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Improved Five- and Six-Point Targeted Essentially Nonoscillatory Schemes with Adaptive Dissipation

Lin Fu

Technical University of Munich, 85748 Garching, Germany

*Ph.D., Chair of Aerodynamics and Fluid Mechanics, Department of Mechanical Engineering; .

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Xiangyu Y. Hu

Technical University of Munich, 85748 Garching, Germany

†Adjunct Teaching Professor, Chair of Aerodynamics and Fluid Mechanics, Department of Mechanical Engineering; .

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and

Nikolaus A. Adams

Technical University of Munich, 85748 Garching, Germany

‡Professor, Chair of Aerodynamics and Fluid Mechanics, Department of Mechanical Engineering; .

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Published Online:27 Dec 2018https://doi.org/10.2514/1.J057370

Abstract

This Paper proposes an improvement of the five- and six-point targeted essentially nonoscillatory (TENO5 and TENO6) schemes by introducing an adaptive dissipation-control strategy. Nonlinear numerical dissipation is controlled by dynamically adjusting the cutoff parameter in the TENO weighting strategy according to the first-order smoothness measure of the local flow scales. For the five-point reconstruction, the dissipation bandwidth of the underlying linear scheme is delayed by introducing slight antidissipation at low wave numbers with small dispersion errors. A new sixth-order scale-separation parameter $τ_{5}$ is derived, and the modified TENO5-A scheme is third-order accurate. For the six-point reconstruction, the dispersion and dissipation errors are optimized separately, resulting in a modified fourth-order TENO6-A scheme. All necessary parameters are determined by spectral analyses and are shown to be problem independent by numerical experiments. A set of benchmark cases, including highly compressible gas dynamics and nearly incompressible and compressible turbulence decay, is considered. Numerical experiments demonstrate that both the proposed TENO5-A and TENO6-A schemes show excellent performance for shocks and broadband turbulence. The turbulence statistics obtained with TENO6-A at coarse resolution are comparable to those from the state-of-the-art implicit large-eddy simulation model and agree well with direct numerical simulation data.

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Volume 57, Number 3March 2019

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Acknowledgments

The first author is partially supported by China Scholarship Council (grant number 201206290022). The second author is partially supported by National Natural Science Foundation of China (grant number 11628206).

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Received19 April 2018
Accepted31 October 2018
Published online27 December 2018

Improved Five- and Six-Point Targeted Essentially Nonoscillatory Schemes with Adaptive Dissipation

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