Cures for expansion shock and shock instability of Roe scheme based on momentum interpolation mechanism

doi:10.1007/s10483-017-2283-8

Abstract

Abstract:

The common defects of the Roe scheme are the non-physical expansion shock and shock instability. By removing the momentum interpolation mechanism (MIM), an improved method with several advantages has been presented to suppress the shock instability. However, it cannot prevent the expansion shock and is incompatible with the traditional curing method for expansion shock. To solve the problem, the traditional curing mechanism is analyzed. Effectiveness of the traditional curing method is discussed, and several defects are identified, one of which leads to incompatibility between curing shock instability and expansion shock. Consequently, an improved Roe scheme is proposed, which is with low computational costs, concise, easy to implement, and robust. More importantly, the proposed scheme can simultaneously solve the problem of shock instability and expansion shock without additional costs.

Key words: three-dimensional problem, perturbation method, variationalprinciple. laminated plate, nonlinearity, momentum interpolation mechanism (MIM), robust, shock instability, curing method, Roe scheme, expansion shock

2010 MSC Number:

76Lxx
76M12

Xuesong LI, Xiaodong REN, Chunwei GU. Cures for expansion shock and shock instability of Roe scheme based on momentum interpolation mechanism. Applied Mathematics and Mechanics (English Edition), 2018, 39(4): 455-466.

TrendMD

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