Comprehensive adaptiv simulation of SPH-based fluids

在计算机动画中，流体模拟采用了多种方法。光滑粒子流体力学（SPH）方法在相同空间分辨率下的视觉合理性优于其他方法，但计算量较大。为了减少SPH模拟的计算量，在前期工作中开发了一种空间自适应方法，该方法的空间自适应率可以达到1:10万甚至更高，比以前的方法提高了三到四个数量级。与均匀粒子分辨率相比，自适应SPH方法对边界几何和固体的单向和双向耦合提出了重大挑战。此外，均匀粒子分辨率下SPH模拟结果的尺度依赖性造成了自适应SPH模型的“内在”不一致性。在项目的第一阶段，基于平面边界几何的SPH核函数边界积分的解析解，在自适应SPH模型与边界几何和固体的单向和双向耦合方面取得了实质性进展。此外，还开发了一种高效的在线优化方法，用于在分辨率细化过程中识别颗粒构型，该方法在大自适应速率下提供了稳定的模拟结果，并显著降低了人工粘度。这直接导致模拟结果在大分辨率范围内具有更大的一致性。此外，开发了高效的数据结构和基于gpu的仿真框架，其中集成了所有已经开发的方法。在第二个项目阶段，三个问题领域是调查的重点。第一个研究重点是基于非平面界面边界积分解析解的自适应SPH模型与边界的鲁棒相互作用，以及自适应SPH模拟中基于粒子的有效边界表示的发展。第二个研究重点探讨了自适应sph多相流体的模拟，考虑了弱可压缩材料（特别是空气）和类似密度的不可压缩材料（涉及双向耦合）。第三个研究重点是对SPH模型和参数的尺度依赖性进行全面的定量研究，并对这些参数进行校正，以确保不同分辨率尺度下流体行为的一致性。

In computer animation, various approaches are used for fluid simulation. The smoothed particle hydrodynamics (SPH) method performs better than other methods at the same spatial resolution in terms of visual plausibility, but requires a comparatively high computational effort. In order to reduce this computational effort of SPH simulations, a spatially adaptive method has been developed in preliminary work, which allows spatial adaptivity rates of 1:1,000,000 and beyond, which is three to four orders of magnitude higher than previous methods.Compared to uniform particle resolutions, adaptive SPH methods pose significant challenges for one- and two-way coupling with boundary geometries and solids. In addition, the scale dependency of SPH simulation results, which is already existing for uniform particle resolutions creates an "intrinsic" inconsistency in adaptive SPH models.In the first phase of the project, substantial progress was made with respect to one- and two-way coupling of adaptive SPH models with boundary geometries and solids, based on an analytical solution of the boundary integral of SPH kernel functions with planar boundary geometries. In addition, an efficient, on-line optimization method for identifying particle configurations during resolution refinement has been developed, which provides a stable simulation result over large adaptivity rates with significantly reduced artificial viscosity. This directly leads to greater consistency of the simulation results over large resolution ranges. Furthermore, efficient data structures and a GPU-based simulation framework were developed, in which all methods that have been developed are integrated.In the second project phase, three problem areas are in the focus of the investigations. The first research focus deals with the robust interaction of adaptive SPH models with boundaries based on analytical solutions of the boundary integral for non-planar interfaces, as well as with the development of efficient particle-based representations of boundaries for adaptive SPH simulations. The second research focus explores the simulation of adaptive SPH-based multiphase fluids, considering both weakly compressible materials, in particular air, and incompressible materials of similar density involving two-way couplings. The third research focus is on the comprehensive quantitative investigation of the scaling dependence of SPH models and parameters, as well as the correction of these parameters with the goal of ensuring consistent fluid behavior across different resolution scales.