; i++)
-        lastAudioTime = stopwatch.Elapsed.TotalSeconds;
+            simBuffer.Add(scenario.Process());
 
-        const int chunkSize = 2048;
+        long totalSimSteps = simBuffer.Count;
-        float[] buffer = new float[chunkSize];
+        long totalOutputSamples = 0;
 
-        Simulation.Initialize(SampleRate);
+        double lastRealTime = stopwatch.Elapsed.TotalSeconds;
+        const int outputChunk = 256;
+        float[] outputBuf = new float[outputChunk];
 
         while (window.IsOpen)
         {
             window.DispatchEvents();
 
-            double currentTime = stopwatch.Elapsed.TotalSeconds;
+            double currentRealTime = stopwatch.Elapsed.TotalSeconds;
-            double elapsed = currentTime - lastAudioTime;
+            double dtSpeed = currentRealTime - lastSpeedUpdateTime;
-            int samplesNeeded = (int)(elapsed * SampleRate);
+            lastSpeedUpdateTime = currentRealTime;
 
-            while (samplesNeeded > 0 && running)
+            // Smoothly transition currentSpeed → desiredSpeed
+            // When toggling, desiredSpeed jumps, but currentSpeed follows with a smooth lerp
+            double smoothingRate = 8.0;   // higher = faster catch‑up
+            currentSpeed += (desiredSpeed - currentSpeed) * (1.0 - Math.Exp(-smoothingRate * dtSpeed));
+
+            // ---------- Generate audio ----------
+            double targetAudioClock = currentRealTime + 0.05;
+
+            while (totalOutputSamples < targetAudioClock * SampleRate && running)
             {
-                int toGenerate = Math.Min(samplesNeeded, chunkSize);
+                int toGenerate = (int)Math.Min(
+                    (long)outputChunk,
+                    (long)(targetAudioClock * SampleRate) - totalOutputSamples
+                );
+                if (toGenerate <= 0) break;
+
+                double maxIndex = readIndex + (toGenerate - 1) * currentSpeed + 2;
+                int requiredSimIndex = (int)Math.Ceiling(maxIndex);
+                while (simBuffer.Count - 1 < requiredSimIndex)
+                {
+                    simBuffer.Add(scenario.Process());
+                    totalSimSteps++;
+                }
+
                 for (int i = 0; i < toGenerate; i++)
                 {
-                    buffer[i] = Simulation.Process();
+                    int i0 = (int)readIndex;
+                    int i1 = i0 + 1;
+                    double frac = readIndex - i0;
+
+                    float y0 = simBuffer[Math.Clamp(i0, 0, simBuffer.Count - 1)];
+                    float y1 = simBuffer[Math.Clamp(i1, 0, simBuffer.Count - 1)];
+                    outputBuf[i] = (float)(y0 + (y1 - y0) * frac);
+
+                    readIndex += currentSpeed;
+
+                    while (readIndex >= 1.0 && simBuffer.Count > 2)
+                    {
+                        simBuffer.RemoveAt(0);
+                        readIndex -= 1.0;
                     }
-                soundEngine.WriteSamples(buffer, toGenerate);
-                samplesNeeded -= toGenerate;
                 }
 
-            lastAudioTime = currentTime;
+                int accepted = soundEngine.WriteSamples(outputBuf, toGenerate);
+                totalOutputSamples += accepted;
+
+                if (accepted < toGenerate)
+                    break;
+            }
+
+            // ---------- Drawing & title ----------
+            if (currentRealTime - lastDrawTime >= drawInterval)
+            {
+                double actualSpeed = totalOutputSamples / (currentRealTime * SampleRate);
+                double simTime = totalSimSteps / (double)SampleRate;
+                string toggleHint = isRealTime ? "[Space] slow mo" : "[Space] real time";
+                window.SetTitle(
+                    $"{toggleHint}  Sim: {simTime:F2}s | " +
+                    $"Speed: {currentSpeed:F4}x → {desiredSpeed:F4}x | " +
+                    $"Actual: {actualSpeed:F2}x"
+                );
 
                 window.Clear(Color.Black);
+                scenario.Draw(window);
                 window.Display();
+                lastDrawTime = currentRealTime;
+            }
         }
 
