Highly efficient and local projection-based stabilized finite element method for natural convection problem

Huang, Pengzhan; Zhao, Jianping; Feng, Xinlong

doi:10.1016/j.ijheatmasstransfer.2014.08.015

Cited by 21 publications

(8 citation statements)

References 32 publications

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“…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by large temperature differences, which results in a considerable density change and the Boussinesq approximation is no longer valid.…”

Section: Introductionmentioning

confidence: 99%

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

Wang

Feng

2019

HFF

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Purpose The purpose of this paper is to propose a new method to solve the incompressible natural convection problem with variable density. The main novel ideas of this work are to overcome the stability issue due to the nonlinear inertial term and the hyperbolic term for conventional finite element methods and to deal with high Rayleigh number for the natural convection problem. Design/methodology/approach The paper introduces a novel characteristic variational multiscale (C-VMS) finite element method which combines advantages of both the characteristic and variational multiscale methods within a variational framework for solving the incompressible natural convection problem with variable density. The authors chose the conforming finite element pair (P2, P2, P1, P2) to approximate the density, velocity, pressure and temperature field. Findings The paper gives the stability analysis of the C-VMS method. Extensive two-dimensional/three-dimensional numerical tests demonstrated that the C-VMS method not only can deal with the incompressible natural convection problem with variable density but also with high Rayleigh number very well. Originality/value Extensive 2D/3D numerical tests demonstrated that the C-VMS method not only can deal with the incompressible natural convection problem with variable density but also with high Rayleigh number very well.

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Section: Introductionmentioning

confidence: 99%

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

Wang

Feng

2019

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

Section: Penalized Finite Element Methodsmentioning

confidence: 99%

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

Zhao

et al. 2019

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Purpose This paper aims to proposes and analyzes a novel recovery-based posteriori error estimator for the stationary natural-convection problem based on penalized finite element method. Design/methodology/approach The optimal error estimates of the penalty FEM are established by using the lower-order finite element pair P1-P0-P1 which does not satisfy the discrete inf-sup condition. Besides, a new recovery type posteriori estimator in view of the gradient recovery and superconvergent theory to deal with the discontinuity of the gradient of numerical solution. Findings The stability, accuracy and efficiency of the proposed method are confirmed by several numerical investigations. Originality/value The provided reliability and efficiency analysis is shown that the true error can be effectively bounded by the recovery-based error estimator.

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“…In fact, in many engineering applications, especially in relation to heat losses from thermal storage systems such as solar collectors, nuclear reactor design, buildings and aircraft cabin insulation, the problem is researched to find means to improve the insulating properties of fluid layers. In [59,60], for the natural convection heat transfer, numerical investigation of this problem is presented. Now, we will test this problem for the Darcy-Brinkman model, which describes double-diffusive phenomena and comes from the combined heat and mass transfer.…”

Section: The Partitioned Square Enclosure Problemmentioning

confidence: 99%

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

Zeng

Huang

2021

Z Angew Math Mech

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This paper proposes a deferred defect-correction method for the time-dependent nonlinear Darcy-Brinkman model based on the mixed finite element method. The presented method combines the deferred correction strategy with the defect-correction method and involves two steps. In the first step, a defect Darcy-Brinkman model is solved. Then in the second step, a correction Darcy-Brinkman model based on the deferred correction approach is solved. Moreover, unconditional stability and convergence of the presented method are deduced. Finally, several numerical examples are given to support the theoretical analysis.

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Highly efficient and local projection-based stabilized finite element method for natural convection problem

Cited by 21 publications

References 32 publications

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

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

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

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

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