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Implicit Frictional Boundary Handling for SPH.
IEEE Transactions on Visualization and Computer Graphics ( IF 4.7 ) Pub Date : 2020-06-23 , DOI: 10.1109/tvcg.2020.3004245
Jan Bender , Tassilo Kugelstadt , Marcel Weiler , Dan Koschier

In this article, we present a novel method for the robust handling of static and dynamic rigid boundaries in Smoothed Particle Hydrodynamics (SPH) simulations. We build upon the ideas of the density maps approach which has been introduced recently by Koschier and Bender. They precompute the density contributions of solid boundaries and store them on a spatial grid which can be efficiently queried during runtime. This alleviates the problems of commonly used boundary particles, like bumpy surfaces and inaccurate pressure forces near boundaries. Our method is based on a similar concept but we precompute the volume contribution of the boundary geometry. This maintains all benefits of density maps but offers a variety of advantages which are demonstrated in several experiments. First, in contrast to the density maps method we can compute derivatives in the standard SPH manner by differentiating the kernel function. This results in smooth pressure forces, even for lower map resolutions, such that precomputation times and memory requirements are reduced by more than two orders of magnitude compared to density maps. Furthermore, this directly fits into the SPH concept so that volume maps can be seamlessly combined with existing SPH methods. Finally, the kernel function is not baked into the map such that the same volume map can be used with different kernels. This is especially useful when we want to incorporate common surface tension or viscosity methods that use different kernels than the fluid simulation.

中文翻译:

SPH的隐式摩擦边界处理。

在本文中,我们提出了一种在平滑粒子流体动力学(SPH)模拟中可靠处理静态和动态刚性边界的新颖方法。我们基于Koschier和Bender最近引入的密度图方法的思想。他们预先计算了实心边界的密度贡献,并将它们存储在空间网格中,可以在运行时对其进行有效查询。这减轻了通常使用的边界粒子的问题,例如凹凸不平的表面和边界附近的压力不正确。我们的方法基于类似的概念,但是我们预先计算了边界几何体的体积贡献。这保留了密度图的所有优势,但提供了多种优势,这些优势已在多个实验中得到了证明。第一,与密度图方法相反,我们可以通过区分核函数以标准SPH方式计算导数。即使对于较低的贴图分辨率,这也将导致平滑的压力,从而与密度贴图相比,预计算时间和存储需求减少了两个数量级以上。此外,这直接适合SPH概念,因此体积图可以与现有SPH方法无缝结合。最终,内核函数没有被烘焙到映射中,因此同一卷映射可用于不同的内核。当我们要合并使用与流体模拟不同的内核的常用表面张力或粘度方法时,这特别有用。即使对于较低的地图分辨率,与密度图相比,预计算时间和内存需求也减少了两个数量级以上。此外,这直接适合SPH概念,因此体积图可以与现有SPH方法无缝结合。最终,内核函数没有被烘焙到映射中,因此同一卷映射可用于不同的内核。当我们要合并使用与流体模拟不同的内核的常用表面张力或粘度方法时,这特别有用。即使对于较低的地图分辨率,与密度图相比,预计算时间和内存需求也减少了两个数量级以上。此外,这直接适合SPH概念,因此体积图可以与现有SPH方法无缝结合。最终,内核函数没有被烘焙到映射中,因此同一卷映射可用于不同的内核。当我们要合并使用与流体模拟不同的内核的常用表面张力或粘度方法时,这特别有用。内核函数未包含在映射中,因此同一卷映射可用于不同的内核。当我们要合并使用与流体模拟不同的内核的常用表面张力或粘度方法时,这特别有用。内核函数未包含在映射中,因此同一卷映射可用于不同的内核。当我们要合并使用与流体模拟不同的内核的常用表面张力或粘度方法时,这特别有用。
更新日期:2020-06-23
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