Adaptive Mesh Experiments For Hyperbolic Partial Differential Equations

Experiments were conducted on mesh moving and local mesh refinement algorithms that are used with a finite difference scheme to solve initial-boundary value problems for vector systems of hyperbolic partial differential equations in one dimension. The mesh moving algorithms move a coarse base mesh by a mesh movement function to follow and isolate spatially distinct phenomena. The local mesh refinement method recursively divides the time step and spatial cells in regions where error indicators are high until a prescribed error tolerance is satisfied. The adaptive mesh algorithms are implemented in a code with an initial mesh generator, a MacCormack finite difference scheme, and an error estimator. Experiments are conducted for several different problems to determine the efficiency of the adaptive methods and their combinations and to gauge their effectiveness in solving one-dimensional problems. (jhd).