Subgrid multiscale stabilized finite element analysis of fully-coupled unified Stokes-Darcy-Brinkman/Transport model

TL;DR

This paper develops a stabilized finite element method for a fully coupled Stokes-Darcy-Brinkman and transport model with variable viscosity, employing subgrid multiscale techniques and implicit Euler time discretization, validated through numerical experiments.

Contribution

It introduces a novel stabilized finite element approach using subgrid multiscale methods for coupled flow and transport with variable viscosity, including detailed theoretical estimates.

Findings

The method provides stable and accurate solutions for the coupled system.

Theoretical a priori and a posteriori estimates are derived.

Numerical experiments confirm the method's credibility.

Abstract

In this study, a stabilized finite element analysis of unified Stokes-Darcy-Brinkman system fully coupled with variable coefficient Advection-Diffusion-Reaction equation(VADR) has been carried out. The viscosity of the fluid, involved in Stokes-Darcy flow, depends on the concentration of the solute, whose transport is described by VADR equation. The algebraic subgrid multiscale approach has been employed to arrive at the stabilized coupled variational formulation. For the time discretization the fully implicit Euler scheme has been used. A detailed derivation of both the apriori and aposteriori estimates for the stabilized subgrid multiscale finite element scheme have been presented. Few numerical experiments have been carried out to verify the credibility of the method.