Abstract An alternative to three existing types of mesh (structured grid, unstructured grid, and gridfree points) — general mesh — is proposed for Computational Fluid Dynamics (CFD). It includes three existing ones and the arbitrary mixing of mesh and points by using a unified framework. Different from the traditional hybrid grid/gridfree methods requiring separate numerical schemes for the respective grid and points zones, a unified numerical method — general volume scheme — is developed for the general mesh to discretize Navier–Stokes (NS) equations. This innovative scheme naturally solves not only all three existing types of mesh but also the arbitrary mixing of mesh and points without requiring overlapped zones. Compared to the existing grid and gridfree based computational methods, the general mesh method is endowed by nature with both the geometric flexibility of points (without topology connectivity) and physical accuracy of mesh (with node connectivity): 1. the meshing is as general, automated, efficient, and flexible as gridfree points but the numerical solution becomes more stable and accurate than the gridfree method; 2. the numerical scheme is as unified, compact, accurate, and robust as the unstructured grid, whereas the meshing becomes incredibly easier than the latter. Meanwhile, the proposed method is comprehensively validated by both low-speed and transonic high-Reynolds number flows. The simulation of HIRENASD demonstrates the potential to improve the convergence by converting the low-quality mesh elements into meshfree points.

中文翻译：

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通用网格法：统一的数值方案

摘要 为计算流体动力学 (CFD) 提出了一种替代三种现有网格类型（结构化网格、非结构化网格和无网格点）的通用网格。它包括三个现有的和使用统一框架的网格和点的任意混合。与传统的混合网格/无网格方法需要针对各个网格和点区域使用单独的数值方案不同，统一的数值方法——通用体积方案——是为通用网格开发的，用于离散 Navier-Stokes (NS) 方程。这种创新方案自然地不仅解决了所有三种现有类型的网格，而且还解决了网格和点的任意混合而无需重叠区域。与现有的基于网格和无网格的计算方法相比，通用网格方法天生具有点的几何灵活性（无拓扑连通性）和网格的物理精度（有节点连通性）： 1. 网格划分与无网格点一样通用、自动化、高效和灵活，但数值解比无网格方法更加稳定和准确；2. 数值方案与非结构化网格一样统一、紧凑、准确和稳健，而网格划分变得比后者容易得多。同时，所提出的方法得到了低速和跨音速高雷诺数流的综合验证。HIRENASD 的模拟展示了通过将低质量网格元素转换为无网格点来提高收敛性的潜力。