The Oseen Type Finite Element Iterative Method for the Stationary Incompressible Magnetohydrodynamics

2017 ◽  
Vol 9 (4) ◽  
pp. 775-794 ◽  
Author(s):  
Xiaojing Dong ◽  
Yinnian He
Keyword(s):  
Reynolds Number ◽  
Finite Element ◽  
Iterative Method ◽  
Mesh Size ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Stability And Convergence ◽  
Stationary Incompressible Magnetohydrodynamics ◽  
Image Position ◽  
Incompressible Magnetohydrodynamics

AbstractIn this article, by applying the Stokes projection and an orthogonal projection with respect to curl and div operators, some new error estimates of finite element method (FEM) for the stationary incompressible magnetohydrodynamics (MHD) are obtained. To our knowledge, it is the first time to establish the error bounds which are explicitly dependent on the Reynolds numbers, coupling number and mesh size. On the other hand, The uniform stability and convergence of an Oseen type finite element iterative method for MHD with respect to high hydrodynamic Reynolds number Re and magnetic Reynolds number Rm, or small δ=1–σ with(C0, C1 are constants depending only on Ω and F is related to the source terms of equations) are analyzed under the condition that . Finally, some numerical tests are presented to demonstrate the effectiveness of this algorithm.

Fully developed MHD turbulence near critical magnetic Reynolds number

1981 ◽  
Vol 104 ◽  
pp. 419-443 ◽  
Author(s):  
J. Léorat ◽  
A. Pouquet ◽  
U. Frisch
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Mhd Equations ◽  
Liquid Sodium ◽  
Turbulent Heat ◽  
Mhd Turbulence

Liquid-sodium-cooled breeder reactors may soon be operating at magnetic Reynolds numbers RM where magnetic fields can be self-excited by a dynamo mechanism (as first suggested by Bevir 1973). Such flows have kinetic Reynolds numbers RV of the order of 107 and are therefore highly turbulent.This leads us to investigate the behaviour of MHD turbulence with high RV and low magnetic Prandtl numbers. We use the eddy-damped quasi-normal Markovian closure applied to the MHD equations. For simplicity we restrict ourselves to homogeneous and isotropic turbulence, but we do include helicity.We obtain a critical magnetic Reynolds number RMc of the order of a few tens (non-helical case) above which magnetic energy is present. RMc is practically independent of RV (in the range 40 to 106). RMc can be considerably decreased by the presence of helicity: when the overall size of the flow L is much larger than the integral scale l0, RMc can drop below unity as suggested by an α-effect argument. When L ≈ l0 the drop can still be substantial (factor of 6) when helicity is a maximum. We examine how the turbulence is modified when RM crosses RMc: presence of magnetic energy, decreased kinetic energy, steepening of kinetic-energy spectrum, etc.We make no attempt to obtain quantitative estimates for a breeder reactor, but discuss some of the possible consequences of exceeding RMc, such as decreased turbulent heat transport. More precise information may be obtained from numerical simulations and experiments (including some in the subcritical regime).

scholarly journals The effort of increasing Reynolds number in POD-Galerkin Reduced Order Methods: from laminar to turbulent flows

2018 ◽  
Author(s):  
Shafqat Ali ◽  
Saddam Hijazi ◽  
Sokratia Georgaka ◽  
Francesco Ballarin ◽  
Giovanni Stabile ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Finite Element ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Reduced Order ◽  
Volume Method ◽  
Reduced Order Methods

We present different strategies to be able to increase Reynolds number in Reduced Order Methods (ROMs), from laminar to turbulent flows, in the context of the incompressible parametrised Navier-Stokes equations. The proposed methodologies are based on different full order discretisation techniques: the finite element method and the finite volume method. For what concerns finite element full order discretisations which in this work aim to be used from low to moderate Reynolds numbers the

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