论文标题
可压缩流的杂交不连续的galerkin公式
Hybridisable discontinuous Galerkin formulation of compressible flows
论文作者
论文摘要
这项工作介绍了在可压缩流的背景下对高阶混合不连续的盖尔金（HDG）方法的评论。此外，提出了在杂交配方中推导Riemann求解器的原始统一框架。该框架首次在HDG上下文中包括HLL和HLLEM RIEMANN求解器以及传统的Lax-Friedrichs和Roe Solvers。 HLL型Riemann求解器由于其阳性保留特性而在超音速案例中证明了它们对ROE的优势。另外，由于其剪切保存，HLLEM在边界层的近似中特异性地置于近似值，这使其相对于HLL和Lax-Friedrichs的精度提高了。提出了一组粘性和无粘性压缩流的相关数值基准。测试用例用于评估所得高阶HDG方案与上述Riemann求解器的竞争力，并配备了基于人工粘度的冲击处理技术。
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.
