High-order accurate entropy stable finite difference schemes for the shallow water magnetohydrodynamics

Duan, Junming; Tang, Huazhong

doi:10.1016/j.jcp.2021.110136

Cited by 26 publications

(11 citation statements)

References 54 publications

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“…One-dimensional numerical schemes capable to do this exist (Zeitlin et al 2015;Bouchut & Lhebrard 2016, but 2-D schemes appeared only recently, cf. Duang & Tang (2021) and references therein. However, they lack rotation and are not sufficiently well tested.…”

Section: Discussionmentioning

confidence: 99%

Coherent magnetic modon solutions in quasi-geostrophic shallow water magnetohydrodynamics

Lahaye

Zeitlin

2022

J. Fluid Mech.

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A class of exact solutions of the magnetohydrodynamic quasi-geostrophic equations (MQG), which result from rotating shallow water magnetohydrodynamics in the limit of small Rossby and magnetic Rossby numbers is constructed analytically. These solutions are magnetic modons, steady-moving dipolar vortices, which are generalizations of the well-known quasi-geostrophic modons. It is shown that various configurations of magnetic modons are possible: with or without external magnetic field, and with or without internal magnetic field trapped inside the dipole. By using the modon solutions as initial conditions for direct numerical simulations of the MQG equations, it is shown that they remain coherent for a long time, running over about a hundred deformation radii without change of form, provided the external and internal magnetic fields are not too strong, and even if a small-amplitude noise is added to initial conditions.

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Section: Discussionmentioning

confidence: 99%

Coherent magnetic modon solutions in quasi-geostrophic shallow water magnetohydrodynamics

Lahaye

Zeitlin

2022

J. Fluid Mech.

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“…Based on the model [1], a large number of numerical discretizations have been constructed [9][10][11][12], including discretizations for the case of non-flat bottom topography.…”

Section: Introductionmentioning

confidence: 99%

Symmetries and conservation laws of the one-dimensional shallow water magnetohydrodynamics equations in Lagrangian coordinates

Капцов¹,

Meleshko²,

Дородницын³

2022

J. Phys. A: Math. Theor.

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Symmetries of the one-dimensional shallow water magnetohydrodynamics equations (SMHD) in Gilman's approximation are studied. The SMHD equations are considered in case of a plane and uneven bottom topography in Lagrangian and Eulerian coordinates. Symmetry classification separates out all bottom topographies which yields substantially different admitted symmetries. The SMHD equations in Lagrangian coordinates were reduced to a single second order PDE. The Lagrangian formalism and Noether's theorem are used to construct conservation laws of the SMHD equations. Some new conservation laws for various bottom topographies are obtained. The results are also represented in Eulerian coordinates. Invariant and partially invariant solutions are constructed.

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“…In [21], authors have presented a framework for entropy stable DG schemes based on the SBP property. This framework has been applied to various hyperbolic systems in [15,26,47].…”

Section: Introductionmentioning

confidence: 99%

Entropy stable discontinuous Galerkin schemes for the special relativistic hydrodynamics equations

Biswas

Kumar

Bhoriya

2022

Computers & Mathematics with Applications

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High-order accurate entropy stable finite difference schemes for the shallow water magnetohydrodynamics

Cited by 26 publications

References 54 publications

Coherent magnetic modon solutions in quasi-geostrophic shallow water magnetohydrodynamics

Coherent magnetic modon solutions in quasi-geostrophic shallow water magnetohydrodynamics

Symmetries and conservation laws of the one-dimensional shallow water magnetohydrodynamics equations in Lagrangian coordinates

Entropy stable discontinuous Galerkin schemes for the special relativistic hydrodynamics equations

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