compressible.h
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Requires: conservation.h
Test cases (1): explosion
Compressible gas dynamics
The Euler system of conservation laws for a compressible gas can be written
with $\rho$ the gas density, $E$ the total energy, $\mathbf{w}$ the gas momentum and $p$ the pressure given by the equation of state
with $\gamma$ the polytropic exponent. This system can be solved using the generic solver for systems of conservation laws.
#include "conservation.h" [api]The conserved scalars are the gas density $\rho$ and the total energy $E$. The only conserved vector is the momentum $\mathbf{w}$. The constant $\gamma$ is represented by *gammao* here, with a default value of 1.4.
scalar rho[], E[];
vector w[];
scalar * scalars = {rho, E};
vector * vectors = {w};
double gammao = 1.4 ;The system is entirely defined by the flux() function called by the generic solver for conservation laws. The parameter passed to the function is the array s which contains the state variables for each conserved field, in the order of their definition above (i.e. scalars then vectors).
void flux (const double * s, double * f, double * e)
{We first recover each value ($\rho$, $E$, $w_x$ and $w_y$) and then compute the corresponding fluxes (f[0], f[1], f[2] and f[3]).
double rho = s[0], E = s[1], wn = s[2], w2 = 0.;
for (int i = 2; i < 2 + dimension; i++)
w2 += sq(s[i]);
double un = wn/rho, p = (gammao - 1.)*(E - 0.5*w2/rho);
f[0] = wn;
f[1] = un*(E + p);
f[2] = un*wn + p;
for (int i = 3; i < 2 + dimension; i++)
f[i] = un*s[i];The minimum and maximum eigenvalues for the Euler system are the characteristic speeds $u \pm \sqrt(\gamma p / \rho)$.
double c = sqrt(gammao*p/rho);
e[0] = un - c; // min
e[1] = un + c; // max
}