Local uniform mesh refinement with moving grids

Local Uniform Mesh Refinement (LUMR) is a powerful technique for solving hyperbolic partial differential equations. However, many problems contain regions where numerical dispersion is very large, such as steep fronts. In these regions, mesh refinement is not very efficient. A better approach in these regions is to locally transform the coordinate system to move with the front. We show how to combine these two approaches in a way that maintains the advantages of LUMR and the effectiveness of moving grids. Experiments with 2-D scalar problems are presented.