A modified multidimensional dissipation technique for AUSM⁺ on triangular grids

Abstract

The carbuncle phenomenon normally occurs numerically in the prediction of shock waves in flow computation. Most efforts to remedy this problem concern numerical treatment of the bow shock wave while many evidences declare that the carbuncle phenomenon problem may be unsolvable. This paper studies the numerical instability of the AUSM⁺ scheme on two-dimensional structured triangular grids. By examining several test cases, it is found that the scheme cannot satisfy robustness against shock-induced anomalies. A more stable version of the AUSM⁺ scheme (so-called AUSM^+δ scheme) is developed by applying the multidimensional dissipation technique to the numerical dissipation term in order to alleviate the shock instability. The dissipation mechanism against perturbations is investigated by applying a linearised discrete analysis to the odd--even decoupling problem. The recursive equations show that the AUSM^+δ scheme is less sensitive to such anomalies than the original scheme. Finally, the scheme is further extended to achieve the second-order solution accuracy and evaluated by solving several test cases.

Keywords:

• AUSM⁺ scheme
• carbuncle phenomenon
• finite volume method
• numerical instability
• shock-capturing method

Acknowledgements

The author is grateful to the Department of Mechanical Engineering Technology, College of Industrial Technology, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand for supporting this research work.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

The author is pleased to acknowledge the College of Industrial Technology, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand for funding this research work.