Rippled shock front solutions for testing hydrodynamic stability simulations

The response of a shock front to arbitrary small perturbations can be calculated analytically. Such rippled shock front solutions are useful for determining the accuracy of hydrodynamic simulation codes such as LASNEX [Comments Plasma Phys. Controlled Fusion 2, 51 (1977)], which are used to compute perturbation growth in inertial fusion targets. The LASNEX fractional errors are of order κ2L2, where κ is the transverse wavenumber of the perturbation, and L is the largest zone dimension. Numerical errors are about 25% for a calculation using 26 zones per transverse wavelength