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

TL;DR

This paper develops a stabilized finite element method for simulating non-Newtonian power-law fluids coupled with advection-diffusion-reaction equations, demonstrating improved accuracy and stability through theoretical analysis and numerical validation.

Contribution

It introduces a time-dependent subgrid multiscale stabilization approach for the coupled non-Newtonian and advection-diffusion-reaction system, with detailed error estimates and validation.

Findings

The method performs better than existing stabilized methods across various flow regimes.

The approach accurately captures shear thinning and thickening behaviors.

Numerical results show enhanced stability and convergence for different Reynolds numbers.

Abstract

This article presents stability and convergence analyses of subgrid multiscale stabilized finite element formulation of non-Newtonian power-law fluid flow model strongly coupled with variable coefficients Advection-Diffusion-Reaction ($VADR$) equation. Considering the highly non-linear viscosity coefficient as solute concentration dependent makes the coupling two way. The stabilized formulation of the transient coupled system is developed based upon time dependent subscales, which ensures inherent consistency of the method. The proposed algebraic expressions of the stabilization parameters appropriately shape up the apriori and aposteriori error estimates. Both the shear thinning and shear thickening properties, indicated by different power-law indices are properly highlighted in theoretical derivations as well as in numerical validations. The numerical experiments carried out for different combinations of small and large Reynolds numbers and power-law indices establish far better performance of time dependent $ASGS$ method in approximating the solution of this coupled system for all the cases over the other well known stabilized finite element methods.