Implicit Frictional Boundary Handling for SPH

Jan Bender, Tassilo Kugelstadt, Marcel Weiler, Dan Koschier
IEEE Transactions on Visualization and Computer Graphics

In this paper, 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. Firstly, 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.

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author = {Jan Bender and Tassilo Kugelstadt and Marcel Weiler and Dan Koschier },
title = {Implicit Frictional Boundary Handling for SPH},
journal = {IEEE Transactions on Visualization and Computer Graphics},
year = {2020},
publisher = {IEEE},

Accurately Solving Physical Systems with Graph Learning

Han Shao, Tassilo Kugelstadt, Wojciech Palubicki, Jan Bender, Sören Pirk, Dominik L. Michels

Iterative solvers are widely used to accurately simulate physical systems. These solvers require initial guesses to generate a sequence of improving approximate solutions. In this contribution, we introduce a novel method to accelerate iterative solvers for physical systems with graph networks (GNs) by predicting the initial guesses to reduce the number of iterations. Unlike existing methods that aim to learn physical systems in an end-to-end manner, our approach guarantees long-term stability and therefore leads to more accurate solutions. Furthermore, our method improves the run time performance of traditional iterative solvers. To explore our method we make use of position-based dynamics (PBD) as a common solver for physical systems and evaluate it by simulating the dynamics of elastic rods. Our approach is able to generalize across different initial conditions, discretizations, and realistic material properties. Finally, we demonstrate that our method also performs well when taking discontinuous effects into account such as collisions between individual rods.

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title={Accurately Solving Physical Systems with Graph Learning},
author={Han Shao and Tassilo Kugelstadt and Wojciech Pa{\l{}}ubicki and Jan Bender and S{\"o}ren Pirk and Dominik L. Michels},

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