Characteristic, local grid refinement techniques for reservoir flow problems

Abstract

Abstract Using a sequential time‐marching approach, we describe and implement effective solution strategies for the equations governing immiscible displacement in a porous medium. By combining adaptive grid refinement with an operator‐splitting technique based on the modified method of characteristics, the saturation equation is treated in a consistent and accurate way. For the pressure equation we construct accurate piecewise linear velocity components from a piecewise linear pressure approximation.