Two dimensional analysis and optimization of hybrid MDCD-TENO schemes

Tan, Raynold and Ooi, Andrew (2021) Two dimensional analysis and optimization of hybrid MDCD-TENO schemes. Journal of Scientific Computing, 90 (1), [64]. (doi:10.1007/s10915-021-01743-1).

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Abstract

In this article, a quasi-linear semi-discrete analysis of shock capturing schemes in two dimensional wavenumber space is proposed. Using the dispersion relation of the two dimensional advection and linearized Euler equations, the spectral properties of a spatial scheme can be quantified in two dimensional wavenumber space. A hybrid scheme ( HYB - MDCD - TENO6 ) which combines the merits of the Minimum Dispersion and Controllable Dissipation ( MDCD ) scheme with the Targeted Essentially Non-Oscillatory ( TENO ) scheme was developed and tested. Using the two dimensional analysis framework, the scheme was spectrally optimized in such a way that the linear part of the scheme can be separately optimized for its dispersion and dissipation properties. In order to compare its performance against existing schemes,
the proposed scheme as well as the baseline schemes were tested against a series of benchmark test cases. It was found that the HYB - MDCD - TENO6 scheme provides similar or better resolution as compared to the baseline TENO6 schemes for the same grid size.

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JOMP_D_21_00184_R3 - Accepted Manuscript

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Accepted/In Press date: 5 December 2021

Published date: 29 December 2021

Additional Information: Funding Information: The authors would like to thank the University of Melbourne for funding this research. The authors would also like to acknowledge the technical advice provided by Dr. Jun Peng from the Institute of Mechanics, Chinese Academy of Science during the preparation of this article. Funding Information: The authors would like to thank the University of Melbourne for funding this research. The authors would also like to acknowledge the technical advice provided by Dr. Jun Peng from the Institute of Mechanics, Chinese Academy of Science during the preparation of this article. Publisher Copyright: © 2021, The Author(s).

Keywords: Computational gas dynamics, Non-linear spectral analysis, Shock capturing finite difference, WENO/TENO schemes