         soundEngine.Dispose();
         window.Dispose();
     }
+
+    private static void OnMouseWheel(object? sender, MouseWheelScrollEventArgs e)
+    {
+        bool wasRealTime = Math.Abs(desiredSpeed - 1.0) < 1e-6;
+
+        if (e.Delta > 0)
+            desiredSpeed *= ScrollFactor;
+        else if (e.Delta < 0)
+            desiredSpeed /= ScrollFactor;
+
+        desiredSpeed = Math.Clamp(desiredSpeed, MinSpeed, MaxSpeed);
+
+        // Update the remembered slow-mo speed (unless we are exactly at 1.0)
+        if (!wasRealTime || Math.Abs(desiredSpeed - 1.0) > 1e-6)
+            lastDesiredSpeed = desiredSpeed;
+
+        // Update isRealTime flag
+        isRealTime = Math.Abs(desiredSpeed - 1.0) < 1e-6;
+    }
+
+    private static void OnKeyPressed(object? sender, KeyEventArgs e)
+    {
+        if (e.Code == Keyboard.Key.Space)
+        {
+            if (isRealTime)
+            {
+                // Switch to the remembered slow speed
+                desiredSpeed = lastDesiredSpeed;
+            }
+            else
+            {
+                // Switch back to real time
+                desiredSpeed = 1.0;
+            }
+            isRealTime = !isRealTime;
+        }
+    }
 }

Scenarios/HelmholtzResonatorScenario.cs

@@ -0,0 +1,133 @@
+using System;
+using FluidSim.Components;
+using FluidSim.Interfaces;
+using FluidSim.Utils;
+using SFML.Graphics;
+using SFML.System;
+
+namespace FluidSim.Core
+{
+    public class HelmholtzResonatorScenario : Scenario
+    {
+        private Solver solver;
+        private Volume0D cavity;
+        private Pipe1D neck;
+        private Connection coupling;
+        private int stepCount;
+        private double time;
+        private double dt;
+        private double ambientPressure = 1.0 * Units.atm;
+
+        public override void Initialize(int sampleRate)
+        {
+            dt = 1.0 / sampleRate;
+
+            // 1‑litre cavity, 10% over‑pressure
+            double cavityVolume = 1e-3;
+            double initialCavityPressure = 1.1 * ambientPressure;
+            cavity = new Volume0D(cavityVolume, initialCavityPressure, 300.0, sampleRate)
+            {
+                Gamma = 1.4,
+                GasConstant = 287.0
+            };
+
+            // Neck: length 10 cm, radius 1 cm
+            double neckLength = 0.1;
+            double neckRadius = 0.01;
+            double neckArea = Math.PI * neckRadius * neckRadius;
+            neck = new Pipe1D(neckLength, neckArea, sampleRate, forcedCellCount: 40);
+            neck.SetUniformState(1.225, 0.0, ambientPressure);
+
+            coupling = new Connection(neck.PortA, cavity.Port)
+            {
+                Area = neckArea,
+                DischargeCoefficient = 0.62,
+                Gamma = 1.4
+            };
+
+            solver = new Solver();
+            solver.SetTimeStep(dt);
+            solver.AddVolume(cavity);
+            solver.AddPipe(neck);
+            solver.AddConnection(coupling);
+
+            // Port A (left) = volume coupling, Port B (right) = open end
+            solver.SetPipeBoundary(neck, isA: true, BoundaryType.VolumeCoupling);
+            solver.SetPipeBoundary(neck, isA: false, BoundaryType.OpenEnd, ambientPressure);
+        }
+
+        public override float Process()
+        {
+            float sample = solver.Step();
+            time += dt;
+            stepCount++;
+
+            double pOpen = neck.GetCellPressure(neck.GetCellCount() - 1);
+            float audio = (float)((pOpen - ambientPressure) / ambientPressure);
+
+            if (stepCount % 20 == 0)
+            {
+                double pCav = cavity.Pressure;
+                double mdotA = neck.PortA.MassFlowRate;   // positive = into pipe (leaving cavity)
+                Console.WriteLine(
+                    $"t={time * 1e3:F2} ms step={stepCount} " +
+                    $"P_cav={pCav:F1} Pa, P_open={pOpen:F1} Pa, " +
+                    $"mdot_A={mdotA * 1e3:F4} g/s, audio={audio:F4}");
+            }
+
+            return audio;
+        }
+
+        public override void Draw(RenderWindow target)
+        {
+            float winW = target.GetView().Size.X;
+            float winH = target.GetView().Size.Y;
+            float centerY = winH / 2f;
+
+            // Cavity rectangle
+            float cavityWidth = 120f;
+            float cavityHeight = 180f;
+            var cavityRect = new RectangleShape(new Vector2f(cavityWidth, cavityHeight));
+            cavityRect.Position = new Vector2f(40f, centerY - cavityHeight / 2f);
+            cavityRect.FillColor = PressureColor(cavity.Pressure);
+            target.Draw(cavityRect);
+
+            // Neck drawn as tapered pipe
+            int n = neck.GetCellCount();
+            float neckStartX = 40f + cavityWidth + 10f;
+            float neckEndX = winW - 60f;
+            float neckLenPx = neckEndX - neckStartX;
+            float dx = neckLenPx / (n - 1);
+            float baseRadius = 20f;
+
+            Vertex[] vertices = new Vertex[n * 2];
+            for (int i = 0; i < n; i++)
+            {
+                float x = neckStartX + i * dx;
+                double p = neck.GetCellPressure(i);
+                float r = baseRadius * (float)(0.5 + 0.5 * Math.Tanh((p - ambientPressure) / (ambientPressure * 0.2)));
+                if (r < 4f) r = 4f;
+                Color col = PressureColor(p);
+                vertices[i * 2] = new Vertex(new Vector2f(x, centerY - r), col);
+                vertices[i * 2 + 1] = new Vertex(new Vector2f(x, centerY + r), col);
+            }
+            target.Draw(vertices, PrimitiveType.TriangleStrip);
+
+            // Open end indicator
+            var arrow = new CircleShape(8f);
+            arrow.Position = new Vector2f(neckEndX - 4f, centerY - 4f);
+            arrow.FillColor = Color.White;
+            target.Draw(arrow);
+        }
+
+        private Color PressureColor(double pressure)
+        {
+            double range = ambientPressure * 0.1;
+            double t = Math.Clamp((pressure - ambientPressure) / range, -1.0, 1.0);
+            byte r = (byte)(t > 0 ? 255 * t : 0);
+            byte b = (byte)(t < 0 ? -255 * t : 0);
+            byte g = (byte)(255 * (1 - Math.Abs(t)));
+            return new Color(r, g, b);
+        }
+    }
+}

