Physics-Based Animation

Christian Dick, Marcus Rogowsky, Rüdiger Westermann

In many numerical simulations of fluids governed by the incompressible Navier-Stokes equations, the pressure Poisson equation needs to be solved to enforce mass conservation. Multigrid solvers show excellent convergence in simple scenarios, yet they can converge slowly in domains where physically separated regions are combined at coarser scales. Moreover, existing multigrid solvers are tailored to specific discretizations of the pressure Poisson equation, and they cannot easily be adapted to other discretizations.
In this paper we analyze the convergence properties of existing multigrid solvers for the pressure Poisson equation in different simulation domains, and we show how to further improve the multigrid convergence rate by using a graph-based extension to determine the coarse grid hierarchy. The proposed multigrid solver is generic in that it can be applied to different kinds of discretizations of the pressure Poisson equation, by using solely the specification of the simulation domain and pre-assembled computational stencils. We analyze the proposed solver in combination with finite difference and finite volume discretizations of the pressure Poisson equation. Our evaluations show that, despite the common assumption, multigrid schemes can exploit their potential even in the most complicated simulation scenarios, yet this behavior is obtained at the price of higher memory consumption.

Solving the Fluid Pressure Poisson Equation Using Multigrid—Evaluation and Improvements

Prashant Goswami, André Eliasson, Pontus Franzén

This paper presents CUDA-based parallelization of implicit incompressible SPH (IISPH) on the GPU. Along with the detailed exposition of our implementation, we analyze various components involved for their costs. We show that our CUDA version achieves near linear scaling with the number of particles and is faster than the multi-core parallelized IISPH on the CPU. We also present a basic comparison of IISPH with the standard SPH on GPU.

Implicit Incompressible SPH on the GPU

Nuttapong Chentanez, Matthias Mueller, Miles Macklin, Tae-Yong Kim

We present the first mesh-based surface tracker that runs entirely on the GPU. The surface tracker is both completely grid-free and fast which makes it suitable for the use in a large, unbounded domain. The key idea for handling topological changes is to detect and delete overlapping triangles as well as triangles that lie inside the volume. The holes are then joined or closed in a robust and efficient manner. Good mesh quality is maintained by a mesh improvement algorithm. In this paper we describe how all these steps can be parallelized to run effi- ciently on a GPU. The surface tracker is guaranteed to produce a manifold mesh without boundary. Our results show the quality and efficiency of the method in both Eulerian and Lagrangian liquid simulations. Our parallel implementation runs more than an order of magnitude faster than the CPU version.

Grid-Free Surface Tracking on the GPU

Markus Huber, Stefan Reinhardt, Daniel Weiskopf, and Bernhard Eberhardt

We evaluate surface tension models in particle-based fluid simulation systems using smoothed particle hydrodynamics (SPH) with a benchmark test. Our benchmark consists of three experiments and a set of analysis methods that are useful for the comparison of surface tension models. Although visual quality is of major interest and is considered as well, we suggest quantification methods for the properties of these models. The goal is to identify if a certain model is suitable for a given scenario and to be able to control the results in the creation of animations. We apply the proposed evaluation methods to three existing surface tension models in combination with different SPH techniques (WCSPH, PCISPH, and IISPH) and perform systematic tests to show the influence of different settings and parameter choices. The surface tension models are chosen from different classes: a pure inter-particle force model, a model based on surface curvature, and a model using a combination of these. Additionally, we present a simple modification to improve the quality of inter-particle force models.

Evaluation of Surface Tension Models for SPH-Based Fluid Animations Using a Benchmark Test

Ľubor Ladický, SoHyeon Jeong, Barbara Solenthaler, Marc Pollefeys, and Markus Gross

Traditional fluid simulations require large computational resources even for an average sized scene with the main bottleneck being a very small time step size, required to guarantee the stability of the solution. Despite a large progress in parallel computing and efficient algorithms for pressure computation in the recent years, realtime fluid simulations have been possible only under very restricted conditions. In this paper we propose a novel machine learning based approach, that formulates physics-based fluid simulation as a regression problem, estimating the acceleration of every particle for each frame. We designed a feature vector, directly modelling individual forces and constraints from the Navier-Stokes equations, giving the method strong generalization properties to reliably predict positions and velocities of particles in a large time step setting on yet unseen test videos. We used a regression forest to approximate the behaviour of particles observed in the large training set of simulations obtained using a traditional solver. Our GPU implementation led to a speed-up of one to three orders of magnitude compared to the state-of-the-art position-based fluid solver and runs in real-time for systems with up to 2 million particles.

Data-Driven Fluid Simulations using Regression Forests