Numerical Schemes for Conservation Laws on Moving Mesh

Abstract

Fluid flows are governed by non-linear partial differential equations and their solutions exhibit localised features like vorticity and shocks. In spite of many advances, their accurate computation still remains challenging task. In this thesis, we review the theory of scalar conservation laws and their numerical solution techniques. In order to compute shocks accurately, we explore the use of moving grids that will automatically adapt the grid resolution to the solution features. We first study finite volume methods on non-uniform grids and then extend the scheme to moving grid case.