Esquemas de Flujo Limitado en Grillas Autoadptivas para Ecuaciones Hiperbólicas Unidimensionales

Abstract

A family of Flux Limited finite-differences schemes in self adapting grids are presented. This kind of schemes resolve rarefraction and shock waves very sharply due to their low numerical viscosity. The criteria employed to adapt the grid minimizes the grid distortion both in space and time. Several known implementation strategies are discussed and a new one is proposed, based on a bound on the maximum cell variation of the solution and the porcentage of points assigned to the fronts. Several solutions of the one dimensional 1-D linear advection equation, Burger's equation, and gas dynamic are shown to illustrate the grid adaptation to capture shocks.