A Local Streamline Eulerian-Lagrangian Method for Two-Phase Flow

Abstract

A method for solving the saturation equation for two-phase now is presented. The method may be viewed as an operator splitting method or as an Eulerian-Lagrangian backtracking procedure or as a modi£ed method of characteristics. For each time step, the method consists of an advection step and a diffusion step. The advection step requires the tracking of streamlines locally around certain integration points. On each streamline we have to solve a nonlinear hyperbolic equation. This is done using a front tracking method. The solution from the tracking step is projected back onto a fixed grid, and we finally have to solve a parabolic heat-type equation.