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Pressure-Correction Projection FEM for Time-Dependent Natural Convection Problem

Part of: Partial differential equations, boundary value problems Incompressible viscous fluids Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  08 March 2017

Jilian Wu ,
Xinlong Feng  and
Fei Liu
Jilian Wu*
Affiliation:
College of Mathematics and Systems Science, Xinjiang University, Urumqi, 830046, P.R. China
Xinlong Feng*
Affiliation:
College of Mathematics and Systems Science, Xinjiang University, Urumqi, 830046, P.R. China
Fei Liu*
Affiliation:
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, P.R. China
*
*Corresponding author. Email addresses:happy_whw@163.com (J. Wu), fxlmath@gmail.com (X. Feng), liufei_2000@163.com (F. Liu)
*Corresponding author. Email addresses:happy_whw@163.com (J. Wu), fxlmath@gmail.com (X. Feng), liufei_2000@163.com (F. Liu)
*Corresponding author. Email addresses:happy_whw@163.com (J. Wu), fxlmath@gmail.com (X. Feng), liufei_2000@163.com (F. Liu)
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Abstract

Pressure-correction projection finite element methods (FEMs) are proposed to solve nonstationary natural convection problems in this paper. The first-order and second-order backward difference formulas are applied for time derivative, the stability analysis and error estimates of the semi-discrete schemes are presented using energy method. Compared with characteristic variational multiscale FEM, pressure-correction projection FEMs are more efficient and unconditionally energy stable. Ample numerical results are presented to demonstrate the effectiveness of the pressure-correction projection FEMs for solving these problems.

Keywords

Time-dependent natural convection problemspressure-correction projection FEMsbackward difference formulastability analysiserror estimate

MSC classification

Secondary: 65N15: Error bounds 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 76D07: Stokes and related (Oseen, etc.) flows 65N12: Stability and convergence of numerical methods 35Q79: PDEs in connection with classical thermodynamics and heat transfer
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 4 , April 2017 , pp. 1090 - 1117
Copyright
Copyright © Global-Science Press 2017 

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Footnotes

Communicated by Jie Shen

References

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