Stabilized subgrid multiscale finite element formulation for advection-diffusion-reaction equation with variable coefficients coupled with Stokes-Darcy equation

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

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 aposterior…

On subgrid multiscale stabilized finite element method for advection-diffusion-reaction equation with variable coefficients

In this study a stabilized finite element method for solving advection-diffusion-reaction equation with spatially variable coefficients has been carried out. Here subgrid scale approach along with algebraic approximation to the sub-scales has been chosen as stabilized method among various other methods. Both a priori and a posteriori finite element error estimates in $L_2$ norms have been derived after introducing the stabilized formulation of the variational form. An expression of the stabilization parameter for this 2D problem has also been derived here. At last numerical experiments are pre…

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

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.

不稳达西-布林克曼问题解的存在性和唯一性研究：用于多相反应流体在多孔介质中的建模

Existence and uniqueness of solutions of unsteady Darcy-Brinkman problem for modelling miscible reactive flows in porous media

本文研究了具有渗透率异质性的多孔介质流动模型，结合了溶质浓度的对流-反应-扩散方程与包含科泰维格应力的不稳达西-布林克曼方程。证明了弱解的存在性，并在二次非线性反应存在时，展示了解的长期行为依赖于初始浓度C₀，且在C₀>1时解在有限时间内爆破。

细薄孔隙域中斯托克斯流与对流输运的均质极限

Homogenized limits of Stokes flow and advective transport in thin perforated domains

研究细薄孔隙域中斯托克斯流与对流输运的均质化模型，推导有效方程并分析不同扩散条件下的对流-扩散行为。

Apriori and aposteriori error estimation of Subgrid multiscale stabilized finite element method for coupled unified Stokes-Brinkman/Transport model

In this study, we present a stabilized finite element analysis for completely unified Stokes-Brinkman problems fully coupled with variable coefficient transient Advection-Diffusion-Reaction equation(VADR). As well we have carried out the stabilized finite element analysis for Stokes-Brinkman model with interface conditions fully coupled with VADR. The viscosity of the fluid, involved in flow problem, 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 variation…