Numerical verification of delta shock waves for pressureless gas dynamics

The subject of this paper is theoretical analysis and numerical verification of delta shock wave existence for pressureless gas dynamic system. The existence of overcompressive delta shock wave solution in the framework of Colombeau generalized functions is proved. This result is verified numerically by specially designed procedure that is based on wave propagation method implemented in CLAWPACK. The method is coupled with dynamic refinement mesh. We also consider a strictly hyperbolic system obtained from the original one by perturbation and change of variables. The same numerical procedure is applied to the perturbed problem. The obtained numerical results in both cases confirm theoretical expectations.