与疖子问题(carbuncle phenomenon or shock instability)全面亲密接触

wangdingxi

In DUNS source codes, Roe average is exploited to evaluate viscous variables (p, u, v, w, t, yi) at cell interfaces, strictly upwind scheme combined with Steger Warming flux vector splitting technique is utilized to interpolate the flux at cell interfaces. References [1,2,3] report that it is inevitable to incur carbuncle phenomenon (a kind of shock instability) for strictly upwind schemes without reasonable remedy. References [1,2,3] also analyze the source of the shock instability and put forward some general and efficient cures for the carbuncle phenomenon and provide many numerical test cases.
[1] Maurizio Pandolfi et al  Numerical Instabilities in Upwind Methods: Analysis and Cures for the “Carbuncle” Phenomenon Journal of Computational Physics 166, 271–301 (2001)
[2] Richard Sanders et al. Multidimensional Dissipation for Upwind Schemes: Stability and Applications to Gas Dynamics JOURNAL OF COMPUTATIONAL PHYSICS 145, 511–537 (1998)
[3] Sung-soo Kim Cures for the shock instability: Development of a shock-stable Roe scheme Journal of Computational Physics 185 (2003) 342–374   Journal of  Computational Physics 185 (2003) 342–374
here is the pressure contours without a cure for its shock instability for supersoinc fluid flow around a cylinder

wangdingxi

mach number contours for fluid flow around a cylinder,the computation is obtained without any remedy for carbuncle phenomenon.the carbuncle phenomenon is obvious in either pressure contours or mach number contours.The shock instability totally destroys the solution obtained

wangdingxi

after a cure is imposed on the computation,the pressure contours and the below mach number contours are free of carbuncle phenomenon.The remedy utilized here is a modified version of that provided in Reference [1,2].We combine the ideas in reference 1 and 2 to get a similiar one which is effective for the cylinder computation and detonation simulation.The original cure in reference[1] makes the DUNS codes more vulnerable to the initiation of the flow field,while the one in reference 2 is effective for the flow around cylinder computation

wangdingxi

[这个贴子最后由wangdingxi在 2004/12/10 12:55pm 第 1 次编辑]

mach number contours after a modified cure is prescribed
the cure is very effetive and efficient.the remedy in reference 2 is not strong enough to completely cure all carbuncle phenomenon in the flow field of detonation simulation,while the one in reference 1 diverges the computation for detonation simulation after 1 iteration

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pressure contours for gas miture(H2:O2:AR=2:1:7) detonation  without a remedy for the carbuncle phenomenon

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here is the temperature contours
we can see two carbuncles in the upper and lower wall respectively
the carbuncles will grow over time

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close-up of pressure contours

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close-up of tempearue contours

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the remedy in reference 2 is prescribed and the carbuncle in the lower wall is cured

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temperature contours with the lower wall shock free of carbuncle

paradize

可不可以详细解释一下
激波不稳定性？

wangdingxi

下面引用由paradize在 2004/12/10 02:20pm 发表的内容：
可不可以详细解释一下
激波不稳定性？

稍后将细述

wangdingxi

a modified cure is implemented and desirable results are obtained
here is the pressure contours for gas mixture detonatin

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temperature contours for gas mixture detonation(H2:O2:AR=2:1:7)