SOLVER rusanov PASS solver flux consistency and reflection symmetry PASS HLLC preserves stationary contact and falls back at expansion vacuum PASS unflanged radiation reflection magnitude and phase PASS radiating mouth conserves reported mass at both orientations PASS radiating mouth reflects rarefaction at either pipe orientation PASS radiating inflow supplies fresh ambient stagnation enthalpy PASS tracer underflow preserves bulk gas and normal concentrations PASS invalid uniform geometry PASS closed pipe conservation PASS profiled pipe conservation PASS volume pipe sealed conservation PASS equal pressure hot contact PASS NASA choked nozzle mass flow PASS inertance units PASS moving volume adiabatic law PASS profile at rest is well balanced PASS pipe connection all four orientations PASS split pipe matches unsplit pipe PASS three volumes shared donor conservation PASS open boundary reports actual conserved flux both ends PASS duplicate and invalid boundary rejection PASS supersonic outlet extrapolates PASS underdefined supersonic inlet rejected PASS closed and open acoustic reflection signs Sod n=100 density L1=0.0233209 Sod n=200 density L1=0.0159539 Sod n=400 density L1=0.0105216 PASS Sod shock tube convergence PASS strong pulse and near-vacuum rarefaction Helmholtz frequency=135.6 analytic lumped=138.508 PASS small-signal Helmholtz resonance PASS invalid volume and timestep rejection PASS fresh-air species conservation across connection PASS unsupported unequal junction rejected PASS unconnected endpoint rejected by solver closed mode n=50 f=171.897 analytic=171.91 closed mode n=100 f=171.914 analytic=171.91 closed mode n=200 f=171.911 analytic=171.91 PASS closed duct acoustic eigenfrequency PASS inertance impulse and dissipative resistance PASS incompatible gas coupling rejected PASS thermal relaxation matches analytic energy decay PASS sealed crankcase compression conserves mass above five bar 36/36 passed SOLVER hlle PASS solver flux consistency and reflection symmetry PASS HLLC preserves stationary contact and falls back at expansion vacuum PASS unflanged radiation reflection magnitude and phase PASS radiating mouth conserves reported mass at both orientations PASS radiating mouth reflects rarefaction at either pipe orientation PASS radiating inflow supplies fresh ambient stagnation enthalpy PASS tracer underflow preserves bulk gas and normal concentrations PASS invalid uniform geometry PASS closed pipe conservation PASS profiled pipe conservation PASS volume pipe sealed conservation PASS equal pressure hot contact PASS NASA choked nozzle mass flow PASS inertance units PASS moving volume adiabatic law PASS profile at rest is well balanced PASS pipe connection all four orientations PASS split pipe matches unsplit pipe PASS three volumes shared donor conservation PASS open boundary reports actual conserved flux both ends PASS duplicate and invalid boundary rejection PASS supersonic outlet extrapolates PASS underdefined supersonic inlet rejected PASS closed and open acoustic reflection signs Sod n=100 density L1=0.0174385 Sod n=200 density L1=0.0110652 Sod n=400 density L1=0.00701807 PASS Sod shock tube convergence PASS strong pulse and near-vacuum rarefaction Helmholtz frequency=135.6 analytic lumped=138.508 PASS small-signal Helmholtz resonance PASS invalid volume and timestep rejection PASS fresh-air species conservation across connection PASS unsupported unequal junction rejected PASS unconnected endpoint rejected by solver closed mode n=50 f=171.897 analytic=171.91 closed mode n=100 f=171.914 analytic=171.91 closed mode n=200 f=171.911 analytic=171.91 PASS closed duct acoustic eigenfrequency PASS inertance impulse and dissipative resistance PASS incompatible gas coupling rejected PASS thermal relaxation matches analytic energy decay PASS sealed crankcase compression conserves mass above five bar 36/36 passed SOLVER hllc PASS solver flux consistency and reflection symmetry PASS HLLC preserves stationary contact and falls back at expansion vacuum PASS unflanged radiation reflection magnitude and phase PASS radiating mouth conserves reported mass at both orientations PASS radiating mouth reflects rarefaction at either pipe orientation PASS radiating inflow supplies fresh ambient stagnation enthalpy PASS tracer underflow preserves bulk gas and normal concentrations PASS invalid uniform geometry PASS closed pipe conservation PASS profiled pipe conservation PASS volume pipe sealed conservation PASS equal pressure hot contact PASS NASA choked nozzle mass flow PASS inertance units PASS moving volume adiabatic law PASS profile at rest is well balanced PASS pipe connection all four orientations PASS split pipe matches unsplit pipe PASS three volumes shared donor conservation PASS open boundary reports actual conserved flux both ends PASS duplicate and invalid boundary rejection PASS supersonic outlet extrapolates PASS underdefined supersonic inlet rejected PASS closed and open acoustic reflection signs Sod n=100 density L1=0.0162129 Sod n=200 density L1=0.0103006 Sod n=400 density L1=0.00654211 PASS Sod shock tube convergence PASS strong pulse and near-vacuum rarefaction Helmholtz frequency=135.6 analytic lumped=138.508 PASS small-signal Helmholtz resonance PASS invalid volume and timestep rejection PASS fresh-air species conservation across connection PASS unsupported unequal junction rejected PASS unconnected endpoint rejected by solver closed mode n=50 f=171.897 analytic=171.91 closed mode n=100 f=171.914 analytic=171.91 closed mode n=200 f=171.911 analytic=171.91 PASS closed duct acoustic eigenfrequency PASS inertance impulse and dissipative resistance PASS incompatible gas coupling rejected PASS thermal relaxation matches analytic energy decay PASS sealed crankcase compression conserves mass above five bar 36/36 passed