Mehdi Vahab
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MATHEMATICS COLLOQUIUM
Speaker: Mehdi Vahab Abstract. The numerical solution for a multiphase/multimaterial system depends on the numerical method for the evolution of interface(s) and the evaluation of geometric information. The adaptation and usage of such information makes it possible to design higher-order numerical methods. Here, we present a hybrid finite volume/level set method to track material discontinuities and capture shocks for two-material hyperbolic systems of conservation laws. Using space-time information from the level set function, high order geometrical information is derived: the face and cell area fractions, and face and cell moments in cut cells. This geometrical approach enables one to calculate high-order flux values. An algebraic method is used to construct a stable flux difference which overcomes the classical cut-cell CFL time step stability constraint. Conservation for mass, momentum, and energy is preserved to machine precision for each material. Convergence studies for smooth solutions, and also solutions containing shocks illustrate the accuracy of the new method. In addition, test results are presented for the classical shock-interface interaction problem in which the Richtmyer-Meshkov instability occurs for suitable parameter regimes. |