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Global Well-posedness of the 3D Generalized Rotating magnetohydrodynamics Equations

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Acta Mathematica Sinica,English Series 2018年第6期34卷 992-1000页

作者： Wei Hua WANG Gang WU School of Mathematical Sciences University of Chinese Academy of Sciences

In this paper, we establish the global well-posedness of the generalized rotating mag- netohydrodynamics equations if the initial data are in χ^1-2α defined by χ^1-2α {u ∈D＇（R^3）：fR^3｜｜^1-2αu^^（ξ）｜d... 详细信息

关键词： magnetohydrodynamics fractional MHD incompressible rotation framework Coriolis force

KINETIC FUNCTIONS IN magnetohydrodynamics WITH RESISTIVITY AND HALL EFFECT

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Acta Mathematica Scientia 2009年第6期29卷 1684-1702页

作者： Philippe G. Le Siddhartha Mishra FlochLaboratoire Jacques-Louis Lions Centre National de la Recherche ScientifiqueUniversit Pierre et Marie Curie (Paris 6) 4 Place Jussieu 75258 Paris France Seminar for Applied Mathematics D-Math ETH HG Raemistrasse Zürich-8092 Switzerland

We consider a nonlinear hyperbolic system of two conservation laws which arises in ideal magnetohydrodynamics and includes second-order terms accounting for magnetic resistivity and Hall effect. We show that the initial value problem for this model may lead to solutions exhibiting complex wave structures, including undercompressive nonclassical shock waves. We investigate numerically the subtle competition that takes place between the hyperbolic, diffusive, and dispersive parts of the system. Following Abeyratne, Knowles, LeFloch, and Truskinovsky, who studied similar questions arising in fluid and solid flows, we determine the associated kinetic function which characterizes the dynamics of undereompressive shocks driven by resistivity and Hall effect. To this end, we design a new class of ＂schemes with eontroled dissipation＂, following recent work by LeFloch and Mohammadian. It is now recognized that the equivalent equation associated with a scheme provides a guideline to design schemes that capture physically relevant, nonclassical shocks. We propose a new class of schemes based on high-order entropy conservative, finite differences for the hyperbolic flux, and high-order central differences for the resistivity and Hall terms. These schemes are tested for several regimes of （co-planar or not） initial data and parameter values, and allow us to analyze the properties of nonclassical shocks and establish the existence of monotone kinetic functions in magnetohydrodynamics.

关键词： hyperbolic conservation law magnetohydrodynamics magnetic resistivity Hall effect undercompressive shock kinetic function

Hyperbolic Divergence Cleaning in Lattice Boltzmann magnetohydrodynamics

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Communications in Computational Physics 2023年第1期33卷 245-272页

作者： Paul J.Dellar OCIAM Mathematical InstituteUniversity of OxfordRadcliffe Observatory QuarterOxford OX26GGUK

magnetohydrodynamics couples the Navier-Stokes and Maxwell’s equations to describe the flow of electrically conducting fluids in magnetic ***’s equations require the divergence of the magnetic field to vanish,but this condition is typically not preserved exactly by numerical *** can develop artifacts because structural properties of the magnetohydrodynamic equations then fail to *** with hyperbolic divergence cleaning permits a nonzero divergence that evolves under a telegraph equation,designed to both damp the divergence,and propagate it away from any sources,such as poorly resolved regions with large spatial gradients,without significantly increasing the computational *** show that existing lattice Boltzmann algorithms for magnetohydrodynamics already incorporate hyperbolic divergence cleaning,though they typically use parameter values for which it reduces to parabolic divergence cleaning under a slowly-varying *** recover hyperbolic divergence cleaning by adjusting the relaxation rate for the trace of the tensor that represents the electric field,and absorb the contribution from the symmetric-traceless part of this tensor using a change of *** experiments confirm that the qualitative behaviour changes from parabolic to hyperbolic when the relaxation time for the trace of the electric field tensor is increased.

关键词： magnetohydrodynamics divergence cleaning telegraph equations matrix collision operators linear viscoelasticity

magnetohydrodynamics convective flow in a vertical slot through a porous medium

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Theoretical & Applied Mechanics Letters 2012年第5期2卷 33-38页

作者： Rajnish Kumar Bal G.Prasad Department of Applied Mathematics Birla Institute of TechnologyPatna CampusMesra BiharIndia Department of Mathematics B.N.CollegePatna UniversityBiharIndia

An analysis is presented with magnetohydrodynamics natural convective flow of a viscous Newtonian fluid saturated porous medium in a vertical slot. The flow in the porous media has been modeled using the Brinkman model. The fully-developed two-dimensional flow from capped to open ends is considered for which a continuum of solutions is obtained. The influence of pertinent parame-ters on the flow is delineated and appropriate conclusions are drawn. The asymptotic behaviour and the volume flux are analyzed and incorporated graphically for the three-parameter family of solution.

