Received: 19 December 2018 Revised: 6 June 2019 Accepted: 23 July 2019 DOI: 10.1002/num.22419 RESEARCH ARTICLE Numerical experiments on a hybrid WENO5 filter for shock-capturing Hossein Mahmoodi Darian 1 Reza Bozorgpour 2 Maziar Shafaee 2 1 School of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran 2 Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran Correspondence Maziar Shafaee, Faculty of New Sciences and Technologies, University of Tehran, North Karegar Street, Tehran, Iran. Email: mshafaee@ut.ac.ir Funding information University of Tehran. 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 com- posed 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 pro- duced 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;1–32. wileyonlinelibrary.com/journal/num © 2019 Wiley Periodicals, Inc. 1