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Hybridisable Discontinuous Galerkin Formulation of Compressible Flows
Archives of Computational Methods in Engineering ( IF 9.7 ) Pub Date : 2020-11-21 , DOI: 10.1007/s11831-020-09508-z
Jordi Vila-Pérez , Matteo Giacomini , Ruben Sevilla , Antonio Huerta

This work presents a review of high-order hybridisable discontinuous Galerkin (HDG) methods in the context of compressible flows. Moreover, an original unified framework for the derivation of Riemann solvers in hybridised formulations is proposed. This framework includes, for the first time in an HDG context, the HLL and HLLEM Riemann solvers as well as the traditional Lax–Friedrichs and Roe solvers. HLL-type Riemann solvers demonstrate their superiority with respect to Roe in supersonic cases due to their positivity preserving properties. In addition, HLLEM specifically outstands in the approximation of boundary layers because of its shear preservation, which confers it an increased accuracy with respect to HLL and Lax–Friedrichs. A comprehensive set of relevant numerical benchmarks of viscous and inviscid compressible flows is presented. The test cases are used to evaluate the competitiveness of the resulting high-order HDG scheme with the aforementioned Riemann solvers and equipped with a shock treatment technique based on artificial viscosity.



中文翻译:

可压缩流的可混合不连续伽勒金公式

这项工作提出了可压缩流的背景下高阶可杂交不连续伽勒金(HDG)方法的审查。此外,提出了用于混合配方中黎曼求解器的推导的原始统一框架。该框架首次在HDG环境中包括HLL和HLLEM Riemann求解器以及传统的Lax–Friedrichs和Roe求解器。HLL型Riemann求解器由于具有正极性,因此在超音速情况下显示出相对于Roe的优越性。此外,HLLEM由于具有剪切力保持性,在边界层的逼近方面特别出色,这使它相对于HLL和Lax–Friedrichs具有更高的精度。提出了一套完整的有关粘性和无粘性可压缩流动的数值基准。

更新日期:2020-11-22
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