High‐order shock capturing schemes for turbulence calculations

Abstract

This work investigates high‐order central compact methods for simulating turbulent supersonic flows that include shock waves. Several different types of previously proposed characteristic filters, including total variation diminishing, monotone upstream‐centered scheme for conservation laws, and weighted essentially non‐oscillatory filters, are investigated in this study. Similar to the traditional shock capturing schemes, these filters can eliminate the numerical instability caused by large gradients in flow fields, but they also improve efficiency compared with classical shock‐capturing schemes. Adding the nonlinear dissipation part of a classical shock‐capturing scheme to a central scheme makes the method suitable for incorporation into any existing central‐based high‐order subsonic code. The amount of numerical dissipation to add is sensed by means of the artificial compression method switch. In order to improve the performance of the characteristic filters, we propose a hybrid approach to minimize the dissipation added by the characteristic filter. Through several numerical experiments (including a shock/density wave interaction, a shock/vortex interaction, and a shock/mixing layer interaction) we show that our hybrid approach works better than the original method, and can be used for future turbulent flow simulations that include shocks. Copyright © 2009 John Wiley & Sons, Ltd.

A massively parallel multi-block hybrid compact–WENO scheme for compressible flows

“…Minor differences are restricted to the immediate vicinity of the straight part of the shock wave at t ¼ 0:2. The pressure extrema listed in the captions are very similar to those reported by [13] using a characteristic filtering method on a single block. The pressure variation through the vortex center at t ¼ 0:35 is plotted in Fig.…”

Numerical dissipation control in high order shock-capturing schemes for LES of low speed flows

“…For a variety of local flow sensors with automatic selection of the proper parameter, depending on different flow type, see [1]. The form of Tauber-Sandham [10] for the filter numerical flux uses the Ducros et al flow sensor as κ l j+1/2 and the Harten artificial compression method formula (ACM) as the flow sensor indicated in [4] and similarly in [11] are part of the Yee & Sjögreen adaptive numerical dissipation control generalization filter formulae. For the numerical experiments presented, we mainly concentrate on the wavelet flow sensor of Yee & Sjögreen, the Ducros et al flow sensor [16] and the artificial compression method flow sensor of [4].…”

“…See, for example, [1][2][3][4][5][6][7][8][9][10][11]. Also see examples of recently developed implicit LES (ILES) methods and comparison of the performance of different numerical schemes (mostly are second to fifth orders) in [12][13][14][15].…”

A shock-capturing methodology based on adaptative spatial filtering for high-order non-linear computations

“…One crucial point in the methodology is the definition of the shock detector, which has to distinguish between shocks and gradients of any other kind in order to limit the range of the shock-capturing dissipation specifically to the regions containing shocks [39]. Detectors estimated from simple gradients [28,30], from second derivatives of pressure or density [32,[36][37][38] such as the Jameson detector, and from WENO-type smoothness criteria [31,40] have in particular been used. Ducros et al [41] also proposed a modified version of the Jameson detector taking into account the local property of compressibility, which is capable of discriminating between turbulent fluctuations and shocks [40,42].…”

“…Detectors estimated from simple gradients [28,30], from second derivatives of pressure or density [32,[36][37][38] such as the Jameson detector, and from WENO-type smoothness criteria [31,40] have in particular been used. Ducros et al [41] also proposed a modified version of the Jameson detector taking into account the local property of compressibility, which is capable of discriminating between turbulent fluctuations and shocks [40,42]. Finally, once the shock-detection sensor is evaluated, the shock region is dealt with by means of a switch which has to specify the type and amount of dissipation to be specified at each grid point.…”