A Numerical Method Based on the Range-Discrete Grid for One-Dimensional Buckley-Leverett Equation

Abstract

A numerical method for solving the one-dimensional Buckley-Leverett equation arising in the process of displacement of oil by water is presented. Instead of using the traditional spatial discrete grids, the numerical algorithm is built on a “range discrete” grid, which is obtained by direct subdivisions in the saturation domain. The range discrete grid describes the discontinuities explicitly and completely, and has an adaptive nature in smooth regions. Grid points are divided into two classes: continuous points and discontinuous points. Numerical solution of the Buckley-Leverett equation is achieved by moving continuous points by tracing characteristics and moving discontinuous points by tracking discontinuities. Numerical examples are presented, and the solutions obtained by the proposed method are found of high precision. Especially, shocks are solved with no dissipation, and the sharpness is maintained.