Scenarios/PipeResonatorScenario.cs

@@ -0,0 +1,184 @@
+using FluidSim.Components;
+using FluidSim.Interfaces;
+using FluidSim.Utils;
+using SFML.Graphics;
+using SFML.System;
+using System;
+
+namespace FluidSim.Core
+{
+    public class PipeResonatorScenario : Scenario
+    {
+        private Solver solver;
+        private Pipe1D pipe;
+        private int stepCount;
+        private double time;
+        private double dt;
+        private double ambientPressure = 1.0 * Units.atm;
+        private bool enableLogging = true;
+
+        public override void Initialize(int sampleRate)
+        {
+            dt = 1.0 / sampleRate;
+
+            double length = 2;
+            double radius = 50 * Units.mm;
+            double area = Units.AreaFromDiameter(radius);
+
+            pipe = new Pipe1D(length, area, sampleRate, forcedCellCount: 80);
+            pipe.SetUniformState(1.225, 0.0, ambientPressure);
+
+            solver = new Solver();
+            solver.SetTimeStep(dt);
+            solver.AddPipe(pipe);
+            // Open end at port A (left), closed end at port B (right)
+            solver.SetPipeBoundary(pipe, isA: true, BoundaryType.OpenEnd, ambientPressure);
+            solver.SetPipeBoundary(pipe, isA: false, BoundaryType.ClosedEnd);
+
+            // Initial pressure pulse
+            int pulseCells = 5;
+            double pulsePressure = 2 * ambientPressure;
+            for (int i = 0; i < pulseCells; i++)
+                pipe.SetCellState(i, 1.225, 0.0, pulsePressure);
+        }
+
+        public override float Process()
+        {
+            float sample = solver.Step();
+            time += dt;
+            stepCount++;
+
+            double pMid = pipe.GetPressureAtFraction(0.5);
+            sample = (float)((pMid - ambientPressure) / ambientPressure);
+
+            Log(sample);
+            return sample;
+        }
+
+        private void Log(float sample)
+        {
+            if (!enableLogging) return;
+            if (stepCount % 10 == 0 && stepCount < 1000)
+            {
+                double pMid = pipe.GetPressureAtFraction(0.5);
+                double pOpen = pipe.GetCellPressure(0);
+                double pClosed = pipe.GetCellPressure(pipe.GetCellCount() - 1);
+                Console.WriteLine(
+                    $"t = {time * 1e3:F3} ms  Step {stepCount:D4}: " +
+                    $"sample = {sample:F3}, " +
+                    $"P_mid = {pMid:F2} Pa ({pMid / ambientPressure:F4} atm), " +
+                    $"P_open = {pOpen:F2} Pa, P_closed = {pClosed:F2} Pa");
+            }
+        }
+
+        public override void Draw(RenderWindow target)
+        {
+            float winWidth = target.GetView().Size.X;
+            float winHeight = target.GetView().Size.Y;
+
+            float pipeCenterY = winHeight / 2f;
+            float margin = 60f;
+            float pipeStartX = margin;
+            float pipeEndX = winWidth - margin;
+            float pipeLengthPx = pipeEndX - pipeStartX;
+            int n = pipe.GetCellCount();
+            float dx = pipeLengthPx / (n - 1);   // spacing between cell centres
+
+            float baseRadius = 25f;
+            float rangeFactor = 1f;
+            float scaleFactor = 5f;
+
+            // ----- smoothstep helper -----
+            static float SmoothStep(float edge0, float edge1, float x)
+            {
+                float t = Math.Clamp((x - edge0) / (edge1 - edge0), 0f, 1f);
+                return t * t * (3f - 2f * t);
+            }
+
+            // ----- Pre‑compute cell positions and radii -----
+            var centers = new float[n];
