# Operator splitting technique using streamline projection for two-phase flow in highly heterogeneous and anisotropic porous media

## TL;DR

This paper introduces a fast, streamline-based numerical method for simulating two-phase flow in highly heterogeneous and anisotropic porous media, emphasizing efficiency and accuracy in high-rate flooding scenarios.

## Contribution

It combines a streamline projection approach with domain decomposition and multigrid preconditioning to improve computational efficiency in complex porous media simulations.

## Key findings

- Validated in 2D and 3D tests with accurate flow front propagation
- Achieved faster computations compared to standard finite volume methods
- Effectively handled high heterogeneity and anisotropy in porous media

## Abstract

In this paper, we present a fast streamline-based numerical method for the two-phase flow equations in high-rate flooding scenarios for incompressible fluids in heterogeneous and anisotropic porous media. A fractional flow formulation is adopted and a discontinuous Galerkin method (DG) is employed to solve the pressure equation. Capillary effects can be neglected in high-rate flooding scenarios. This allows us to present an improved streamline approach in combination with the one-dimensional front tracking method to solve the transport equation. To handle the high computational costs of the DG approximation, domain decomposition is applied combined with an algebraic multigrid preconditioner to solve the linear system. Special care at the interior interfaces is required and the streamline tracer has to include a dynamic communication strategy. The method is validated in various two- and three-dimensional tests, where comparisons of the solutions in terms of approximation of flow front propagation with standard fully-implicit finite volume methods are provided.