Uniform temporal convergence of numerical schemes for incompressible miscible displacement

TL;DR

This paper proves that a class of numerical schemes called HMM discretisations converge uniformly in time when modeling incompressible miscible displacement in porous media, ensuring reliable simulation results.

Contribution

It establishes the uniform temporal convergence of HMM discretisations for modeling incompressible miscible displacement, a result not previously demonstrated.

Findings

HMM schemes converge uniformly in time for concentration.

The convergence applies to hybrid finite volume, mimetic finite difference, and mixed finite volume methods.

Provides theoretical validation for numerical simulations of miscible displacement.

Abstract

The Hybrid Mimetic Mixed (HMM) family of discretisations includes the Hybrid Finite Volume method, the Mimetic Finite Difference method and the Mixed Finite Volume method. This note demonstrates that HMM discretisations of the equations describing the single-phase, miscible displacement through a porous medium of one incompressible fluid by another converge uniformly in time for the concentration variable.