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De-Kang Mao

2012-10-17
15:00:00 - 17:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk I am going to introduce a conservative front- tracking method for the 2D Euler system developed in [D. K. Mao, Towards front-tracking based on conservation in two space dimensions II, tracking discontinuities in capturing fashion, J. Comput. Phys., 226, 1550-1588(2007)] and [D. K. Mao, Towards front tracking based on conservation in two space dimensions, SIAM. J. Sci. Comput., 22, 113-151(2000)] and references cited therein. In the method, the movement of material interfaces is locally described by 1D PDE's derived from the Euler system, and the tracking is realized by locally discretizing these 1D PDE's in a conservative fashion. The method is thus conservative, and is good in preserving physical structures of the tracked material interfaces. A numerical surface dissipation is designed in the tracking, which stabilizes the tracked interfaces and eliminates the numerical artifacts usually caused by numerical dissipation observed in many other methods. Numerical simulation of two shock-bubble interactions described in [J. F. Hass & B. Sturtevant, Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities, J. Fluid Mech., 181, 41-76(1987)] is presented to show the efficiency and effectiveness of the method.