A space–time CESE scheme for shallow water magnetohydrodynamics equations with variable bottom topography

Saleem, M.; Zia, Saqib; Qamar, Shamsul

doi:10.1007/s40430-016-0678-4

Cited by 3 publications

(2 citation statements)

References 34 publications

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“…The consideration of the shallow water equations in the presence of a magnetic field (SMHD) is a relatively new area of magnetohydrodynamics. One of the first models to describe SMHD was presented in [1] (the Gilman model), and since then, many papers by various authors have been devoted to studying this model, including its stability [2], numerical simulation [3][4][5][6][7][8], and conservation laws [9,10] (see, for example, a more detailed review in [9]).…”

Section: Introductionmentioning

confidence: 99%

Invariant conservative finite-difference schemes for the one-dimensional shallow water magnetohydrodynamics equations in Lagrangian coordinates

Kaptsov,

Dorodnitsyn

2024

Open Communications in Nonlinear Mathematical Physics

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Invariant finite-difference schemes for the one-dimensional shallow water equations in the presence of a magnetic field for various bottom topographies are constructed. Based on the results of the group classification recently carried out by the authors, finite-difference analogues of the conservation laws of the original differential model are obtained. Some typical problems are considered numerically, for which a comparison is made between the cases of a magnetic field presence and when it is absent (the standard shallow water model). The invariance of difference schemes in Lagrangian coordinates and the energy preservation on the obtained numerical solutions are also discussed.

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Section: Introductionmentioning

confidence: 99%

Invariant conservative finite-difference schemes for the one-dimensional shallow water magnetohydrodynamics equations in Lagrangian coordinates

Kaptsov,

Dorodnitsyn

2024

Open Communications in Nonlinear Mathematical Physics

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show abstract

“…The consideration of the shallow water equations in the presence of a magnetic field (SMHD) is a relatively new area of magnetohydrodynamics. One of the first models to describe SMHD was presented in [1] (the Gilman model), and since then, many papers by various authors have been devoted to studying this model, including its stability [2], numerical simulation [3][4][5][6][7], and conservation laws [8,9] (see, for example, a more detailed review in [8]).…”

Section: Introductionmentioning

confidence: 99%

Conservative invariant finite‐difference schemes for the modified shallow water equations in Lagrangian coordinates

2022

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The one-dimensional modified shallow water equations in Lagrangian coordinates are considered.Relations between symmetries and conservation laws in Lagrangian coordinates, in mass Lagrangian variables and Eulerian coordinates are discussed. For equations in Lagrangian coordinates, invariant finite-difference schemes are constructed. These schemes admit all conservation laws, which are related to Lie symmetries admitted by the differential model via Noether's theorem: they possess the difference analogs of the conservation laws of mass, momentum, energy, the law of center-of-mass motion for horizontal, inclined, and parabolic bottom topographies. The invariant conservative difference schemes are tested numerically in comparison with an ad hoc approximation-invariant scheme.

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Numerical simulation of sediment deposition and trapping efficiency estimation in settling basins, considering secondary flows

Lakzian

Saghi

Kooshki

2020

International Journal of Sediment Research

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A space–time CESE scheme for shallow water magnetohydrodynamics equations with variable bottom topography

Cited by 3 publications

References 34 publications

Invariant conservative finite-difference schemes for the one-dimensional shallow water magnetohydrodynamics equations in Lagrangian coordinates

Invariant conservative finite-difference schemes for the one-dimensional shallow water magnetohydrodynamics equations in Lagrangian coordinates

Conservative invariant finite‐difference schemes for the modified shallow water equations in Lagrangian coordinates

Numerical simulation of sediment deposition and trapping efficiency estimation in settling basins, considering secondary flows

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