On Solving the MHD Problem for Several Classes of Three-Dimensional Domains Within the Framework of Discrete Potential Theory

Inna Eduardovna Stepanova (), Igor Ivanovich Kolotov and Alexey Valerijevich Shchepetilov
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Inna Eduardovna Stepanova: Scmidt Institute of Physics of the Earth, Russian Academy of Sciences, 123995 Moscow, Russia
Igor Ivanovich Kolotov: Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
Alexey Valerijevich Shchepetilov: Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia

Mathematics, 2025, vol. 13, issue 23, 1-18

Abstract: The MHD (magnetic hydrodynamics) boundary problem in three-dimensional domains of certain types is considered within the framework of discrete potential theory. The discrete character of the information obtained from remote sensing of the Earth and planets of the Solar System can be taken into account when using the basic principles of this theory. This approach makes it possible to reconstruct the spatial distribution of magnetic fields and the velocity field with relatively high accuracy using the heterogeneous data in some network points. In order to restore the magnetic image of a planet with a so-called dynamo, the subsequent approximations approach is implemented. The unknown physical field is represented as a sum of terms of different magnitudes. Such an approach allows us to simplify the nonlinear partial differential equation system of magnetic hydrodynamics and extend it to discrete magnetic field and velocity vectors. The solution of the simplified MHD equation system is constructed for some classes of bounded domains in Cartesian coordinates in three-dimensional space.

Keywords: uniqueness; magnetic hydrodynamics; discrete potential; m-tuply connected domains (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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