新型高低速流统一算法及其叶轮机应用

New General Scheme for Flows at All Speeds and Its Application to Turbomachinery

对于可压缩/不可压缩混合流动或高低速混合流动问题,目前没有较好的解决方法。基于Roe格式及预处理方法,提出了全速度Roe格式。全速度Roe格式是将Roe格式与低速Roe格式通过一个与本地马赫数相关的函数联合而得到的。与标准Roe格式相比,对亚音速流动,全速度Roe格式中声速对数值耗散的影响随着马赫数变化而变化。与预处理Roe格式相比,全速度Roe格式简单易于实现,而且没有计算稳定性的限制,不需要采用全局截断处理,从而在理论上对高低速流动具有一致精度。事实上,全速度Roe格式意味着可以通过直接改变Roe格式的非线性特征值,解决可压不可压流动统一计算精度的问题。这是对统一算法的新观点。数值模拟表明,全速度Roe格式具有与预处理Roe格式一样的激波捕获能力、极低速流动准确模拟能力。

In order to solve the problem of mixed compressible and incompressible flows, All-Speed-Roe scheme is proposed. Based on Roe scheme and preconditioning technology, Low-Speed-Roe scheme is derived. Then, All-Speed-Roe scheme is obtained by uniting Roe scheme and Low-Speed-Roe scheme with the function of local Mach number. Compared with Roe scheme, the effect of acoustic speed on numerical dissipation changes when Mach numbers changes for subsonic flows. Compared with preconditioned Roe scheme, it is easier to realize, and needn’t to be cut off by the global Mach number by overcoming the problem of computational instability. Therefore, All-Speed-Roe scheme has uniform accuracy for all flows speeds in theory. In fact, All-Speed-Roe scheme means that the scheme for all flows speeds can be obtained by directly modifying the non-linear eigenvalues. It is a new viewpoint for all-speed schemes. Numerical experiments show that All-Speed-Roe scheme can capture shock and accurately simulate very low Mach number flows. It indicates that All-Speed-Roe scheme has at least the same ability as preconditioned Roe scheme.