Numerical validation of an upscaled sharp-diffuse interface model for stratified miscible flows

A new model based on a mixed sharp and diffuse interface approach has been derived recently for miscible stratified displacements in porous media. It is an upscaled two-dimensional model tracking the interfaces between the fluid layers. The aim of the paper is to compare numerically the results provided by this upscaled model with the ones obtained using the classical three-dimensional model for miscible and compressible displacements in slightly deformable porous media. We construct for each model a numerical scheme based on a Euler semi-implicit method for the time discretization coupled with a mixed finite element approach for the space discretization. For the numerical simulations we focus on the example of the pollution of an aquifer. Computations are provided for various settings, especially when the flow is not quasi-horizontal.