TY - JOUR T1 - Simulation of shock-containing flows using a compact finite difference scheme and a weighed essentially non-oscillatory filter TT - شبیه‌سازی جریان‌های شامل شوک با روش تفاضل محدوده فشرده و فیلتر ضرورتاً غیرنوسانی وزن‌دار JF - mdrsjrns JO - mdrsjrns VL - 17 IS - 5 UR - http://mme.modares.ac.ir/article-15-10205-en.html Y1 - 2017 SP - 201 EP - 210 KW - Hybrid filter KW - Shock sensor KW - Shock-capturing schemes KW - Compact finite-difference schemes KW - Weighted essentially non-oscillatory schemes N2 - In the present paper, a hybrid filter is introduced to simultaneously preserve the stability and accuracy and also to eliminate unwanted oscillations in the 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 the fifth-order weighted essentially non-oscillatory scheme. Using a shock-detecting sensor, the hybrid filter reduces to the linear sixth-order filter in smooth regions and to the fifth-order weighted essentially non-oscillatory filter in shock regions in order to eliminate unwanted oscillations produced by the non-dissipative spatial discretization method. The filter performance and accuracy of the results are examined through several test cases including the linear wave equation and one- and two-dimensional Euler equations of gas dynamics. The results are compared by that of a hybrid filter which is composed of the linear sixth-order and the second-order linear filter and that of the fifth-order weighted essentially non-oscillatory scheme. M3 ER -