用HLLC Riemann解算器求解可压缩流的无网格方法
A meshless method for compressible flows with the HLLC Riemann solver
摘要：
HLLC Riemann解算器可以同时解决激波和接触不连续性问题，是计算流体动力学界研究可压缩流动问题的常用网格方法。虽然它被报道用于无网格方法，关键的信息和程序，以实现这一计划的框架内的无网格方法没有得到充分澄清。此外，无网格HLLC求解器处理可压缩液体流动的能力还不完全清楚，因为很少有相关的研究报告。因此，在这项研究中，进行了全面的调查维非分裂HLLC黎曼解的最小二乘无网格方法。采用加强气体状态方程使该方法能够有效地处理单相气体和/或液体，而直接将理想气体状态方程应用于可压缩液体流动可能会遇到很大的困难，在关联状态变量。欧拉方程的空间导数由最小二乘近似计算，通量项由HLLC格式在维非分裂模式中计算。完成了气液激波管、圆柱运动激波、通道内超声速流动和翼型跨音速外流场的数值模拟。目前的方法是通过广泛的比较所产生的数值结果与各种可用的数据，如精确解，有限体积网格法的结果，实验测量或其他参考结果进行验证。
英文摘要：
The HLLC Riemann solver, which resolves both the shock waves and contact discontinuities, is popular to the computational fluid dynamics community studying compressible flow problems with mesh methods. Although it was reported to be used in meshless methods, the crucial information and procedure to realise this scheme within the framework of meshless methods were not clarified fully. Moreover, the capability of the meshless HLLC solver to deal with compressible liquid flows is not completely clear yet as very few related studies have been reported. Therefore, a comprehensive investigation of a dimensional non-split HLLC Riemann solver for the least-square meshless method is carried out in this study. The stiffened gas equation of state is adopted to capacitate the proposed method to deal with single-phase gases and/or liquids effectively, whilst direct applying the perfect gas equation of state for compressible liquid flows might encounter great difficulties in correlating the state variables. The spatial derivatives of the Euler equations are computed by a least-square approximation and the flux terms are calculated by the HLLC scheme in a dimensional non-split pattern. Simulations of gas and liquid shock tubes, moving shock passing a cylinder, internal supersonic flows in channels and external transonic flows over aerofoils are accomplished. The current approach is verified by extensive comparisons of the produced numerical outcomes with various available data such as the exact solutions, finite volume mesh method results, experimental measurements or other reference results.
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