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

Abstract

This survey enfolds rigorous analysis of the defect‐correction finite element (FE) method for the time‐dependent conduction‐convection problem which based on the Crank‐Nicolson scheme. The method consists of two steps: solve a nonlinear problem with an added artificial viscosity term on a FE grid and correct the solutions on the same grid using a linearized defect‐correction technique. The stability and optimal error estimate of the fully discrete scheme are derived. As a consequence, the effectiveness of the method to deal with high Reynolds number is illustrated in several numerical experiments. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 681–703, 2017

A novel characteristic variational multiscale FEM for incompressible natural convection problem with variable density

“…For natural convection problem, which has a wide range of applications in many research fields (Wu et al , 2017b, 2016), the density difference in the fluid occurring due to temperature gradient is the driving mechanism of fluid motion[1]. In case that the density variation is small, it can be modeled by using a Boussinesq approximation, which treats the density as a constant but with an added buoyancy force, and most literature studies the constant density natural convection based on the Boussinesq approximation (Boland and Layton, 1990; Du et al , 2015; Feng et al , 2011; Huang et al , 2015, 2013, 2012; Liao, 2012, 2010; Si et al , 2014; Szumbarski et al , 2014; Su et al , 2017a, 2017b, 2014a, 2014b; Sun et al , 2011; Davis, 1983; Wang et al , 2018a, 2018b; Wu et al , 2015b, 2017a, 2016; Zhang et al , 2016, 2018]). However, in most geophysical flows and many other situations, fluid motion is usually driven by large temperature differences, which results in a considerable density change and the Boussinesq approximation is no longer valid.…”

Recovery-based error estimator for the natural-convection problem based on penalized finite element method

“…As we know, the above bilinear and trilinear forms have following important estimates (Su et al , 2017; Huang et al , 2012, 2015; Layton and Tobiska, 1998; Luo, 2006; Su et al , 2014a, 2014b): where are two fixed positive constants depending only on Ω.…”

“…Natural-convection (NC) problem, namely, buoyancy-driven flows which occur frequently in practical problems are atmospheric fronts, katabatic winds in nature, room ventilation, heating general, nuclear reaction systems, fire control in life, dense gas dispersion, natural ventilation, solar collectors, insulation with double pane window and cooling of electronic equipment in industry (Boland and Layton, 1990a;Çıbık and Kaya, 2011;Sankhavara and Shukla, 2006;Wu et al, 2017aWu et al, , 2017bSu et al, 2017;Schmidt-Nielsen, 2011;Wu et al, 2016) [1]. In this article, a posteriori recovery-based error estimator based on penalized FEM is presented to solve the NC problem.…”

Recovery-Based Error Estimator for Natural Convection Equations Based on Defect-Correction Methods

“…The defect-correction method (DCM) is an iterative improvement technique for improving the accuracy of computational solutions without introducing mesh refinement [ 28 , 29 , 30 , 31 ]. In general, the basic idea can be briefly described as follows.…”