Stability and convergence of iterative finite element methods for the thermally coupled incompressible MHD flow

2020 ◽  
Vol 30 (12) ◽  
pp. 5103-5141
Author(s):  
Jinting Yang ◽  
Tong Zhang
Keyword(s):  
Finite Element ◽  
Iterative Method ◽  
Bounded Domain ◽  
Finite Element Methods ◽  
Mhd Flow ◽  
Mhd Equations ◽  
Stability And Convergence ◽  
Physical Parameters ◽  
Content Type ◽  
Incompressible Mhd

Purpose The purpose of this paper is to propose three iterative finite element methods for equations of thermally coupled incompressible magneto-hydrodynamics (MHD) on 2D/3D bounded domain. The detailed theoretical analysis and some numerical results are presented. The main results show that the Stokes iterative method has the strictest restrictions on the physical parameters, and the Newton’s iterative method has the higher accuracy and the Oseen iterative method is stable unconditionally. Design/methodology/approach Three iterative finite element methods have been designed for the thermally coupled incompressible MHD flow on 2D/3D bounded domain. The Oseen iterative scheme includes solving a linearized steady MHD and Oseen equations; unconditional stability and optimal error estimates of numerical approximations at each iterative step are established under the uniqueness condition. Stability and convergence of numerical solutions in Newton and Stokes’ iterative schemes are also analyzed under some strong uniqueness conditions. Findings This work was supported by the NSF of China (No. 11971152). Originality/value This paper presents the best choice for solving the steady thermally coupled MHD equations with different physical parameters.

scholarly journals Some advances in high-performance finite element methods

2019 ◽  
Vol 36 (8) ◽  
pp. 2811-2834 ◽  
Author(s):  
Song Cen ◽  
Cheng Jin Wu ◽  
Zhi Li ◽  
Yan Shang ◽  
Chenfeng Li
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
High Performance ◽  
Displacement Function ◽  
Content Type ◽  
Reissner Plate ◽  
Long Time ◽  
History Of ◽  
Function Element ◽  
Element Method

Purpose The purpose of this paper is to give a review on the newest developments of high-performance finite element methods (FEMs), and exhibit the recent contributions achieved by the authors’ group, especially showing some breakthroughs against inherent difficulties existing in the traditional FEM for a long time. Design/methodology/approach Three kinds of new FEMs are emphasized and introduced, including the hybrid stress-function element method, the hybrid displacement-function element method for Mindlin–Reissner plate and the improved unsymmetric FEM. The distinguished feature of these three methods is that they all apply the fundamental analytical solutions of elasticity expressed in different coordinates as their trial functions. Findings The new FEMs show advantages from both analytical and numerical approaches. All the models exhibit outstanding capacity for resisting various severe mesh distortions, and even perform well when other models cannot work. Some difficulties in the history of FEM are also broken through, such as the limitations defined by MacNeal’s theorem and the edge-effect problems of Mindlin–Reissner plate. Originality/value These contributions possess high value for solving the difficulties in engineering computations, and promote the progress of FEM.

An efficient iterative algorithm for the natural convection equations based on finite element method

2018 ◽  
Vol 28 (3) ◽  
pp. 584-605 ◽  
Author(s):  
Lei Wang ◽  
Jian Li ◽  
Pengzhan Huang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Convection ◽  
Iterative Method ◽  
Error Correction ◽  
Computational Time ◽  
Content Type ◽  
Natural Convection Problem ◽  
New Iterative Method ◽  
Element Method

Purpose This paper aims to propose a new highly efficient iterative method based on classical Oseen iteration for the natural convection equations. Design/methodology/approach First, the authors solve the problem by the Oseen iterative scheme based on finite element method, then use the error correction strategy to control the error arising. Findings The new iterative method not only retains the advantage of the Oseen scheme but also saves computational time and iterative step for solving the considered problem. Originality/value In this work, the authors introduce a new iterative method to solve the natural convection equations. The new algorithm consists of the Oseen scheme and the error correction which can control the errors from the iterative step arising for solving the nonlinear problem. Comparing with the classical iterative method, the new scheme requires less iterations and is also capable of solving the natural convection problem at higher Rayleigh number.

scholarly journals An Analytical Study of Internal Heating and Chemical Reaction Effects on MHD Flow of Nanofluid with Convective Conditions

Crystals ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 1523
Author(s):  
Haroon Ur Rasheed ◽  
Saeed Islam ◽  
Maha M. Helmi ◽  
Sam Alsallami ◽  
Zeeshan Khan ◽  
...  
Keyword(s):  
Mhd Flow ◽  
Skin Friction Coefficient ◽  
Thermal Dissipation ◽  
Stability And Convergence ◽  
Physical Parameters ◽  
Electrically Conductive ◽  
Physical Constraints ◽  
Coupled Equations ◽  
Mass And Heat Transfer ◽  
And Diffusion

This research investigates the influence of the combined effect of the chemically reactive and thermal radiation on electrically conductive stagnation point flow of nanofluid flow in the presence of a stationary magnetic field. Furthermore, the effect of Newtonian heating, thermal dissipation, and activation energy are considered. The boundary layer theory developed the constitutive partial differential momentum, energy, and diffusion balance equations. The fundamental flow model is changed to a system of coupled ordinary differential equations (ODEs) via proper transformations. These nonlinear-coupled equations are addressed analytically by implementing an efficient analytical method, in which a Mathematica 11.0 programming code is developed for numerical simulation. For optimizing system accuracy, stability and convergence analyses are carried out. The consequences of dimensionless parameters on flow fields are investigated to gain insight into the physical parameters. The result of these physical constraints on momentum and thermal boundary layers, along with concentration profiles, are discussed and demonstrated via plotted graphs. The computational outcomes of skin friction coefficient, mass, and heat transfer rate under the influence of appropriate parameters are demonstrated graphically.

Sign in / Sign up

Export Citation Format

Share Document