Adaptive Mesh Computation of Magnetic Hydrodynamic Equilibrium

L.M. Degtyarev and V.V. Drozdov
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L.M. Degtyarev: Keldysh Institute of Applied Mathematics, USSR Academy of Sciences, Russia
V.V. Drozdov: Keldysh Institute of Applied Mathematics, USSR Academy of Sciences, Russia

International Journal of Modern Physics C (IJMPC), 1991, vol. 02, issue 01, 30-38

Abstract: In stationary problems of mathematical physics an error of the finite-difference method||z||=||u−uh||is determined by the number of grid nodesNso that asN→∞, asymptotically$\left\| z \right\| = C\left( {\frac{1}{N}} \right)^m .$The accuracy order m depends on the approximation of an original differential problem by a difference problem, while the constantCdepends on the solution derivatives and the grid stephdistribution. The value of||z||may be decreased by redistributing the grid points. An optimal computational grid is determined by both the region in which the original differential problem is solved and by the solution structure. Such technique will be called the method of grids adaptive to the solution.In this paper the ideology of the method of adaptive grids is presented for one-dimensional problems. A presentation of the method for two-dimensional MHD equilibrium problems is given. The main points of the method for three-dimensional MHD problems is discussed.

Date: 1991
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DOI: 10.1142/S0129183191000056

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