Special Relativistic Riemann Problem Solver
One-dimensional Riemann problems have been proven to be useful tools to benchmark numerical hydrodynamic codes since they can be solved to arbitrary precision. This library implements such a solver for special relativistic hydrodynamics based on the scheme presented by Rezzolla et al. (2003) [doi: 10.1017/S0022112002003506].
Installation
This package can be obtained via pypi
pip install srrp
Example Usage
The solution of a Riemann Problem producing a rarefaction-shock pattern could look like the following code (see also examples/rarefaction-shock.py)
import matplotlib.pyplot as plt
import numpy as np
import srrp
'''
Reproduction of (parts of) Figure 3 from
Rezzolla, Zanott, Pons (2003), J.Fluid Mech. 479, 199
DOI: 10.1017/S0022112002003506
'''
if __name__ == '__main__':
gamma = 5/3
stateL = srrp.State(rho=1, pressure=1, vx=0.5, vt=0)
stateR = srrp.State(rho=0.125, pressure=0.1, vx=0, vt=0)
xs = np.linspace(0, 1, 500)
t = 0.4
x0 = 0.5
solver = srrp.Solver()
solution = solver.solve(stateL, stateR, gamma)
for wave in solution.waves:
print(wave)
for idx, state in enumerate(solution.states):
print(f'{idx}: {state}')
xis = (xs - x0) / t
states = solution.getState(xis)
plt.plot(xs, states.rho, label="rho")
plt.plot(xs, states.pressure, label="pressure")
plt.plot(xs, states.vx, label="vx")
plt.plot(xs, states.vt, label="vt")
plt.legend(loc='upper right')
plt.grid(True, ls='--')
plt.xlabel('x')
plt.show()For more examples visit the examples folder.