关键词： natural convection porous medium magnetohydrodynamics Brinkman model vertical slot

The Richtmyer-Meshkov instability of a double-layer interface in convergent geometry with magnetohydrodynamics

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Matter and Radiation at Extremes 2018年第4期3卷 207-218页

作者： Yuan Li Ravi Samtaney Vincent Wheatley Mechanical Engineering King Abdullah University of Science and TechnologySaudi Arabia Mechanical and Mining Engineering The University of QueenslandAustralia

The interaction between a converging cylindrical shock and double density interfaces in the presence of a saddle magnetic field is numerically investigated within the framework of ideal *** fluids of differing densities are initially separated by the two perturbed cylindrical *** initial incident converging shock is generated from a Riemann problem upstream of the first *** effect of the magnetic field on the instabilities is studied through varying the field *** shows that the Richtmyer-Meshkov and Rayleigh-Taylor instabilities are mitigated by the field,however,the extent of the suppression varies on the interface which leads to non-axisymmetric growth of the *** degree of asymmetry of the interfacial growth rate is increased when the seed field strength is increased.

关键词： magnetohydrodynamics Double density interfaces Converging shock Richtmyer-Meshkov instability

High-Order Gas-Kinetic Methods for Idealmagnetohydrodynamics

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Communications in Nonlinear Science and Numerical Simulation 1999年第2期4卷 141-146页

作者： Huazhong TANG(LSEC, Institute of Computational Mathematics, Academia Sinica, Beijing 100080, China) LSEC Institute of Computational Mathematics Academia Sinica Beijing 100080 China

This article is to study extension of gas-kinetic theory based flux splittingmethods to ideal magnetohydrodynamics (MHD) equations. Uniform high-order gaskinetic methods are presented, based on TVD type Runge-Kutta time discretization andtechnique of the initial reconstruction. The numerical results have been given to showrobustness of our schemes.

关键词： magnetohydrodynamics flux-spittting gas-kinetic schemes

Effects of plasma radiation on the nonlinear evolution of neo-classical tearing modes in tokamak plasmas with reversed magnetic shear

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Chinese Physics B 2023年第10期32卷 548-555页

作者：姜帅王正汹魏来刘桐 Key Laboratory of Materials Modification by Beams of the Ministry of Education School of PhysicsDalian University of TechnologyDalian 116024China

Effects of plasma radiation on the nonlinear evolution of neo-classical double tearing modes(NDTMs)in tokamak plasmas with reversed magnetic shear are numerically investigated based on a set of reduced magnetohydrodynamics(MHD)*** with different separations △_(rs)=|r_(s2)-r_(s1)|between the two same rational surfaces are *** the small △_(rs)cases,the plasma radiation destabilizes the NDTMs and makes the kinetic energy still grow gradually in the late nonlinear ***,the NDTM harmonics with high mode numbers reach a high level in the presence of plasma radiation,forming a broad spectrum of MHD perturbations that induces a radially broadened region of MHD *** a result,the profiles of safety factors also enter a nonlinear oscillation *** the intermediate △_(rs)case,the plasma radiation can advance the explosive burst of kinetic energy that results from the fast driven reconnection between the two rational surfaces,because it can further promote the destabilizing effects of bootstrap current perturbation on the magnetic island near the outer rational *** the large △_(rs)case,through destabilizing the outer islands significantly,the plasma radiation can even induce the explosive burst in the reversed magnetic shear configuration where the burst cannot be induced in the absence of plasma radiation.

关键词： neoclassical tearing mode magnetohydrodynamics nonlinear phenomena

Effects of q-profiles of a weak magnetic shear on energetic ion excited q=1 mode in tokamak plasmas

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Chinese Physics B 2016年第1期25卷 690-696页

作者：李泽宇王先驱王晓钢 State Key Lab of Nuclear Physics and Technology School of PhysicsPeking UniversityBeijing 100871China Institute of Fusion Science.School of Physical Science and Technology Southwest Jiaotong UniversityChengdu 610031China Department of Physics Harbin Institute of TechnologyHarbin 150001China

In this paper, we study the effect of safety factor profiles, particularly with a very weak magnetic shear, on the m/n = 1 mode excited by energetic ions in tokamak plasmas. It is found that the profile plays a significant role in the onset of the mode, and the thresholds for the instability are also derived. The numerical results for configurations with conventional or reversed non monotonic magnetic shears are discussed. The effects of radial location of rational surfaces, edge q value, and flatness of q-profile on the energetic ion excited mode are further analyzed in detail.

关键词： safety factor profile magnetohydrodynamics tokamak energetic particles

Nonlinear Simulations of Coalescence Instability Using a Flux Difference Splitting Method

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Plasma Science and Technology 2016年第7期18卷 714-719页

作者：马骏秦宏于治李德徽 Institute of Plasma Physics Chinese Academy of Sciences Department of Modern Physics University of Science and Technology of China Plasma Physics Laboratory Princeton University

A flux difference splitting numerical scheme based on the finite volume method is applied to study ideal/resistive magnetohydrodynamics. The ideal/resistive MHD equations are cast as a set of hyperbolic conservation laws, and we develop a numerical capability to solve the weak solutions of these hyperbolic conservation laws by combining a multi-state Harten-Lax-Van Leer approximate Riemann solver with the hyperbolic divergence cleaning technique, high order shock-capturing reconstruction schemes, and a third order total variance diminishing Runge-Kutta time evolving scheme. The developed simulation code is applied to study the long time nonlinear evolution of the coalescence instability. It is verified that small structures in the instability oscillate with time and then merge into medium structures in a coherent manner. The medium structures then evolve and merge into large structures, and The physics of this interesting nonlinear dynamics this trend continues through all scale-lengths is numerically analyzed.

关键词： magnetohydrodynamics nonlinear silnulation finite volume method,coalescence instability