+            var radii = new float[n];
+            for (int i = 0; i < n; i++)
+            {
+                double p = pipe.GetCellPressure(i);
+                float deviation = (float)Math.Tanh((p - ambientPressure) / ambientPressure / rangeFactor);
+                radii[i] = baseRadius * (1f + deviation * scaleFactor);
+                if (radii[i] < 2f) radii[i] = 2f;
+                centers[i] = pipeStartX + i * dx;
+            }
+
+            // ----- Build triangle‑strip vertices -----
+            int segmentsPerCell = 8;   // smoothness
+            int totalPoints = n + (n - 1) * segmentsPerCell;
+            Vertex[] stripVertices = new Vertex[totalPoints * 2];   // top + bottom for each point
+            int idx = 0;
+
+            for (int i = 0; i < n; i++)
+            {
+                // ---- Cell centre ----
+                float x = centers[i];
+                float r = radii[i];
+                double p = pipe.GetCellPressure(i);
+                Color col = PressureColor(p);
+
+                stripVertices[idx++] = new Vertex(new Vector2f(x, pipeCenterY - r), col);
+                stripVertices[idx++] = new Vertex(new Vector2f(x, pipeCenterY + r), col);
+
+                // ---- Intermediate segments after this cell (if not last) ----
+                if (i < n - 1)
+                {
+                    for (int s = 1; s <= segmentsPerCell; s++)
+                    {
+                        float t = s / (float)segmentsPerCell;
+                        float st = SmoothStep(0f, 1f, t);
+                        float xi = centers[i] + (centers[i + 1] - centers[i]) * t;
+                        float ri = radii[i] + (radii[i + 1] - radii[i]) * st;
+                        double pi = pipe.GetCellPressure(i) * (1 - t) + pipe.GetCellPressure(i + 1) * t;
+                        Color coli = PressureColor(pi);
+
+                        stripVertices[idx++] = new Vertex(new Vector2f(xi, pipeCenterY - ri), coli);
+                        stripVertices[idx++] = new Vertex(new Vector2f(xi, pipeCenterY + ri), coli);
+                    }
+                }
+            }
+
+            // Draw the pipe as a triangle strip
+            var pipeMesh = new VertexArray(PrimitiveType.TriangleStrip, (uint)stripVertices.Length);
+            for (int i = 0; i < stripVertices.Length; i++)
+                pipeMesh[(uint)i] = stripVertices[i];
+            target.Draw(pipeMesh);
+
+            // ----- Closed end indicator (right) -----
+            float wallThickness = 8f;
+            var wall = new RectangleShape(new Vector2f(wallThickness, winHeight * 0.6f));
+            wall.Position = new Vector2f(pipeEndX, pipeCenterY - winHeight * 0.6f / 2f);
+            wall.FillColor = new Color(180, 180, 180);
+            target.Draw(wall);
+        }
+
+        /// <summary>Blue (low) → Green (ambient) → Red (high).</summary>
+        private Color PressureColor(double pressure)
+        {
+            double range = ambientPressure * 0.05;  // ±5% gives full colour swing
+            double t = (pressure - ambientPressure) / range;
+            t = Math.Clamp(t, -1.0, 1.0);
+
+            byte r, g, b;
+            if (t < 0)
+            {
+                double factor = -t;
+                r = 0;
+                g = (byte)(255 * (1 - factor));
+                b = (byte)(255 * factor);
+            }
+            else
+            {
+                double factor = t;
+                r = (byte)(255 * factor);
+                g = (byte)(255 * (1 - factor));
+                b = 0;
+            }
+            return new Color(r, g, b);
+        }
+    }
+}

