all of the changes

include/FluidSim/OpenEndRadiation.hpp

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+#pragma once
+#include <cmath>
+
+namespace fluidsim::port {
+// Causal unflanged circular-pipe reflection fit, Silva et al. (2009), Eq. 16.
+// R(s)=-(1+n*a/c*s)/(1+d*a/c*s+e*(a/c*s)^2).
+// Trapezoidal state integration supports the solver's variable CFL timestep.
+class OpenEndRadiation {
+public:
+    double process(double incident, double scaled_dt) {
+        if (!initialized_) { position_ = incident; previous_ = incident; initialized_ = true; }
+        constexpr double n = .167, d = n + 2*.6133;
+        constexpr double e = (d*d-n*n-1)/2;
+        const double h = scaled_dt*.5;
+        const double rhs = velocity_ + h/e*(previous_ + incident - position_ - d*velocity_);
+        const double next_velocity = (rhs - h/e*(position_ + h*velocity_)) /
+                                     (1 + h*d/e + h*h/e);
+        position_ += h*(velocity_ + next_velocity);
+        velocity_ = next_velocity;
+        previous_ = incident;
+        return -(position_ + n*velocity_);
+    }
+private:
+    double position_{}, velocity_{}, previous_{};
+    bool initialized_{};
+};
+} // namespace fluidsim::port