Implicit Density Projection for Volume Conserving Liquids

Tassilo Kugelstadt, Andreas Longva, Nils Thuerey, Jan Bender
IEEE Transactions on Visualization and Computer Graphics

We propose a novel implicit density projection approach for hybrid Eulerian/Lagrangian methods like FLIP and APIC to enforce volume conservation of incompressible liquids. Our approach is able to robustly recover from highly degenerate configurations and incorporates volume-conserving boundary handling. A problem of the standard divergence-free pressure solver is that it only has a differential view on density changes. Numerical volume errors, which occur due to large time steps and the limited accuracy of pressure projections, are invisible to the solver and cannot be corrected. Moreover, these errors accumulate over time and can lead to drastic volume changes, especially in long-running simulations or interactive scenarios. Therefore, we introduce a novel method that enforces constant density throughout the fluid. The density itself is tracked via the particles of the hybrid Eulerian/Lagrangian simulation algorithm. To achieve constant density, we use the continuous mass conservation law to derive a pressure Poisson equation which also takes density deviations into account. It can be discretized with standard approaches and easily implemented into existing code by extending the regular pressure solver. Our method enables us to relax the strict time step and solver accuracy requirements of a regular solver, leading to significantly higher performance. Moreover, our approach is able to push fluid particles out of solid obstacles without losing volume and generates more uniform particle distributions, which makes frequent particle resampling unnecessary. We compare the proposed method to standard FLIP and APIC and to previous volume correction approaches in several simulations and demonstrate significant improvements in terms of incompressibility, visual realism and computational performance.

» Show Videos
» Show BibTeX

author = {Tassilo Kugelstadt and Andreas Longva and Nils Thuerey and Jan Bender},
title = {Implicit Density Projection for Volume Conserving Liquids},
journal = {IEEE Transactions on Visualization and Computer Graphics},
year = {2021},
publisher = {IEEE},
volume = {27},
number = {4},
doi={ 10.1109/TVCG.2019.2947437},

Accurately Solving Rod Dynamics with Graph Learning

Han Shao, Tassilo Kugelstadt, Torsten Hädrich, Wojciech Palubicki, Jan Bender, Sören Pirk, Dominik L. Michels
Advances in Neural Information Processing Systems (NeurIPS 2021)

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 rod dynamics 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 for rod dynamics. 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. We demonstrate that it also performs well when taking discontinuous effects into account such as collisions between individual rods. Finally, to illustrate the scalability of our approach, we simulate complex 3D tree models composed of over a thousand individual branch segments swaying in wind fields.

» Show Videos
» Show BibTeX

title={Accurately Solving Rod Dynamics with Graph Learning},
author={Han Shao and Tassilo Kugelstadt and Torsten H\"{a}drich and Wojciech Pa\l{}ubicki and Jan Bender and S\"{o}ren Pirk and Dominik L. Michels},
booktitle={Advances in Neural Information Processing Systems (NeurIPS)},

Fast Corotated Elastic SPH Solids with Implicit Zero-Energy Mode Control

Tassilo Kugelstadt, Jan Bender, José Antonio Fernández-Fernández, Stefan Rhys Jeske, Fabian Löschner, Andreas Longva
Proceedings of the ACM on Computer Graphics and Interactive Techniques (Best Paper Award at SCA)

We develop a new operator splitting formulation for the simulation of corotated linearly elastic solids with Smoothed Particle Hydrodynamics (SPH). Based on the technique of Kugelstadt et al. [KKB2018] originally developed for the Finite Element Method (FEM), we split the elastic energy into two separate terms corresponding to stretching and volume conservation, and based on this principle, we design a splitting scheme compatible with SPH. The operator splitting scheme enables us to treat the two terms separately, and because the stretching forces lead to a stiffness matrix that is constant in time, we are able to prefactor the system matrix for the implicit integration step. Solid-solid contact and fluid-solid interaction is achieved through a unified pressure solve. We demonstrate more than an order of magnitude improvement in computation time compared to a state-of-the-art SPH simulator for elastic solids.

We further improve the stability and reliability of the simulation through several additional contributions. We introduce a new implicit penalty mechanism that suppresses zero-energy modes inherent in the SPH formulation for elastic solids, and present a new, physics-inspired sampling algorithm for generating high-quality particle distributions for the rest shape of an elastic solid. We finally also devise an efficient method for interpolating vertex positions of a high-resolution surface mesh based on the SPH particle positions for use in high-fidelity visualization.

» Show Videos
» Show BibTeX

author = {Kugelstadt, Tassilo and Bender, Jan and Fern{\'{a}}ndez-Fern{\'{a}}ndez, Jos{\'{e}} Antonio and Jeske, Stefan Rhys and L{\"{o}}schner, Fabian and Longva, Andreas},
title = {Fast Corotated Elastic SPH Solids with Implicit Zero-Energy Mode Control},
year = {2021},
issue_date = {September 2021},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {4},
number = {3},
url = {https://doi.org/10.1145/3480142},
doi = {10.1145/3480142},
journal = {Proc. ACM Comput. Graph. Interact. Tech.},
month = sep,
articleno = {33},
numpages = {21},
keywords = {Smoothed Particle Hydrodynamics, fluid simulation, deformable solids, solid-fluid coupling}

Previous Year (2020)
Disclaimer Home Visual Computing institute RWTH Aachen University