Category: Fluids

Xinxin Zhang, Robert Bridson

Solving the N-body problem, i.e. the Poisson problem with point sources, is a common task in graphics and simulation. The naive direct summation of the kernel function over all particles scales quadratically, rendering it too slow for large problems, while the optimal Fast Multipole Method has drastic implementation complexity and can sometimes carry too high an overhead to be practical. We present a new Particle-Particle Particle-Mesh (PPPM) algorithm which is fast, accurate, and easy to implement even in parallel on a GPU. We capture long-range interactions with a fast multigrid solver on a background grid with a novel boundary condition, while short-range interactions are calculated directly with a new error compensation to avoid error from the background grid. We demonstrate the power of PPPM with a new vortex particle smoke solver, which features a vortex segment-approach to the stretching term, potential flow to enforce no-stick solid boundaries on arbitrary moving solid boundaries, and a new mechanism for vortex shedding from boundary layers. Comparison against a simpler Vortex-in-Cell approach shows PPPM can produce significantly more detailed results with less computation. In addition, we use our PPPM solver for a Poisson surface reconstruction problem to show its potential as a general-purpose Poisson solver.

Particle-particle Particle-mesh (PPPM) Fast Summation for Fluids and Beyond

Nuttapong Chentanez, Matthias Mueller, Tae-Yong Kim

We propose a new method to simulate large scale water phenomena by combining particle, 3D grid and height field methods. In contrast to most hybrid approaches that use particles to simulate foam and spray only, we also represent the bulk of water near the surface with both particles and a grid depending on the regions of interest and switch between those two representations during the course of the simulation. For the coupling we leverage the recent idea of tracking the water surface with a density field in grid based methods. Combining particles and a grid simulation then amounts to adding the density field of the particles and the one stored on the grid. For open scenes, we simulate the water outside of the 3D grid domain by solving the Shallow Water Equations on a height field. We propose new methods to couple these two domains such that waves travel naturally across the border. We demonstrate the effectiveness of our approach in various scenarios including a whale breaching simulation, all running in real-time or at interactive rates.

Coupling 3D Eulerian, Height Field and Particle Methods for the Simulation of Large Scale Liquid Phenomena

Florian Reichl,  Matthäus G. Chajdas,  Jens Schneider, and  Rüdiger Westermann

We describe the design of an interactive rendering system for particle-based fluid simulations comprising hundreds of millions of particles per time step. We present a novel binary voxel representation for particle positions in combination with random jitter to drastically reduce memory and bandwidth requirements. To avoid a time-consuming preprocess and restrict the workload to what is seen, the construction of this representation is embedded into front-to-back GPU ray-casting. For high speed rendering, we ray-cast spheres and extend on total-variation-based image de-noising models to smooth the fluid surface according to data specific boundary conditions. The regular voxel structure permits highly efficient ray-sphere intersection testing as well as classification of foam particles at runtime on the GPU. Foam particles are rendered volumetrically by reconstructing densities from the binary representation on-the-fly. The particular design of our system allows scrubbing through high-resolution animated fluids at interactive rates.

Interactive Rendering of Giga-Particle Fluid Simulations

Omri Azencot, Steffen Weißmann, Maks Ovsjanikov, Max Wardetzky, Mirela Ben-Chen

Fluid simulation plays a key role in various domains of science including computer graphics. While most existing work addresses fluids on bounded Euclidean domains, we consider the problem of simulating the behavior of an incompressible fluid on a curved surface represented as an unstructured triangle mesh. Unlike the commonly used Eulerian description of the fluid using its time-varying velocity field, we propose to model fluids using their vorticity, i.e., by a (time varying) scalar function on the surface. During each time step, we advance scalar vorticity along two consecutive, stationary velocity fields. This approach leads to a variational integrator in the space continuous setting. In addition, using this approach, the update rule amounts to manipulating functions on the surface using linear operators, which can be discretized efficiently using the recently introduced functional approach to vector fields. Combining these time and space discretizations leads to a conceptually and algorithmically simple approach, which is efficient, time-reversible and conserves vorticity by construction. We further demonstrate that our method exhibits no numerical dissipation and is able to reproduce intricate phenomena such as vortex shedding from boundaries.

