Skew-symmetric splitting of high-order central schemes with nonlinear filters for computational aeroacoustics turbulence with shocks

Authors

Bjorn Sjögreen, Multid Analyses ABFollow
Helen C. Yee, NASA Ames Research CellterFollow
Alan A. Wray, NASA Ames Research CenterFollow

Date of this Version

2019

Citation

ShockWaves (2019) 29:1117–1132

https://doi.org/10.1007/s00193-019-00925-z

Comments

U.S. government work

Abstract

A class of high-order nonlinear filter schemes by Yee et al. (J Comput Phys 150:199–238, 1999), Sjögreen and Yee (J Comput Phys 225:910–934, 2007), and Kotov et al. (Commun Comput Phys 19:273–300, 2016; J Comput Phys 307:189–202, 2016) is examined for long-time integrations of computational aeroacoustics (CAA) turbulence applications. This class of schemes was designed for an improved nonlinear stability and accuracy for long-time integration of compressible direct numerical simulation and large eddy simulation computations for both shock-free turbulence and turbulence with shocks. They are based on the skew-symmetric splitting version of the high-order central base scheme in conjunction with adaptive low-dissipation control via a nonlinear filter step to help with stability and accuracy capturing at shock-free regions as well as in the vicinity of discontinuities. The central dispersion-relation-preserving schemes as well as classical central schemes of arbitrary orders fit into the framework of skew-symmetric splitting of the inviscid flux derivatives. Numerical experiments on CAA turbulence test cases are validated.