HIGH-RESOLUTION, NONOSCILLATORY SCHEMES FOR UNSTEADY COMPRESSIBLE FLOWS

High-resolution explicit finite difference nonoscillatory shock-capturing schemes based on Harten's essentially nonoscillatory interpolation using reconstruction via primitive function approach with N = 3 are described for simulating unsteady compressible flows. The extension to nonlinear system is done by using Roe's method, which permits the use of different scalar schemes for different characteristic fields. For multidimensional problems, Strang-type dimensional splitting is adopted. Numerical simulations of unsteady shock diffraction by an elliptic cylinder and shock wave propagating through a convergent-divergent nozzle are included to illustrate the performance of the schemes.