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.
