Projection and partitioned solution for two-phase flow problems

Multiphase flow through porous media is a highly nonlinear process that can be solved numerically with the aid of finite elements (FE) in space and finite differences (FD) in time. For an accurate solution much refined FE grids are generally required with the major computational effort consisting of the resolution to the nonlinearity frequently obtained with the classical Picard linearization approach. The efficiency of the repeated solution to the linear systems within each individual time step represents the key to improve the performance of a multiphase flow simulator. The present paper discusses the performance of the projection solvers (GMRES with restart, TFQMR, and BiCGSTAB) for two global schemes based on a different nodal ordering of the unknowns (ORD1 and ORD2) and a scheme (SPLIT) based on the straightforward inversion of the lumped mass matrix which allows for the preliminary elimination and substitution of the unknown saturations. It is shown that SPLIT is between two and three time faster than ORD1 and ORD2, irrespective of the solver used.