Parallel two-grid finite element method for the time-dependent natural convection problem with non-smooth initial data

Liang, Hongxia; Zhang, Tong

doi:10.1016/j.camwa.2018.12.002

Cited by 3 publications

(2 citation statements)

References 41 publications

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“…Another attractive research field is natural convection heat flow in fluid flow modelling as in Šarler et al (2004Šarler et al ( ), Sheikhi et al (2018, Liang and Zhang (2019). The meshless local Petrov-Galerkin method has been expressed by Sheikhi et al to solve natural convection heat transfer in turbulent regimes which is governed by NS and energy equations.…”

Section: Introductionmentioning

confidence: 99%

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On the BEM solution of convection–diffusion type equations involving variable convective coefficients

Fendoğlu,

Bozkaya,

Tezer-Sezgin

2024

Fluid Dyn. Res.

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In this study, numerical solutions of the unsteady convection–diffusion type equations of variable convective coefficients are investigated by two effective techniques alternative to direct boundary element method (BEM). That is, the domain boundary element and the dual reciprocity BEMs with the fundamental solution of convection–diffusion equation are used in space to transform the governing differential equations into equivalent integral equations while a backward finite difference scheme is utilized in time discretization. The fruitfulness of these combined techniques are shown by the implementation of the techniques for some widely investigated fluid dynamics problems. In fact, the lid-driven cavity flow is solved, and precise results are attained as benchmarks for assessing the accuracy of the aforementioned methods. Further, the application of the methods is extended for the natural convection flow which is governed mainly by the convection–diffusion type equations accompanied by the velocity components as variable convective coefficients. The obtained numerical results reveal that the domain BEM which uses the fundamental solution of convection–diffusion equation captures the characteristics and physical advancement of the fluid flow quite well at various combined values of the problem physical parameters.

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Section: Introductionmentioning

confidence: 99%

“…They have obtained results for higher values of Rayleigh numbers. Liang and Zhang (2019) have used two-grid FEM to solve the natural convection problem while ( Šarler et al 2004) has used DRBEM with fundamental solution of Laplace equation to solve the steady natural convection problem in a porous medium.…”

Section: Introductionmentioning

confidence: 99%

On the BEM solution of convection–diffusion type equations involving variable convective coefficients

Fendoğlu,

Bozkaya,

Tezer-Sezgin

2024

Fluid Dyn. Res.

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Fully decoupled, linear and unconditional stability implicit/explicit scheme for the natural convection problem

Zhang

2022

Applicable Analysis

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A Novel Two-Level Method for the Stationary Natural Convection Problem and the Parallel Implementations

Zhang¹,

Chen

et al. 2023

Preprint

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Parallel two-grid finite element method for the time-dependent natural convection problem with non-smooth initial data

Cited by 3 publications

References 41 publications

On the BEM solution of convection–diffusion type equations involving variable convective coefficients

On the BEM solution of convection–diffusion type equations involving variable convective coefficients

Fully decoupled, linear and unconditional stability implicit/explicit scheme for the natural convection problem

A Novel Two-Level Method for the Stationary Natural Convection Problem and the Parallel Implementations

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