The range of multiphase models has increased in the last 4 years in variety, complexity, and sophistication. Many more three-dimensional codes have been developed, some of the first n-component groundwater models have appeared, and specialized models are more intricate as well. There are clear trends toward p-s multiphase formulations, which should be more robust than p-p for general applications, less-restrictive assumptions (e.g., more mobile phases), Newton-Raphson iteration for nonlinear discrete equations, which should be more robust than Picard, and iterative linear-equation solvers of conjugate-gradient type with ILU-like preconditioners, which have been the solvers of choice in petroleum simulation for about a decade. Temporal discretizations are mostly fully implicit or sequentially implicit, with a wide range of essentially standard spatial finite-difference, finite-volume, and finite-element schemes.
Nonequilibrium partitioning is included in some more-limited models, but not in those with many components and phases. Macroscopic multiphase relationships are of traditional forms, generally non-hysteretic, awaiting better fundamental understanding of the physical processes. Recent developments in discretization techniques, such as mixed finite-element methods, Lagrangian and Eulerian-Lagrangian schemes, local grid refinement, domain decomposition, and multigrid algorithms, generally have not been implemented in the practical arena represented by these models. These techniques offer greater efficiency and accuracy than standard schemes in scalar computing environments, with still greater advantages on vector and parallel machines. Currently, most codes appear to be designed for scalar machines, with little emphasis on vectorizability or parallelizability.