A highly scalable numerical framework for reservoir simulation on UG4 platform

Abstract: The modeling and simulation of multiphase fluid flow receive significant attention in reservoir engineering. Many time discretization schemes for multiphase flow equations are either explicit or semi-implicit, relying on the decoupling between the saturation equation and the pressure equation. In this study, we delve into a fully coupled and fully implicit framework for simulating multiphase flow in heterogeneous porous media, considering gravity and capillary effects. We utilize the Vertex-Centered Finite Volume Method for spatial discretization and propose an efficient implementation of interface conditions for heterogeneous porous media within the current scheme. Notably, we introduce the Linearly Implicit Extrapolation Method (LIMEX) with an error estimator, adapted for the first time to multiphase flow problems. To solve the resulting linear system, we employ the BiCGSTAB method with the Geometric Multigrid (GMG) preconditioner. The implementations of models and methods are based on the open-source software: UG4. The results from parallel computations on the supercomputer demonstrate that the scalability of our proposed framework is sufficient, supporting a scale of thousands of processors with Degrees of Freedom (DoF) extending up to billions.