An adaptive grid finite difference method for conservation laws

Abstract Adaptive grid finite difference methods for computing time-accurate solutions of nonlinear hyperbolic conservation laws in one space dimension are studied. The basic approach is to decouple the determination of the moving grid from the solution of the differential equation on the moving grid. The grid is determined by an elliptic grid generation technique suitably modified for time-accurate computations. Two methods, Godunov's scheme and an artificial viscosity method, are used to discretize the differential equation. The technique is applied to problems involving the Buckley-Leverett equation modelling the flow of two immiscible fluids in a porous medium. Substantial improvement in computational efficiency is obtained by using the adaptive grid technique. Extensions of this approach to several space dimensions and systems of equations are discussed.