Lax shock

The Lax shock solution is a weak solution to a hyperbolic conservation law that develops when characteristics cross, forming a discontinuity (shock wave). It was introduced by Peter Lax as part of his work on weak solutions and entropy conditions in conservation laws.

In compressible fluid flow (e.g., Euler equations), a Lax shock represents a compressive shock wave, ensuring that entropy increases across the discontinuity. Physically, this corresponds to a shock where information propagates correctly, preventing nonphysical solutions like rarefaction shocks.

In the left half of the tube primitive variables are (p_l, v_l, T_l) = (3.528, 0.698, 0.0276), while over the right half they are (p_r, v_r, T_r) = (0.571, 0.0, 0.004).

The stabilization parameters are tau 2001 and 2006 discontinuity capturing.

The time step is 1e-4 s while the space discretization is of 1e-3 m for a total length of 2 m.

Details can be found in setup.txt, fluid_ic_bc.hpp, props.txt and mesh.geo files.

Results

Gales results well agree with the reference solution.

References

Park & Munz “Multiple pressure variables methods for
fluid fl
ow at all Mach numbers” (2005) Int. J. Numer. Meth. Fluids