The modified characteristics finite element method for time-dependent Darcy-Brinkman problem

Abstract

Purpose This study aims to capture the effective behavior of double-diffusion problem, which arises from the combined heat and mass transfer in porous medium and develop the modified characteristics finite element method. Design/methodology/approach The proposed finite element method deals with the nonlinear term temporal term by modified characteristics method. Then, the authors compute the velocity, pressure, temperature and concentration using the decoupled technique. Finally, to show the efficiency of the method, the authors give some numerical examples. Findings From the numerical results, one can see that the method has a good accuracy, which shows that the method can simulate this Darcy–Brinkman problem well. Originality/value The originality lies in the fact that the proposed scheme is the first time for solving the Darcy–Brinkman problem, which is a more complicated model, and includes the velocity, pressure, temperature and concentration.

A modified characteristics projection finite element method for the non‐stationary incompressible thermally coupled MHD equations

“…Jing et al [42] combined the projection method with the modified characteristics method to study the characteristics projection finite element method for the unsteady incompressible MHD equation. Some other results can be found in previous works [43][44][45][46][47][48][49][50].…”

Finite Element Iterative Methods for the Stationary Double-Diffusive Natural Convection Model

“…Next, assuming that it holds for n = k, we prove that it is valid for (13) with n = k + 1 and applying (2), ( 3) and (4) yield…”

“…Moreover, we consider the iterative error estimates of iterative method I. Making use of (12) and (13) yields the error equations…”

“…Based on the idea of curvature stabilization, Çıbık et al [ 12 ] discussed a family of second order time stepping methods for the Darcy–Brinkman equations. A decoupled finite element method called the modified characteristics method was considered in [ 13 ]. Rajabi et al performed the detailed uncertainty propagation analysis and variance-based global sensitivity analysis on the widely adopted double-diffuse convection benchmark problem of a square porous cavity with horizontal temperature and concentration gradients in [ 14 ].…”

Deferred defect‐correction finite element method for the Darcy‐Brinkman model

“…Due to important applications, this model has been widely employed in industry and engineering [7][8][9]. At the time of writing, there are some works devoted to the development of efficient numerical methods for the problem (1) (see [10][11][12][13][14][15][16][17] and the references therein). Applying the Fourier-Galerkin spectral method, Shao et al [18] have obtained a high-accurate reference solution for the double-diffusive convection in a confined saturated porous medium.…”