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Stationary twodimensional magnetohydrodynamic flows with shocks: characteristic analysis and grid convergence study
 J. Comput. Phys
"... Five model flows of increasing complexity belonging to the class of stationary twodimensional planar fieldaligned magnetohydrodynamic (MHD) flows are presented which are well suited to the quantitative evaluation of MHD codes. The physical properties of these five flows are investigated using char ..."
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Cited by 4 (2 self)
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Five model flows of increasing complexity belonging to the class of stationary twodimensional planar fieldaligned magnetohydrodynamic (MHD) flows are presented which are well suited to the quantitative evaluation of MHD codes. The physical properties of these five flows are investigated using characteristic theory. Grid convergence criteria for flows belonging to this class are derived from characteristic theory, and grid convergence is demonstrated for the numerical simulation of the five model flows with a standard highresolution finite volume numerical MHD code on structured bodyfitted grids. In addition, one model flow is presented which is not fieldaligned, and it is discussed how grid convergence can be studied for this flow. By formal grid convergence studies of magnetic flux conservation and other flow quantities, it is investigated whether the Powell source term approach to controlling the ∇·Bconstraint leads to correct results for the class of flows under consideration. c ○ 2001 Academic Press Key Words: magnetohydrodynamics; shock waves; theory of characteristics; stability and convergence of numerical methods. 1.
Unconditionally Stable Explicit Schemes for the Approximation of Conservation Laws
"... We consider explicit schemes for homogeneous conservation laws which satisfy the geometric CourantFriedrichsLewy condition in order to guarantee stability but allow a time step with CFLnumber larger than one. A brief overview over existing unconditionally stable schemes for hyperbolic conservatio ..."
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Cited by 1 (0 self)
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We consider explicit schemes for homogeneous conservation laws which satisfy the geometric CourantFriedrichsLewy condition in order to guarantee stability but allow a time step with CFLnumber larger than one. A brief overview over existing unconditionally stable schemes for hyperbolic conservation laws is provided, although the focus is on LeVeque's large time step Godunov scheme. For this scheme we explore the question of entropy consistency for the approximation of onedimensional scalar conservation laws with convex ux function and describe a possible way to extend the scheme to the twodimensional case. Numerical calculations and analytical results show that an increase of accuracy can be obtained because the error introduced by the modi ed evolution step of the large time step Godunov scheme may be less important than the error due to the projection step.
Photospheric processes and magnetic flux tubes
, 709
"... Abstract. New highresolution observations reveal that smallscale magnetic flux concentrations have a delicate substructure on a spatial scale of 0.1 ′ ′. Their basic structure can be interpreted in terms of a magnetic flux sheet or tube that vertically extends through the ambient weakfield or fie ..."
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Abstract. New highresolution observations reveal that smallscale magnetic flux concentrations have a delicate substructure on a spatial scale of 0.1 ′ ′. Their basic structure can be interpreted in terms of a magnetic flux sheet or tube that vertically extends through the ambient weakfield or fieldfree atmosphere with which it is in mechanical equilibrium. A more refined interpretation comes from new threedimensional magnetohydrodynamic simulations that are capable of reproducing the corrugated shape of magnetic flux concentrations and their signature in the visible continuum. Faculae are another manifestation of smallscale magnetic flux concentrations. It is shown that the characteristic asymmetric shape of the contrast profile of faculae is an effect of radiative transfer across the rarefied atmosphere of the magnetic flux concentration. Also discussed are threedimensional radiation magnetohydrodynamic simulations of the integral layers from the top of the convection zone to the midchromosphere. They show a highly dynamic chromospheric magnetic field, marked by rapidly moving filaments of stronger than average magnetic field that form in the compression zone downstream and along propagating shock fronts. The simulations confirm the picture of flux concentrations that strongly expand through the photosphere into a more homogeneous, space filling chromospheric field. Future directions in the simulation of smallscale
On some deficiencies of the AUFS scheme for Euler flows and possible fixes
"... The AUFSscheme by Sun and Takayama is a flux splitting scheme without breakdown of discrete shock profiles, usually called carbuncle, but still with a fine resolution of entropy waves. Unfortunately, in numerical tests, the viscosity on entropy waves turns out to be too small and the viscosity on s ..."
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The AUFSscheme by Sun and Takayama is a flux splitting scheme without breakdown of discrete shock profiles, usually called carbuncle, but still with a fine resolution of entropy waves. Unfortunately, in numerical tests, the viscosity on entropy waves turns out to be too small and the viscosity on shear waves to be too high. In this paper, we provide fixes to overcome these deficiencies.
A note on magnetic monopoles and the one dimensional MHD Riemann problem
, 2001
"... INTRODUCTION The evolution in time of a magnetic field B is determined by an electric field E through the induction equation [4, 8, 12, 14] + r\ThetaE = 0; (1) one of Maxwell's equations. The magnetic field must also satisfy r\DeltaB = 0. This constraint expresses the absence of magnetic mo ..."
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INTRODUCTION The evolution in time of a magnetic field B is determined by an electric field E through the induction equation [4, 8, 12, 14] + r\ThetaE = 0; (1) one of Maxwell's equations. The magnetic field must also satisfy r\DeltaB = 0. This constraint expresses the absence of magnetic monopoles, which have never been observed experimentally. Since (1) implies @ t (r\DeltaB) = 0 this constraint is often treated as an initial condition, which will be preserved under subsequent evolution. The induction equation (1) is combined with the equations of gas dynamics to describe the behaviour of compressible electrically conducting fluids subject to magnetic fields. For nonrelativistic fluids, where Maxwell's displacement current may be neglected, the combined system is referred to as the magnetohydrodynamic (MHD) equations. The compressible ideal (inviscid and perfectly conducting) MHD equations may be written as a hyperbolic system of conservation laws in the form [7, 9, 11] @ 6 6
and
, 2001
"... A free boundary problem for nonlinear magnetohydrodynamics (MHD) with general large initial data is investigated. The existence, uniqueness, and regularity of global solutions are established with large initial data in H 1. It is showed that neither shock waves nor vacuum and concentration in the so ..."
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A free boundary problem for nonlinear magnetohydrodynamics (MHD) with general large initial data is investigated. The existence, uniqueness, and regularity of global solutions are established with large initial data in H 1. It is showed that neither shock waves nor vacuum and concentration in the solutions are developed in a finite time, although there is a complex interaction between the hydrodynamic and magnetodynamic effects. An existence theorem of global solutions with large discontinuous initial data is also established.