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Study of the effects of artificial dissipation and other numerical parameters on shock wave resolution

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Abstract

The effects induced by numerical schemes and mesh geometry on the solution of two-dimensional supersonic inviscid flows are investigated in the context of the compressible Euler equations. Five different finite difference schemes are considered: the Beam and Warming implicit approximate factorization algorithm, the original Steger and Warming flux vector splitting algorithm, the van Leer approach on performing the flux vector splitting and two different novel finite difference interpretations of the Liou AUSM\(^+\) scheme. Special focus is given to the shock wave resolution capabilities of each scheme for the solution of an external supersonic inviscid flows around a blunt body. Significant changes in the shock structure are observed, mainly due to special properties of the scheme in use and the influence of the domain transformation procedure. Perturbations in the supersonic flow upstream of the shock are also seen in the solution, which is a non-physical behavior. Freestream subtraction, flux limiting and the explicit addition of artificial dissipation are employed in order to circumvent these problems. One of the AUSM\(^+\) formulations presented here is seen to be particularly more robust in avoiding the appearance of some of these numerically induced disturbances and non-physical characteristics in the solution. Good agreement is achieved with both numerical and experimental results available in the literature.

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Acknowledgements

The authors wish to express their gratitude to the São Paulo Research Foundation, FAPESP, which has supported the present research under the Research Grants No. 2013/07375-0 and No. 2021/00147-8. The authors also gratefully acknowledge the support for the present research provided by Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq, under the Research Grant No. 309985/2013-7.

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Authors and Affiliations

  1. Instituto Tecnológico de Aeronáutica, São José dos Campos, 12228-900, São Paulo, Brazil

    Frederico Bolsoni Oliveira

  2. Instituto de Aeronáutica e Espaço, São José dos Campos, 12228-904, São Paulo, Brazil

    João Luiz F. Azevedo

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  1. Frederico Bolsoni Oliveira
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  2. João Luiz F. Azevedo
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Correspondence to Frederico Bolsoni Oliveira.

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Oliveira, F.B., Azevedo, J.L.F. Study of the effects of artificial dissipation and other numerical parameters on shock wave resolution. J Braz. Soc. Mech. Sci. Eng. 46, 51 (2024). https://doi.org/10.1007/s40430-023-04617-9

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