An adaptive wavelet viscosity method for systems of hyperbolic conservation laws

For the Burgers’ equation as an example for a hyperbolic conservation law, we have considered in our previous paper [CGK] a weak formulation with a stabilization to handle discontinuities, commonly called a viscosity approach. Numerically, this was realized by locally introducing degrees of freedom around the discontinuities by means of an adaptive wavelet method in an a-posteriori fashion. In the present paper, we apply this method to systems of conservation laws, specifically, Euler’s equations for gas dynamics. Moreover, as the viscosity stabilization produces some Gibbs phenomena, we discuss different postprocessing techniques known from data and image processing together with a number of numerical comparisons.