Shock stability of a novel flux splitting scheme

Weiping Wei; Youlin Shang; Hongwei Jiao; Pujun Jia; Weiping Wei; Youlin Shang; Hongwei Jiao; Pujun Jia

doi:10.3934/math.2024364

AIMS Mathematics

2024, Volume 9, Issue 3: 7511-7528. doi: 10.3934/math.2024364

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Research article

Shock stability of a novel flux splitting scheme

1.
College of Information Engineering, Henan University of Science and Technology, Luoyang 471023, China
2.
School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China
3.
School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China

Received: 19 October 2023 Revised: 24 January 2024 Accepted: 05 February 2024 Published: 21 February 2024
MSC : 58J45, 76J20

This article introduced the HLL-CPS-T flux splitting scheme, which is characterized by low dissipation and robustness. A detailed theoretical analysis of the dissipation and shock stability of this scheme was provided. In comparison to Toro's TV flux splitting scheme, the HLL-CPS-T scheme not only exhibits accurate capture of contact discontinuity, but also demonstrates superior shock stability, as evidenced by its absence of 'carbuncle' phenomenon. Through an examination of the disturbance attenuation properties of physical quantities in the TV and HLL-CPS-T schemes, an inference was derived: The shock stability condition for an upwind method in the velocity perturbation was damped. Theoretical analysis was given to verify the reasonableness of this inference. Numerical experiments were carefully selected to test the robustness of the new splitting scheme.
- low dissipation,
- flux splitting scheme,
- shock stability,
- upwind method
Citation: Weiping Wei, Youlin Shang, Hongwei Jiao, Pujun Jia. Shock stability of a novel flux splitting scheme[J]. AIMS Mathematics, 2024, 9(3): 7511-7528. doi: 10.3934/math.2024364

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Abstract

This article introduced the HLL-CPS-T flux splitting scheme, which is characterized by low dissipation and robustness. A detailed theoretical analysis of the dissipation and shock stability of this scheme was provided. In comparison to Toro's TV flux splitting scheme, the HLL-CPS-T scheme not only exhibits accurate capture of contact discontinuity, but also demonstrates superior shock stability, as evidenced by its absence of 'carbuncle' phenomenon. Through an examination of the disturbance attenuation properties of physical quantities in the TV and HLL-CPS-T schemes, an inference was derived: The shock stability condition for an upwind method in the velocity perturbation was damped. Theoretical analysis was given to verify the reasonableness of this inference. Numerical experiments were carefully selected to test the robustness of the new splitting scheme.

References

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