A moving mesh method for one-dimensional hyperbolic conservation laws

We develop an adaptive method for solving one-dimensional systems of hyperb olic conservation laws that employs a high resolution Godunov-type scheme f or the physical equations, in conjunction with a moving mesh PDE governing the motion of the spatial grid points. Many other moving mesh methods devel oped to solve hyperbolic problems use a fully implicit discretization for t he coupled solution-mesh equations, and so suffer from a significant degree of numerical sti ness. We employ a semi-implicit approach that couples the moving mesh equation to an efficient, explicit solver for the physical PDE , with the resulting scheme behaving in practice as a two-step predictor-co rrector method. In comparison with computations on a fixed, uniform mesh, o ur method exhibits more accurate resolution of discontinuities for a simila r level of computational work.