# A virtual element method for the miscible displacement of incompressible fluids in porous media

## TL;DR

This paper develops a virtual element method for simulating the displacement of incompressible fluids in porous media, providing a new numerical approach with theoretical analysis and practical testing.

## Contribution

It introduces the first application of virtual element methods to complex fluid flow problems involving miscible displacement, combining discretization, time stepping, and analysis.

## Key findings

- The method is effective on regular test cases.
- The method performs well on realistic scenarios.
- Theoretical analysis confirms stability and convergence.

## Abstract

In the present contribution, we construct a virtual element (VE) discretization for the problem of miscible displacement of one incompressible fluid by another, described by a time-dependent coupled system of nonlinear partial differential equations. Our work represents a first study to investigate the premises of virtual element methods (VEM) for complex fluid flow problems. We combine the VEM discretization with a time stepping scheme and develop a complete theoretical analysis of the method under the assumption of a regular solution. The scheme is then tested both on a regular and on a more realistic test case.