UNSTABLE GODUNOV DISCRETE PROFILES FOR STEADY SHOCK-WAVES

Given a system of n conservation laws ut + f(u)(x) = 0, the steady sho ck waves, when processed by the Godunov scheme, admit rather simple di screte profiles. One shows that the linear stability of these profiles depends only on the location of the eigenvalues of some endomorphism of an (n - 1)-dimensional space. Applying our theory to the gas dynami cs with the perfect gas law p = (gamma - 1)rho e, we construct unstabl e profiles for values of gamma between 1 and gamma and rather strong shocks. Since gamma is an element of]7/5, 5/3[, our result applies to the air but not to monoatomic gases. Finally, we illustrate this anal ysis by some numerical experiments, both with gamma < gamma and gamma > gamma.