Numerical experiments on a hybrid WENO5 filter for shock‐capturing

Abstract

In the present paper, a hybrid filter is introduced for high accurate numerical simulation of shock-containing flows. The fourth-order compact finite difference scheme is used for the spatial discretization and the third-order Runge-Kutta scheme is used for the time integration. After each time-step, the hybrid filter is applied on the results. The filter is composed of a linear sixth-order filter and the dissipative part of a fifth-order weighted essentially nonoscillatory scheme (WENO5). The classic WENO5 scheme and the WENO5 scheme with adaptive order (WENO5-AO) are used to form the hybrid filter. Using a shock-detecting sensor, the hybrid filter reduces to the linear sixth-order filter in smooth regions for damping high frequency waves and reduces to the WENO5 filter at shocks in order to eliminate unwanted oscillations produced by the nondissipative spatial discretization method. The filter performance and accuracy of the results are examined through several test cases including the advection, Euler and Navier-Stokes equations. The results are compared with that of a hybrid second-order filter and also that of the WENO5 and WENO5-AO schemes. KEYWORDS compact finite-difference schemes, high-order methods, hybrid filter, shock sensor, shock-capturing schemes, weighted essentially nonoscillatory schemes Numer Methods Partial Differential Eq. 2019;35:2375-2406. wileyonlinelibrary.com/journal/num