A Dynamically-Moving Adaptive Grid Method Based on a Smoothed Equidistribution Principle along Coordinate Lines

In this paper a time-dependent moving-grid method is described to numerically solve timedependent partial differential equations (PDEs) in two space dimensions involving fine scale structures such as steep moving fronts, emerging steep layers, pulses and shocks. The method is based on an equidistribution principle along coordinate lines in the two spatial directions. Smoothing in the spatial direction is employed to control grid clustering and expansion. Additional smoothing in the temporal direction ensures a smooth progression of the grid points in time by preventing the points from responding too quickly to current values of the weightfunctions. Numerical results are given for a (parabolic) reactiondiffusion model and a (hyperbolic) rotating-pulse model.