Time dependent subgrid multiscale stabilized finite element analysis of fully coupled transient Navier–Stokes‐transport model

Abstract

AbstractIn this paper, a fully coupled system of transient Navier–Stokes fluid flow model and unsteady variable coefficient advection–diffusion–reaction transport model has been studied through subgrid multiscale stabilized finite element method. In particular algebraic approach of approximating the subscales has been considered to arrive at the stabilized variational formulation of the coupled system and standard expressions for the stabilization parameters have been proposed. The unknown subgrid scales are considered to be time dependent. The consideration of the fluid viscosity coefficient depending upon the concentration of the solute mass makes this coupling strong. Fully implicit backward Euler scheme has been employed for time discretization. Stability analysis of the stabilized formulation has been conducted. Furthermore detailed derivations of both and error estimates for the stabilized finite element scheme have been carried out. The performance of the proposed scheme is validated for benchmark problems as well as the credibility of the stabilized method is also established well through various numerical experiments.