In this paper, we present an effective prismatic mesh generation method for viscous flow simulations. To address the prismatic mesh collisions in recessed cavities or slit areas, we exploit 3D tensors controlled anisotropic volume harmonic field to generate prismatic meshes. Specially, a well-fitting tetrahedral mesh is first constructed to serve as the discrete computation domain of volume harmonic fields. Then, 3D tensors are exploited to control the volume harmonic field that better fits the shape geometry. From the topological perspective, the generation of the prismatic mesh can be treated as a topology-preserved morphing of the viscous wall. Therefore, iso-surfaces in the volume harmonic field should be homeomorphic to the viscous wall while fitting its shapes. Finally, a full prismatic mesh can be induced by estimating the forward directions and visible regions in the volume harmonic field. Moreover, to be compatible with different simulation situations, the thickness of prismatic meshes should be variable. Our approach provides local adjustable thickness of prismatic meshes, which can be achieved by controlling local 3D tensors. The proposed anisotropic volume harmonic field based prismatic meshes are efficient and robust, and a full prismatic mesh can be guaranteed without low quality collisions. Various experiments have shown that our proposed prismatic meshes have obvious advantages in terms of efficiency and effectiveness.

中文翻译：

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基于各向异性体积谐波场的棱镜网格生成

在本文中，我们提出了一种用于粘性流模拟的有效棱柱网格生成方法。为了解决凹腔或狭缝区域中的棱柱形网格碰撞，我们利用3D张量控制的各向异性体积谐波场来生成棱柱形网格。特别地，首先构造一个拟合良好的四面体网格，以用作体积谐波场的离散计算域。然后，利用3D张量来控制更适合形状几何体的体积谐波场。从拓扑的角度来看，棱柱形网格的生成可以被视为粘性壁的拓扑保留变形。因此，体积谐波场中的等值面应与粘性壁同胚，同时使其形状合适。最后，通过估计体积谐波场中的正向方向和可见区域，可以生成完整的棱柱网格。而且，为了与不同的模拟情况兼容，棱柱形网格的厚度应该是可变的。我们的方法提供了局部可调的棱柱网格厚度，这可以通过控制局部3D张量来实现。所提出的基于各向异性体积谐波场的棱柱形网格是高效且鲁棒的，并且可以确保完整的棱柱形网格而不会发生低质量的碰撞。各种实验表明，我们提出的棱形网格在效率和有效性方面具有明显的优势。我们的方法提供了局部可调的棱柱网格厚度，这可以通过控制局部3D张量来实现。所提出的基于各向异性体积谐波场的棱柱形网格是高效且鲁棒的，并且可以确保完整的棱柱形网格而不会发生低质量的碰撞。各种实验表明，我们提出的棱形网格在效率和有效性方面具有明显的优势。我们的方法提供了局部可调的棱柱网格厚度，这可以通过控制局部3D张量来实现。所提出的基于各向异性体积谐波场的棱柱形网格是高效且鲁棒的，并且可以确保完整的棱柱形网格而不会发生低质量的碰撞。各种实验表明，我们提出的棱形网格在效率和有效性方面具有明显的优势。