Two-level variational multiscale method based on the decoupling approach for the natural convection problem

Du, Binbin; Su, Haiyan; Feng, Xinlong

doi:10.1016/j.icheatmasstransfer.2014.12.004

Cited by 22 publications

(14 citation statements)

References 24 publications

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“…(19), we give the numerical pressure, the numerical temperature and the numerical streamline with λ = 1, ν = 1, Ra = 10, 000 by C-VMS method. We can see that C-VMS method gives the good results that conform with the practical phenomenon and conform with Du's [17] very well.…”

Section: Four Obstacles Problemsupporting

confidence: 76%

The characteristic variational multiscale method for time dependent conduction–convection problems

GUI

Liu

et al. 2015

International Communications in Heat and Mass Transfer

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Section: Four Obstacles Problemsupporting

confidence: 76%

The characteristic variational multiscale method for time dependent conduction–convection problems

GUI

Liu

et al. 2015

International Communications in Heat and Mass Transfer

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“…Besides, there are four rectangular insulators in this square cavity and the size and location can be found in this figure. Despite the simplicity of its geometry and boundary conditions, it has characteristics of a very complex flow which occurs in many practical engineering applications (refer to ).…”

Section: Numerical Experimentsmentioning

confidence: 99%

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

Feng

2016

Numerical Methods Partial

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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

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“…Due to the coupling of three variables among the natural convection equations, finding the numerical solutions becomes a difficult task, much attention has been attracted in recent years. For example, we can refer to Du et al, Wu et al, Zhang et al, and Zhang et al for the variational multiscale methods, for the projection method, for the decoupled method, for iteration methods, and the references therein, all above mentioned works are one order schemes and 2D case.…”

Section: Introductionmentioning

confidence: 99%

Stability and convergence of two‐grid Crank‐Nicolson extrapolation scheme for the time‐dependent natural convection equations

Liang

Zhang

2019

Math Methods in App Sciences

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In this paper, we consider the Crank-Nicolson extrapolation scheme for the 2D/3D unsteady natural convection problem. Our numerical scheme includes the implicit Crank-Nicolson scheme for linear terms and the recursive linear method for nonlinear terms. Standard Galerkin finite element method is used to approximate the spatial discretization. Stability and optimal error estimates are provided for the numerical solutions. Furthermore, a fully discrete two-grid Crank-Nicolson extrapolation scheme is developed, the corresponding stability and convergence results are derived for the approximate solutions. Comparison from aspects of the theoretical results and computational efficiency, the two-grid Crank-Nicolson extrapolation scheme has the same order as the one grid method for velocity and temperature in H 1 -norm and for pressure in L 2 -norm. However, the two-grid scheme involves much less work than one grid method. Finally, some numerical examples are provided to verify the established theoretical results and illustrate the performances of the developed numerical schemes. KEYWORDSCrank-Nicolson extrapolation scheme, error estimates, stability, the natural convection equations, two-grid method MSC CLASSIFICATION 65N15; 65N30; 76D07Math Meth Appl Sci. 2019;42:6165-6191.wileyonlinelibrary.com/journal/mma

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Two-level variational multiscale method based on the decoupling approach for the natural convection problem

Cited by 22 publications

References 24 publications

The characteristic variational multiscale method for time dependent conduction–convection problems

The characteristic variational multiscale method for time dependent conduction–convection problems

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

Stability and convergence of two‐grid Crank‐Nicolson extrapolation scheme for the time‐dependent natural convection equations

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