Parallel Finite Element Simulation of Miscible Displacements in Porous Media

In this work, parallel finite element techniques for the simulation of miscible displacements in porous media are addressed. The pressure equation is approximated by Galerkin's method and the velocity field computed through a post-processing approach to recover the required accuracy. The concentration equation is approximated in space by the Streamline Upwind Petrov Galerkin (SUPG) plus a discontinuity-capturing operator. The resulting semi-discrete equations are approximated in time by a predictor-multicorrector algorithm. To increase the robustness of our solution scheme, the feedback control theory is used to select the proper time-step. The pressure, velocity and concentration linear systems of 'equations are solved with parallel element-by-element iterative techniques. Performance measurements on two different machines, the CRAY Y-MP and the CRAY C90, for a five-spot pattern with high mobility ratio on random heterogeneous media are presented to show that the numerical techniques employed are accurate and result in a fast code.