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Tang, Huazhong; Xu, Kun

doi:10.1023/a:1007593601466

Cited by 14 publications

(1 citation statement)

References 11 publications

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“…In the study of non-conducting fluids, for example such described by the compressible Euler equations, entropy principles, and positivity preserving properties have been studied for many schemes. Those include Godunov scheme [9], Lax scheme [22], and its variants, see e.g., [28,34,32]. Positivity preserving properties often refer to the fact that density, internal energy, or pressure of the solution should maintain positive as it evolves in time.…”

Section: Introductionmentioning

confidence: 99%

Monolithic parabolic regularization of the MHD equations and entropy principles

Dao,

Nazarov

2022

Preprint

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We show at the PDE level that the monolithic parabolic regularization of the equations of ideal magnetohydrodynamics (MHD) is compatible with all the generalized entropies, fulfills the minimum entropy principle, and preserves the positivity of density and internal energy. We then numerically investigate this regularization for the MHD equations using continuous finite elements in space and explicit strong stability preserving Runge-Kuta methods in time. The artificial viscosity coefficient of the regularization term is constructed to be proportional to the entropy residual of MHD. It is shown that the method has a high order of accuracy for smooth problems and captures strong shocks and discontinuities accurately for non-smooth problems.

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Section: Introductionmentioning

confidence: 99%

Monolithic parabolic regularization of the MHD equations and entropy principles

Dao,

Nazarov

2022

Preprint

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Generalized Lax-Friedrichs Schemes for Linear Advection Equation with Damping

Jiang

Wei

2011

Information Computing and Applications

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Entropy solutions of the compressible Euler equations

Svärd

2016

Bit Numer Math

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Abstract. We consider the three-dimensional Euler equations of gas dynamics on a bounded periodic domain and a bounded time interval. We prove that Lax-Friedrichs scheme can be used to produce a sequence of solutions with ever finer resolution for any appropriately bounded (but not necessarily small) initial data. Furthermore, we show that if the density remains strictly positive in the sequence of solutions at hand, a subsequence converges to an entropy solution. We provide numerical evidence for these results by computing a sensitive Kelvin-Helmholtz problem.

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Untitled

Cited by 14 publications

References 11 publications

Monolithic parabolic regularization of the MHD equations and entropy principles

Monolithic parabolic regularization of the MHD equations and entropy principles

Generalized Lax-Friedrichs Schemes for Linear Advection Equation with Damping

Entropy solutions of the compressible Euler equations

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