A finite element variational multiscale method for steady-state natural convection problem based on two local gauss integrations

2013 ◽  
Vol 30 (2) ◽  
pp. 361-375 ◽  
Author(s):  
Yunzhang Zhang ◽  
Yanren Hou ◽  
Haibiao Zheng
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Natural Convection ◽  
Multiscale Method ◽  
Variational Multiscale Method ◽  
Variational Multiscale ◽  
Convection Problem ◽  
Natural Convection Problem

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

2019 ◽  
Vol 29 (2) ◽  
pp. 580-601 ◽  
Author(s):  
Weilong Wang ◽  
Jilian Wu ◽  
Xinlong Feng
Keyword(s):  
Finite Element ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Variable Density ◽  
Content Type ◽  
Variational Multiscale ◽  
Numerical Tests ◽  
Convection Problem ◽  
The Stability ◽  
Natural Convection Problem

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.

scholarly journals A Finite Element Variational Multiscale Method Based on Two Local Gauss Integrations for Stationary Conduction-Convection Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yu Jiang ◽  
Liquan Mei ◽  
Huiming Wei ◽  
Weijun Tian ◽  
Jiatai Ge
Keyword(s):  
Exact Solution ◽  
Finite Element ◽  
Numerical Test ◽  
Multiscale Method ◽  
Additional Cost ◽  
Good Precision ◽  
Variational Multiscale Method ◽  
Theory Analysis ◽  
Element Level ◽  
Variational Multiscale

A new finite element variational multiscale (VMS) method based on two local Gauss integrations is proposed and analyzed for the stationary conduction-convection problems. The valuable feature of our method is that the action of stabilization operators can be performed locally at the element level with minimal additional cost. The theory analysis shows that our method is stable and has a good precision. Finally, the numerical test agrees completely with the theoretical expectations and the “ exact solution,” which show that our method is highly efficient for the stationary conduction-convection problems.

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