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Godunov-type methods for the hydrodynamic equations on moving grids. (Godunov-Typ Verfahren für die Gleichungen der Hydrodynamik auf bewegten Gittern.) (German) Zbl 0901.76050

Karlsruhe: Forschungszentrum Karlsruhe, iii, 144 S. (1997).
Summary: The PhD thesis presents Godunov-type schemes for the Euler equations on moving grids. The numerical method is based on a finite-volume approach in the space-time domain. The fluxes are calculated using the approximate solution of Riemann problems. Several Riemann solvers are extended to moving grids, and higher order methods are developed. For application of the method, we concentrate on the simulation of moving material interfaces. We extend the Euler equations by an additional equation to get a regularization of the discontinuous flux function. Then the well-known methods of constructing approximate Riemann solvers can be used even at a material interface. The results of one-dimensional test problems are presented and discussed. Another application is the supersonic shock problem. The results of simulation show the efficiency and robustness of these methods also in two space dimensions.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
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