Comprehensive adaptiv simulation of SPH-based fluids

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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.