AI 中文总结
提出一种保守型Godunov类无网格格式，通过二阶重构、HLLC求解器及界面切向松弛机制，实现弱可压缩多相流的高精度模拟，并在多个基准测试中验证了其有效性。
AI 中文摘要
我们提出了一种Godunov类无网格水动力学格式，用于弱可压缩单相和多相流的数值模拟。该方法在粒子间界面处对原始变量进行一致的二阶空间重构，应用斜率限制，并使用亚声速HLLC近似黎曼求解器求解移动黎曼问题。粒子以准拉格朗日物质速度输运，该速度包含一种固有的自松弛机制，可抑制各向异性粒子分布的形成。在物质界面附近，使用单侧重整化梯度来处理密度不连续性，并对每个相独立地应用斜率限制。通过将松弛机制约束为沿界面切向作用，保持了物质界面的拉格朗日特性。对于同相粒子相互作用，黎曼问题以两个物质速度的算术平均为中心；对于跨相相互作用，则以接触波速度为中心。这一选择自然消除了跨相界面的虚假质量通量。该方法在一系列具有挑战性的基准测试中得到了验证，包括无粘泰勒-格林涡、物质界面平流、静水平衡附近的重力表面波、开尔文-亥姆霍兹不稳定性以及重力分层下的瑞利-泰勒不稳定性。
英文摘要
We present a Godunov-type mesh-free hydrodynamics scheme for the numerical simulation of weakly compressible single- and multiphase flows. The method employs a consistent second-order spatial reconstruction of the primitive variables at the inter-particle interface, applies slope limiting, and solves the moving Riemann problem using a subsonic HLLC approximate Riemann solver. Particles are advected with a quasi-Lagrangian material velocity incorporating an inherent self-relaxation mechanism that suppresses the formation of anisotropic particle distributions. Near material interfaces, one-sided renormalized gradients are used to handle density discontinuities and slope limiting is applied for each phase independently. The Lagrangian character of material interfaces is preserved by constraining the relaxation mechanism to act tangentially to the interface. For same-phase particle interactions, the Riemann problem is centered at the arithmetic mean of the two material velocities. For cross-phase interactions, it is centered at the contact-wave velocity. This choice naturally eliminates spurious mass fluxes across phase boundaries. The methodology is validated on a set of challenging benchmarks, including the inviscid Taylor-Green vortex, material interface advection, surface gravity waves near hydrostatic equilibrium, the Kelvin-Helmholtz instability, and the Rayleigh-Taylor instability under gravitational stratification.
