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Numerical simulation of points of shock wave interaction by a locally inertial Godunov Method with dynamic time dilation.

PDE and Applied Math Seminar

Speaker: Zeke Vogler, UC-Davis
Location: 1147 MSB
Start time: Tue, Feb 28 2012, 4:10PM

We introduce a locally inertial Godunov method with dynamical time dilation, and use it to simulate a one parameter family of initial data obtained by matching a critically expanding Friedmann-Robertson-Walker (FRW) spacetime Lipschitz continuously to the inside of a static Tolmann-Oppenheimer-Volkoff (TOV) solution, creating a point of shock wave interaction at the interface. The forward time solution generates a point of shock wave interaction and resolves the secondary reflected wave (an incoming shock wave) in a simple model for an explosion into a static singular isothermal sphere. The backward time solutions indicate black hole formation from a smooth underlying solution via collapse associated with an incoming rarefaction wave. This is a definitive numerical demonstration that the locally inertial Godunov method is a viable first order numerical method for simulating shock waves in Standard Schwarzschild Coordinates.