An HMM--ELLAM scheme on generic polygonal meshes for miscible incompressible flows in porous media
This work addresses the need for accurate numerical simulation of miscible flows in porous media on complex meshes, which is important for applications like oil recovery and groundwater contamination.
The paper presents a numerical scheme for miscible displacement in porous media, combining a characteristic method for advection and a finite volume method for diffusion on generic polygonal meshes. The scheme includes a Darcy velocity reconstruction with local consistency and improved treatment of injection well cells for better fluid conservation.
We design a numerical approximation of a system of partial differential equations modelling the miscible displacement of a fluid by another in a porous medium. The advective part of the system is discretised using a characteristic method, and the diffusive parts by a finite volume method. The scheme is applicable on generic (possibly non-conforming) meshes as encountered in applications. The main features of our work are the reconstruction of a Darcy velocity, from the discrete pressure fluxes, that enjoys a local consistency property, an analysis of implementation issues faced when tracking, via the characteristic method, distorted cells, and a new treatment of cells near the injection well that accounts better for the conservativity of the injected fluid.