An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Flux-corrected transport techniques for multidimensional compressible magnetohydrodynamics
Journal of Computational Physics
A higher-order Godunov method for multidimensional ideal magnetohydrodynamics
SIAM Journal on Scientific Computing
An approximate Riemann solver for ideal magnetohydrodynamics
Journal of Computational Physics
A simple finite difference scheme for multidimensional magnetohydrodynamical equations
Journal of Computational Physics
Journal of Computational Physics
A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
A solution-adaptive upwind scheme for ideal magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
Hyperbolic divergence cleaning for the MHD equations
Journal of Computational Physics
On the use of higher-order finite-difference schemes on curvilinear and deforming meshes
Journal of Computational Physics
Journal of Computational Physics
A high-wavenumber viscosity for high-resolution numerical methods
Journal of Computational Physics
Short Note: Hyperviscosity for shock-turbulence interactions
Journal of Computational Physics
An unsplit, cell-centered Godunov method for ideal MHD
Journal of Computational Physics
An unsplit Godunov method for ideal MHD via constrained transport
Journal of Computational Physics
A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics
Journal of Computational Physics
An unsplit Godunov method for ideal MHD via constrained transport in three dimensions
Journal of Computational Physics
Localized artificial diffusivity scheme for discontinuity capturing on curvilinear meshes
Journal of Computational Physics
An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics
Journal of Computational Physics
Suitability of artificial bulk viscosity for large-eddy simulation of turbulent flows with shocks
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
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This paper proposes a new strategy that is very simple, divergence-free, high-order accurate, yet has an effective discontinuous-capturing capability for simulating compressible magnetohydrodynamics (MHD). The new strategy is to construct artificial diffusion terms in a physically-consistent manner, such that the artificial terms act as a diffusion term only in the curl of magnetic field to capture numerical discontinuities in the magnetic field while not affecting the divergence field (thus maintaining divergence-free constraint). The physically-consistent artificial diffusion terms are built into the induction equations in a conservation law form at a partial-differential-equation level. The proposed method may be viewed as adding an artificial magnetic resistivity to the induction equations, and is inherently divergence-free both ideal and resistive MHD, with and without shock waves, and also both inviscid and viscous flows. The method is based on finite difference method with co-located variable arrangement, and we show that any linear finite difference scheme in an arbitrary order of accuracy can be used to discretize the modified governing equations to ensures the divergence-free and the global conservation constraints numerically at the discretization level. The artificial magnetic resistivity is designed to localize automatically in regions of discontinuity in the curl of magnetic field and vanish wherever the flow is sufficiently smooth with respect to the grid scale, thereby maintaining the desirable high-order accuracy of the employed discretization scheme in smooth regions. Two-dimensional smooth and non-smooth ideal MHD problems are considered to validate the capability of the proposed method.