Two-phase flow using Multi-Point Flux Approximation/Finite Volume Method (2ph-MPFA)
Description
This repository is a collection of implementations using cell centered finite volume methods, specifically Multi-Point Flux Approximation, in order to discretize the incompressible two-phase flow equation (two-dimensional, only).
To approximate the solutions at each time step, we can use:
- a classical Newton iterative scheme (a sequential implicity);
- IMplicity Pressure Explicit Saturation scheme (IMPES);
- Streamline approach.
- modified-IMPES.
For more information on the MPFA discretization, we refer to:
- I. Aavatsmark: An introduction to multipoint flux approximations for quadrilateral grids, Comput. Geosci. 6(3-4) 405-432.
- Gao, Z. and Wu, J. (2011), A linearity-preserving cell-centered scheme for the heterogeneous and anisotropic diffusion equations on general meshes. Int. J. Numer. Meth. Fluids, 67: 2157-2183. https://doi.org/10.1002/fld.2496
- F.R.L. Contreras, P.R.M. Lyra, M.R.A. Souza, D.K.E. Carvalho (2016), A cell-centered multipoint flux approximation method with a diamond stencil coupled with a higher order finite volume method for the simulation of oil–water displacements in heterogeneous and anisotropic petroleum reservoirs. Computers & Fluids, Volume 127, Pages 1-16.
- J. C. Teixeira, L. J. N. Guimarães, D. K. E. Carvalho (2021), Streamline-based simulation in highly heterogeneous and anisotropic petroleum reservoirs using a non-orthodox MPFA method and an adaptive timestep strategy with unstructured meshes, Jour. Petr. Sci. and Eng., Volume 201.
Requirements
The modules are compatible with the MATLAB, and it is assumed that all folders are in the MATLAB path. The code has been tested with Matlab R2018a and R2019a.
Cite
If you use 2ph-MPFA, please cite: