Subgrid multiscale stabilized finite element analysis of non-Newtonian Casson model fully coupled with Advection-Diffusion-Reaction equations

TL;DR

This paper develops a stabilized finite element method for simulating non-Newtonian Casson fluid flow coupled with advection-diffusion-reaction equations, with stability, convergence analysis, and numerical validation.

Contribution

It introduces a novel subgrid multiscale stabilized formulation for coupled non-Newtonian fluid and ADR equations, including stability and convergence proofs.

Findings

Optimal convergence rates achieved.

Stable numerical solutions demonstrated.

Effective handling of variable viscosity and coupling.

Abstract

In this paper we have studied subgrid multiscale stabilized formulation with dynamic subscales for non-Newtonian Casson fluid flow model tightly coupled with variable coefficients ADR ($VADR$) equation. The Casson viscosity coefficient is taken to be dependent upon solute mass concentration. This paper presents the stability and convergence analyses of the stabilized finite element solution. The proposed expressions of the stabilization parameters helps in obtaining optimal order of convergences. Appropriate numerical experiments have been provided.