Implementation of a Two-Dimensional Hydrodynamic Shock Code Based Upon the Weighted Average Flux Method

摘要

Numerical modeling of shock propagation and reflection is of interest to the Department of Defense (DoD). Propriety state-of-the-art codes based upon E. F. Toro's weighted average flux (WAF) method are being used to investigate complex shock reflection phenomena. Here we develop, test, and validate a one-dimensional hydrodynamic shock code. We apply WAF to Gudonov's first-order upwind method to achieve second-order accuracy. Oscillations, typical of second- order methods, are then removed using adaptive weight limiter functions based upon total variation diminishing (TVD) flux limiters. An adaptive Riemann solver routine is also implemented to improve computational efficiency. This one- dimensional code is then extended into two dimensions via Warming and Beam's variation on dimensional splitting. The numerical capabilities of the two- dimensional code are demonstrated by modeling the detonation of a cylindrically symmetric explosive with the axis of the cylinder oriented horizontally above an ideal surface.