Delta shocks interactions and the wave front tracking method

Abstract

The subject of this paper is numerical verification of delta shock waves interaction for a pressureless gas dynamics system using the approximated Wave Front Tracking algorithm. We approach the subject in two different ways. The first way is by perturbing the system with a small pressure term. The obtained perturbed system is strictly hyperbolic. We use the new bounds on the strength of elementary waves in the Wave Front Tracking algorithm. That allows us to get a global solution for initial data with arbitrary large total variation, provided that the perturbing parameter is small enough. The second approach is by using a shadow wave solution concept. The paper ends with the comparison of the solutions obtained in these two ways.