Functional Fluids on Surfaces

Todd Keeler, Robert Bridson

We tackle deep water simulation in a scalable way, solving 3D irrotational flow using only variables stored in a mesh of the surface of the water, in time proportional to the rendered mesh. The heart of our method is a novel boundary integral equation formulation that is amenable to explicit mesh tracking with unstructured triangle meshes. Our method complements FFT style waves as it is able to handle solid boundaries. It is less memory intensive than volumetric methods and inherently handles the near-infinite depth of the deep ocean. We demonstrate acceleration techniques using the FMM and GPU computing. The natural Lagrangian motion of our model gives inherent adaptivity to our simulation without the need for direct mesh operations.

Ocean Waves Animation using Boundary Integral Equations and Explicit Mesh Tracking

James Gregson, Ivo Irkhe, Nils Thuerey, Wolfgang Heidrich

We explore the connection between fluid capture, simulation and proximal methods, a class of algorithms commonly used for inverse problems in image processing and computer vision. Our key finding is that the proximal operator constraining fluid velocities to be divergence-free is directly equivalent to the pressure-projection methods commonly used in incompressible flow solvers. This observation lets us treat the inverse problem of fluid tracking as a constrained flow problem all while working in an efficient, modular framework. In addition it lets us tightly couple fluid simulation into flow tracking, providing a global prior that significantly increases tracking accuracy and temporal coherence as compared to previous techniques. We demonstrate how we can use these improved results for a variety of applications, such as re-simulation, detail enhancement, and domain modification. We furthermore give an outlook of the applications beyond fluid tracking that our proximal operator framework could enable by exploring the connection of deblurring and fluid guiding.

From Capture to Simulation – Connecting Forward and Inverse Problems in Fluids

Bo Reng, Chenfeng Li, Xiao Yan, Ming C. Lin, Javier Bonet, Shi-Min Hu

This paper presents a versatile and robust SPH simulation approach for multiple-fluid flows. The spatial distribution of different phases or components is modeled using the volume fraction representation, the dynamics of multiple-fluid flows is captured by using an improved mixture model, and a stable and accurate SPH formulation is rigorously derived to resolve the complex transport and transformation processes encountered in multiple-fluid flows. The new approach can capture a wide range of realworld multiple-fluid phenomena, including mixing/unmixing of miscible and immiscible fluids, diffusion effect and chemical reaction etc. Moreover, the new multiple-fluid SPH scheme can be readily integrated into existing state-of-the-art SPH simulators, and the multiple-fluid simulation is easy to set up. Various examples are presented to demonstrate the effectiveness of our approach.

Multiple-Fluid SPH Simulation Using a Mixture Model

Fang Da, Christopher Batty, Eitan Grinspun

We present a triangle mesh-based technique for tracking the evolution of three-dimensional multimaterial interfaces undergoing complex deformations. It is the first non-manifold triangle mesh tracking method to simultaneously maintain intersection-free meshes and support the proposed broad set of multimaterial remeshing and topological operations. We represent the interface as a non-manifold triangle mesh with material labels assigned to each half-face to distinguish volumetric regions. Starting from proposed application-dependent vertex velocities, we deform the mesh, seeking a non-intersecting, watertight solution. This goal necessitates development of various collision-safe, label-aware non-manifold mesh operations: multimaterial mesh improvement; T1 and T2 processes, topological transitions arising in foam dynamics and multi-phase flows; and multimaterial merging, in which a new interface is created between colliding materials. We demonstrate the robustness and effectiveness of our approach on a range of scenarios including geometric flows and multiphase fluid animation.

Multimaterial Mesh-Based Surface Tracking