Application of bandwidth-optimized WENO schemes to DNS of shock–turbulence interaction problems

Abstract

High-order bandwidth-optimized weighted essentially non-oscillatory (WENO) schemes with limiters are applied in this study to a wide variety of problems. A comparison of the performance of these schemes with three-point and four-point stencils is shown for one-dimensional and two-dimensional test problems. For the one-dimensional and two-dimensional test cases, these schemes show their advantage over the standard fifth-order and the seventh-order WENO schemes proposed in the literature in capturing the small-scale structures appearing in these flows. Effects of the limiter threshold values are discussed for the bandwidth-optimized WENO schemes. Further, the bandwidth-optimized WENO schemes with limiters are compared with other variants of the WENO scheme found in the literature. Direct numerical simulation of supersonic channel flow is also performed with the bandwidth-optimized WENO scheme (with three-point stencil) with limiter, and the results are found to be in good agreement with the literature. This scheme is then used for performing DNS of shock train in a turbulent channel flow. KeywordsDNS • Bandwidth-optimized WENO scheme • Compressible channel flow • Shock train Abbreviations LES Large eddy simulation DNS Direct numerical simulation WENO3P-LIM-'P' Bandwidth-optimized third-order weighted essentially non-oscillatory (WENO) scheme with relative total variation limiter [1,2]. 'P' is the numerical threshold value of limiter. Candidate stencil has three points. Set of candidate stencils is symmetric at the interface. Total number of points used for the flux reconstruction at the interface is 6 WENO4P-LIM-'P' Bandwidth-optimized fourth-order WENO scheme with relative total variation limiter [1,2]. 'P' is the numerical threshold value of limiter. Candidate stencil has four points. Set of candidate Communicated by D. Zeidan.