高超声速加热计算的全速HLL型格式的统一构造
A unified construction of all-speed HLL-type schemes for hypersonic heating computations
摘要：
本文建立了一个发展高超声速加热计算的全速HLL型格式的统一框架。这种统一的构造方法结合了两种有效的改进技术：激波鲁棒性改进和低马赫数修正。它是通过适当修改的HLL框架中的局部黎曼问题的近似解，从而在两个全速HLL型计划，即ASHLLC和ASHLLEM求解器。从数值分析和实验结果表明，新提出的格式不仅保留了他们的原始版本的理想性能，但也能够提供精确和强大的解决方案，从低马赫数不可压缩的高超音速可压缩的制度的复杂流动。因此，ASHLLC和ASHLLEM格式都可以作为高超声速加热计算的可靠方法。
英文摘要：
In this paper, a unified framework to develop all-speed HLL-type schemes for hypersonic heating computations is constructed. Such a unified construction method combines two effective improving techniques: a shock robustness improvement and a low-Mach number fix. It is implemented by properly modifying the approximate solutions of the local Riemann problem in the HLL framework, resulting in two all-speed HLL-type schemes, namely ASHLLC and ASHLLEM solvers. Results from both numerical analysis and experiments demonstrate that the newly proposed schemes not only preserve desirable properties of their original versions, but are also able to provide accurate and robust solutions for complex flows ranging from low-Mach number incompressible to hypersonic compressible regimes. Thus, both the ASHLLC and ASHLLEM schemes can be used as reliable methods for hypersonic heating computations.
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