4.7 Article

A projection method for the non-stationary incompressible MHD coupled with the heat equations

Related references

Note: Only part of the references are listed.
Article Mathematics, Applied

Uniform Stability and Convergence with Respect to (ν, μ, s, 1-σ) of the Three Iterative Finite Element Solutions for the 3D Steady MHD Equations

Yinnian He et al.

Summary: This paper presents the Stokes, Newton, and Oseen iterative finite element methods for the 3D steady MHD equations. The methods approximate the solution pair ((u, B), p) of the equations by combining iterative methods with the finite element method. The paper provides uniform stability and convergence results for the iterative finite element solutions under convergence conditions and demonstrates the efficiency of the methods through numerical tests.

JOURNAL OF SCIENTIFIC COMPUTING (2022)

Article Computer Science, Interdisciplinary Applications

Second order unconditional linear energy stable, rotational velocity correction method for unsteady incompressible magneto-hydrodynamic equations

Ke Zhang et al.

Summary: In this paper, a second order decoupled time discretization method for solving the unsteady incompressible magneto-hydrodynamic equations is presented. The method utilizes rotational velocity correction projection scheme and extrapolation algorithm to handle the hydrodynamic equation and the magnetic equation nonlinear terms respectively. The unconditional energy stability of the proposed scheme is proven using the Gauge-Uzawa format. Numerical experiments including accuracy test, stability test, flow around a cylinder test and driven cavity flow problem are conducted to verify the effectiveness of the presented scheme.

COMPUTERS & FLUIDS (2022)

Article Computer Science, Interdisciplinary Applications

Unconditional stability and error estimates of the modified characteristics FEMs for the time-dependent thermally coupled incompressible MHD equations

Zhiyong Si et al.

Summary: This paper focuses on the modified characteristics finite element methods for the time-dependent thermally coupled incompressible MHD equations. The introduced characteristic time-discrete system, utilizing the modified characteristics tracking scheme, demonstrates unconditional stability and optimal convergence orders. Numerical results validate the efficiency and robustness of the proposed method.

COMPUTERS & FLUIDS (2022)

Article Mathematics, Applied

A consistent projection finite element method for the incompressible MHD equations

Yang Yang et al.

Summary: This paper introduces a consistent projection finite element method for the incompressible MHD equations, combining the advantages of gauge and Uzawa methods within a variational framework. The stability and error estimates of velocity, pressure, and magnetic field are proven using the variational method under certain assumptions, and numerical experiments are conducted to validate the method's effectiveness.

APPLICABLE ANALYSIS (2021)

Article Thermodynamics

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

Jinting Yang et al.

INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW (2020)

Article Mathematics, Applied

A rotational velocity-correction projection method for unsteady incompressible magnetohydrodynamics equations

Jixiang Guan et al.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2020)

Article Thermodynamics

Parallel two-step finite element algorithm for the stationary incompressible magnetohydrodynamic equations

Yuan Ping et al.

INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW (2019)

Article Thermodynamics

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

Weilong Wang et al.

INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW (2019)

Article Mathematics, Applied

Stable finite element methods preserving del • B=0 exactly for MHD models

Kaibo Hu et al.

NUMERISCHE MATHEMATIK (2017)

Article Mathematics, Applied

Error analysis of first-order projection method for time-dependent magnetohydrodynamics equations

Rong An et al.

APPLIED NUMERICAL MATHEMATICS (2017)

Article Thermodynamics

Unconditional convergence of the Euler semi-implicit scheme for the 3D incompressible MHD equations Numerical implementation

Guo-Dong Zhang et al.

INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW (2015)

Article Mathematics, Applied

A gauge-Uzawa finite element method for the time-dependent Viscoelastic Oldroyd flows

Zhiyong Si et al.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2015)

Article Mathematics, Applied

Two-Level Newton Iterative Method for the 2D/3D Stationary Incompressible Magnetohydrodynamics

Xiaojing Dong et al.

JOURNAL OF SCIENTIFIC COMPUTING (2015)

Article Mathematics, Applied

New development in freefem++

F. Hecht

JOURNAL OF NUMERICAL MATHEMATICS (2012)

Article Engineering, Multidisciplinary

Convergence of three iterative methods based on the finite element discretization for the stationary Navier-Stokes equations

Yinnian He et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2009)

Article Computer Science, Interdisciplinary Applications

On numerical realizability of thermal convection

Zbigniew P. Piotrowski et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2009)

Article Mathematics, Applied

The gauge-Uzawa finite element method - Part II: The Boussinesq equations

Ricardo H. Nochetto et al.

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES (2006)

Article Mathematics, Applied

Semi-implicit Euler scheme for generalized Newtonian fluids

Lars Diening et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2006)

Article Mathematics, Applied

The gauge-Uzawa finite element method. Part I: The Navier-Stokes equations

RH Nochetto et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2005)

Article Mathematics, Applied

Large solutions to the initial-boundary value problem for planar magnetohydrodynamics

DH Wang

SIAM JOURNAL ON APPLIED MATHEMATICS (2003)