• Advances in aircraft and spacecraft science
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• 제9권5호
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• pp.463-477
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• 2022

This study compares various ways of calculating flows for the problems with the presence of shock waves by first-order schemes and higher-order DG method on the tests from the Quirk list, namely: Quirk's problem and its modifications, shock wave diffraction at a 90 degree corner, the problem of double Mach reflection. It is shown that the use of HLLC and Godunov's numerical schemes flows in calculations can lead to instability, the Rusanov-Lax-Friedrichs scheme flow can lead to high dissipation of the solution. The most universal in heavy production calculations are hybrid schemes flows, which allow the suppression of the development of instability and conserve the accuracy of the method.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2005년도 추계 학술대회논문집
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• pp.131-134
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• 2005

Conventional high order interpolation schemes are limitative in several aspects mainly because they need data of neighboring cells at the reconstruction step. However, discontinuous Galerkin method and spectral volume method, two high order flux schemes which will be analyzed and compared in this paper, have an important benefit that they are not necessary to determine the flow gradients from data of neighboring cells or elements. These two schemes construct polynomial of variables within a cell so that even near wall or discontinuity, the high order does not deteriorate.