Self-adjusting grid methods for one-dimensional hyperbolic conservation laws (Q1058829)

It is shown how to automatically adjust the grid to follow the dynamics of the numerical solution of hyperbolic conservation laws. The grid motion is determind by averaging the local characteristic velocities of the equations with respect to the amplitudes of the signals. The resulting algorithm is a simple extension of many currently popular Godunov-type methods. Computer codes using one of these methods can be easily modified to add the moving mesh as an option. Numerical examples are given that illustrate the improved accuracy of Godunov's and Roe's methods on a self-adjusting mesh.