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

Document Type

Article

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.