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- W1668361492 abstract "An approximate Riemann solver needed in a high-order Godunov-type scheme for ideal MHD is developed in this thesis. The Riemann solver consists of the initial guess, the calculation of the two fast shock speeds and post-shock states, the performance of two possible rotations, the calculation of the two slow shock speeds and post-shock states, and the improvement of the initial guess. The Riemann solver includes all the discontinuities in ideal MHD.The extension of the Piecewise Parabolic Method in ideal MHD is presented based on the Riemann solver. The code starts from a set of normal physical variables. A cubic polynomial is used to interpolate each of Riemann invariants. The values of those physical variables at edges of computational zones are obtained through the interpolated Riemann invariants. The monotonicity constraint is applied to those point values of physical variables. A parabola is used for the internal structure of a zone. The set of time-averaged fluxes is calculated by the Riemann solver. The conserved quantities are updated by adding the net flux advected into each zone. After the dynamical step in a Lagrangian grid, the conserved quantities are mapped onto a fixed Eulerian grid. The two-dimensional scheme is built upon the technique of dimension splitting.The scheme is applied to wave steepening, propagation of shocks, various shock tube problems, the penetration of a solar wind filament, and MHD shock interactions with a cloud. The results of these applications show that the scheme has the principal advantages of a Godunov-type scheme, i.e., the robust operation in the presence of very strong discontinuities, thin shock fronts with little attendant noise generation, and thin contact and tangential discontinuities." @default.
- W1668361492 created "2016-06-24" @default.
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- W1668361492 date "1993-01-01" @default.
- W1668361492 modified "2023-09-24" @default.
- W1668361492 title "Numerical simulations for ideal magnetohydrodynamics" @default.
- W1668361492 hasPublicationYear "1993" @default.
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