Scenarios/Scenario.cs

@@ -0,0 +1,23 @@
+using SFML.Graphics;
+
+namespace FluidSim.Core
+{
+    public abstract class Scenario
+    {
+        /// <summary>
+        /// Initialize the scenario with a given audio sample rate.
+        /// </summary>
+        public abstract void Initialize(int sampleRate);
+
+        /// <summary>
+        /// Advance one simulation step and return an audio sample.
+        /// The step size is 1 / sampleRate seconds.
+        /// </summary>
+        public abstract float Process();
+
+        /// <summary>
+        /// Draw the current simulation state onto the given SFML render target.
+        /// </summary>
+        public abstract void Draw(RenderWindow target);
+    }
+}

Scenarios/SodShockTubeScenario.cs

@@ -0,0 +1,158 @@
+using System;
+using FluidSim.Components;
+using FluidSim.Utils;
+using SFML.Graphics;
+using SFML.System;
+
+namespace FluidSim.Core
+{
+    public class SodShockTubeScenario : Scenario
+    {
+        private Solver solver;
+        private Pipe1D pipe;
+        private int stepCount;
+        private double time;
+        private double dt;
+        private double ambientPressure = 1.0 * Units.atm;
+        private const double GasConstant = 287.0;
+
+        public override void Initialize(int sampleRate)
+        {
+            dt = 1.0 / sampleRate;
+            double length = 1.0;
+            double area = 1.0;
+            int nCells = 200;
+
+            pipe = new Pipe1D(length, area, sampleRate, forcedCellCount: nCells);
+            pipe.SetUniformState(0.125, 0.0, 0.1 * ambientPressure);  // right state
+
+            // Left half high pressure
+            for (int i = 0; i < nCells / 2; i++)
+                pipe.SetCellState(i, 1.0, 0.0, ambientPressure);
+
+            solver = new Solver();
+            solver.SetTimeStep(dt);
+            solver.AddPipe(pipe);
+            solver.SetPipeBoundary(pipe, isA: true, BoundaryType.ClosedEnd);
+            solver.SetPipeBoundary(pipe, isA: false, BoundaryType.ClosedEnd);
+        }
+
+        public override float Process()
+        {
+            float sample = solver.Step();
+            time += dt;
+            stepCount++;
+
+            double pMid = pipe.GetPressureAtFraction(0.5);
+            float audio = (float)((pMid - ambientPressure) / ambientPressure);
+
+            bool log = true;
+
+            if (log)
+            {
+                int n = pipe.GetCellCount();
+                Console.WriteLine($"step {stepCount}:");
+                Console.WriteLine("i    rho (kg/m³)   p (Pa)       T (K)     u (m/s)");
+                for (int i = 0; i < n; i++)
+                {
+                    if (i % 10 == 0)
+                    {
+                        double rho = pipe.GetCellDensity(i);
+                        double p = pipe.GetCellPressure(i);
+                        double u = pipe.GetCellVelocity(i);
+                        double T = p / (rho * GasConstant);   // GasConstant = 287.0
+                        Console.WriteLine($"{i,-4} {rho,10:F4}   {p,10:F1}   {T,8:F2}   {u,10:F4}");
+                    }
+                }
+                Console.WriteLine();
+            }
+
+            return audio;
+        }
+
+        public override void Draw(RenderWindow target)
+        {
+            float winW = target.GetView().Size.X;
+            float winH = target.GetView().Size.Y;
+            float centerY = winH / 2f;
+            float margin = 40f;
+            float pipeStartX = margin;
+            float pipeEndX = winW - margin;
+            float pipeLenPx = pipeEndX - pipeStartX;
+            int n = pipe.GetCellCount();
+            float dx = pipeLenPx / (n - 1);
