Second order fully discrete and divergence free conserving scheme for time-dependent conduction–convection equations

Second order fully discrete defect‐correction scheme for nonstationary conduction‐convection problem at high Reynolds number

“…The method we study in this article is to combine the defect‐correction FE method with the Crank‐Nicolson scheme for solving the nonstationary conduction‐convection problems with high Reynolds number, which includes two steps: solve one stabilized artificial viscosity nonlinear equations in the defect step and correct the residual by a linearized problem in the correction step for a few steps. But different from , our proposed scheme is second order in both time and space. The numerical application experience show that the preferable results of high Reynolds number can be obtained only when with fine enough meshing in FE modal simulation.…”

“…Recently, Kaya and coworker considered the synthesis of a subgrid stabilization method with defect‐correction method for the stationary natural convection problem. Besides, a two‐level defect‐correction Oseen iterative stabilized FE methods for the stationary conduction‐convection equations is given by Su et al . Moreover, a defect‐correction method for unsteady conduction‐convection problems is proposed by Si et al in and Zhang et al considered a defect‐correction mixed FE method for steady‐state natural convection problem in .…”

“…Then, Luo provided more comprehensive analysis of the standard mixed FE method for the nonstationary conduction-convection problems in [2,3]. Recently, Si et al and Su et al did some further research for the nonstationary conduction-convection equations [4,5].Concretely, high-order schemes are more attractive for the first-order schemes are not sufficiently accurate for large time approximations of the unsteady problems. And Crank-Nicolson scheme is one of the popular stable schemes with second-order accuracy [6].…”

“…Recently, Kaya and coworker [19] considered the synthesis of a subgrid stabilization method with defect-correction method for the stationary natural convection problem. Besides, a two-level defect-correction Oseen iterative stabilized FE methods for the stationary conduction-convection equations is given by Su et al [5]. Moreover, a defect-correction method for unsteady conduction-convection problems is proposed by Si et al in [4] and Zhang et al considered a defect-correction mixed FE method for steady-state natural convection problem in [20].The method we study in this article is to combine the defect-correction FE method with the Crank-Nicolson scheme for solving the nonstationary conduction-convection problems with high Reynolds number, which includes two steps: solve one stabilized artificial viscosity nonlinear equations in the defect step and correct the residual by a linearized problem in the correction step for a few steps.…”

A New Variational Multiscale FEM for the Steady-State Natural Convection Problem with Bubble Stabilization

“…In recent years, many scholars have devoted a huge amount of research to the development of natural convection equations that can be found in literatures ( [1,2,3,5,6,8,9,14,13,12] and the references therein). Christie and Mitchell [1] and Boland and Layton [2,3] gave some numerical analysis and numerical results for the natural convection equations, respectively.…”