A PARALLELIZABLE CHARACTERISTIC SCHEME FOR 2 PHASE FLOW .1. SINGLE POROSITY MODELS

Abstract

We propose a new numerical method designed for the parallel solution of the governing equations of two phase immiscible flow in a porous medium. The method combines hybridized mixed finite elements, the modified method of characteristics, and domain decomposition iteration and has several distinctive features; it is naturally parallelizable in distributed memory machines, it has very low storage requirements, explicit upwinding techniques are not necessary to stabilize the solution (thus reducing the effects of numerical diffusion), the scheme runs very rapidly (large linear systems do not have to be constructed and solved), it can use fairly long time steps, and the implementation at the level of code development is quite simple. These properties make the new scheme competitive even on serial machines.