Geodesic
Implementation of the iterative algorithm for numerical solution of 2D magnetogasdynamics problems
Matematičeskoe modelirovanie, Tome 32 (2020) no. 1, pp. 50-70

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We study an algorithm of making a numerical solution to the equations of magnetic gas dynamics (MHD), approximated by a completely conservative Eulerian-Lagrangian difference scheme (PCRS). The governing system describing a high-temperature matter dynamics is solved taking into account the conductive (electron, ion) and radiative heat transfer. The scheme is implicit for the calculations related to the “Lagrangian” moving grid, and the corresponding difference equations are solved by an iterative method with a consistent account of physical processes. We consider various combinations of difference equations grouped according to physical processes. The convergence criteria for the studied iteration process are obtained and validated through numerical experiments with model and application problems.
Keywords: magnetic gas dynamics, plasma dynamics, Z-pinch, implicit completely conservative difference scheme, iterative method. 
@article{MM_2020_32_1_a3,
     author = {A. Yu. Krukovskiy and V. A. Gasilov and Yu. A. Poveschenko and Yu. S. Sharova and L. V. Klochkova},
     title = {Implementation of the iterative algorithm for numerical solution of {2D} magnetogasdynamics problems},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {50--70},
     publisher = {mathdoc},
     volume = {32},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2020_32_1_a3/}
}
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A. Yu. Krukovskiy; V. A. Gasilov; Yu. A. Poveschenko; Yu. S. Sharova; L. V. Klochkova. Implementation of the iterative algorithm for numerical solution of 2D magnetogasdynamics problems. Matematičeskoe modelirovanie, Tome 32 (2020) no. 1, pp. 50-70. http://geodesic.mathdoc.fr/item/MM_2020_32_1_a3/