+            float baseRadius = 60f;
+
+            Vertex[] vertices = new Vertex[n * 2];
+            for (int i = 0; i < n; i++)
+            {
+                float x = pipeStartX + i * dx;
+
+                double p = pipe.GetCellPressure(i);
+                double rho = pipe.GetCellDensity(i);
+                double T = p / (rho * GasConstant);           // temperature in Kelvin
+
+                // Radius from pressure (exaggerated deviation)
+                float r = baseRadius * (float)(p / ambientPressure * 2);
+                if (r < 4f) r = 4f;
+
+                // Colour from temperature
+                Color col = TemperatureColor(T);
+
+                vertices[i * 2] = new Vertex(new Vector2f(x, centerY - r), col);
+                vertices[i * 2 + 1] = new Vertex(new Vector2f(x, centerY + r), col);
+            }
+            target.Draw(vertices, PrimitiveType.TriangleStrip);
+
+            // Diaphragm marker (faint white line at initial interface)
+            float diaphragmX = pipeStartX + (n / 2) * dx;
+            var line = new RectangleShape(new Vector2f(2f, winH * 0.5f));
+            line.Position = new Vector2f(diaphragmX - 1f, centerY - winH * 0.25f);
+            line.FillColor = new Color(255, 255, 255, 80);
+            target.Draw(line);
+        }
+
+        /// <summary>
+        /// Custom temperature‑to‑hue mapping that matches the given Sod‑tube hue values:
+        ///   250 K → 176, 300 K → 122, 350 K → 120?, 450 K → 71.
+        /// Interpolates piecewise linearly, clamping outside [250,450].
+        /// </summary>
+        private Color TemperatureColor(double T)
+        {
+            // 1. Map temperature to hue (0–360)
+            double[] Tknots = { 250, 282, 353, 450 };
+            double[] Hknots = { 176, 179, 122, 71 };
+            double hue;
+            if (T <= Tknots[0]) hue = Hknots[0];
+            else if (T >= Tknots[^1]) hue = Hknots[^1];
+            else
+            {
+                int i = 0;
+                while (i < Tknots.Length - 1 && T > Tknots[i + 1]) i++;
+                double frac = (T - Tknots[i]) / (Tknots[i + 1] - Tknots[i]);
+                hue = Hknots[i] + frac * (Hknots[i + 1] - Hknots[i]);
+            }
+
+            // 2. Convert hue to RGB (S = 1, V = 1)
+            double h = hue / 60.0;
+            int sector = (int)Math.Floor(h);
+            double f = h - sector;
+            byte p = 0;
+            byte q = (byte)(255 * (1 - f));
+            byte tByte = (byte)(255 * f);
+            byte v = 255;
+
+            byte r, g, b;
+            switch (sector % 6)
+            {
+                case 0: r = v; g = tByte; b = p; break;
+                case 1: r = q; g = v; b = p; break;
+                case 2: r = p; g = v; b = tByte; break;
+                case 3: r = p; g = q; b = v; break;
+                case 4: r = tByte; g = p; b = v; break;
+                default: r = v; g = p; b = q; break;
+            }
+            return new Color(r, g, b);
+        }
+    }
+}

Utils/Units.cs

@@ -21,10 +21,10 @@ namespace FluidSim.Utils
 
         public static double Celsius(double tC) => tC + 273.15;
 
-        public static double AreaFromRadius(double radius, double unit = mm) =>
+        public static double AreaFromRadius(double radius) =>
-            Math.PI * (radius * unit) * (radius * unit);
+            Math.PI * (radius) * (radius);
 
-        public static double AreaFromDiameter(double diameter, double unit = mm) =>
+        public static double AreaFromDiameter(double diameter) =>
-            Math.PI * 0.25 * (diameter * unit) * (diameter * unit);
+            Math.PI * 0.25 * (diameter) * (diameter);
     }
 }