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physics.flu-dyn2023★ 2 cited
Invariant Finite-Difference Schemes for Cylindrical One-Dimensional MHD Flows with Conservation Laws Preservation
E. I. Kaptsov, V. A. Dorodnitsyn, S. V. Meleshko
On the basis of the recent group classification of the one-dimensional magnetohydrodynamics (MHD) equations in cylindrical geometry, the construction of symmetry-preserving finite-…
physics.flu-dyn2022★ 3 cited
Symmetries and conservation laws of the one-dimensional shallow water magnetohydrodynamics equations in Lagrangian coordinates
S. V. Meleshko, V. A. Dorodnitsyn, E. I. Kaptsov
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 an…