Category: Fluids

Zhi Yuan, Fan Chen, Ye Zhao

Fluid animation practitioners face great challenges from the complexity of flow dynamics and the high cost of numerical simulation. A major hindrance is the uncertainty of fluid behavior after simulation resolution increases and extra turbulent effects are added. In this paper, we propose to regulate fluid animations with predesigned flow patterns. Animators can design their desired fluid behavior with fast, low-cost simulations. Flow patterns are then extracted from the results by the Lagrangian Coherent Structure (LCS) that represents major flow skeleton. Therefore, the final high-quality animation is confined towards the designed behavior by applying the patterns to drive high-resolution and turbulent simulations. The pattern regulation is easily computed and achieves controllable variance in the output. The method makes it easy to design special fluid effects, which increases the usability and scalability of various advanced fluid modeling technologies.

Pattern Guided Smoke Animation with Lagrangian Coherent Structure

 

Karthik Raveendran, Chris Wojtan, Greg Turk

We present a new algorithm for enforcing incompressibility for Smoothed Particle Hydrodynamics (SPH) by preserving uniform density across the domain. We propose a hybrid method that uses a Poisson solve on a coarse grid to enforce a divergence free velocity field, followed by a local density correction of the particles. This avoids typical grid artifacts and maintains the Lagrangian nature of SPH by directly transferring pressures onto particles. Our method can be easily integrated with existing SPH techniques such as the incompressible PCISPH method as well as weakly compressible SPH by adding an additional force term. We show that this hybrid method accelerates convergence towards uniform density and permits a significantly larger time step compared to earlier approaches while producing similar results. We demonstrate our approach in a variety of scenarios with significant pressure gradients such as splashing liquids.

Hybrid Smoothed Particle Hydrodynamics

Nuttapong Chentanez, Matthias Mueller

We present a multigrid method for solving the linear complementarity problem (LCP) resulting from discretizing the Poisson equation subject to separating solid boundary conditions in an Eulerian liquid simulation’s pressure projection step. The method requires only a few small changes to a multigrid solver for linear systems. Our generalized solver is fast enough to handle 3D liquid simulations with separating boundary conditions in practical domain sizes. Previous methods could only handle relatively small 2D domains in reasonable time because they used expensive quadratic programming (QP) solvers. We demonstrate our technique in several practical scenarios in which the omission of separating boundary conditions results in disturbing artifacts of liquid sticking to walls.

A Fluid Pressure Solver Handling Separating Solid Boundary Conditions

Ruogang Huang, Zeki Melek, John Keyser

In this work, we describe an automated method for directing the control of a high resolution gaseous fluid simulation based on the results of a lower resolution preview simulation. Small variations in accuracy between low and high resolution grids can lead to divergent simulations, which is problematic for those wanting to achieve a desired behavior. Our goal is to provide a simple method for ensuring that the high resolution simulation matches key properties from the lower resolution simulation. We first let a user specify a fast, coarse simulation that will be used for guidance. Our automated method samples the data to be matched at various positions and scales in the simulation, or allows the user to identify key portions of the simulation to maintain. During the high resolution simulation, a matching process ensures that the properties sampled from the low resolution simulation are maintained. This matching process keeps the different resolution simulations aligned even for complex systems, and can ensure consistency of not only the velocity field, but also advected scalar values. Because the final simulation is naturally similar to the preview simulation, only minor controlling adjustments are needed, allowing a simpler control method than that used in prior keyframing approaches.

Preview-Based Sampling for Controlling Gaseous Simulations

Haimasree Bhattacharya, Yue Gao, Adam W. Bargteil

In this paper, we present a straightforward, easy to implement method for particle skinning—generating surfaces from animated particle data. We cast the problem in terms of constrained optimization and solve the optimization using a level-set approach. The optimization seeks to minimize the thin-plate energy of the surface, while staying between surfaces defined by the union of spheres centered at the particles. Our approach skins each frame independently while preserving the temporal coherence of the underlying particle animation. Thus, it is well-suited for environments where particle skinning is treated as a post-process, with each frame generated in parallel. We demonstrate our method on data generated by a variety of fluid simulation techniques and simple particle systems.

A Level-set Method for Skinning Animated Particle Data

Ryoichi Ando, Reiji Tsuruno

We present a new particle-based method that explicitly preserves thin fluid sheets for animating liquids. Our primary contribution is a meshless particle-based framework that splits at thin points and collapses at dense points to prevent the breakup of liquid. In contrast to existing surface tracking methods, the proposed framework does not suffer from numerical diffusion or tangles, and robustly handles topology changes by the meshless representation. As the underlying fluid model, we use Fluid-Implicit-Particle (FLIP) with weak spring forces to generate smooth particle-based liquid animation that maintains an even spatial particle distribution in the presence of eddying or inertial motions. The thin features are detected by examining stretches of distributions of neighboring particles by performing Principle Component Analysis (PCA), which is used to reconstruct thin surfaces with anisotropic kernels. Our algorithm is intuitively implemented, easy to parallelize and capable of producing visually complex thin liquid animations.

A Particle-based Method for Preserving Fluid Sheets

Michael Lentine, Mridul Aanjaneya, Ronald Fedkiw

Momentum conservation has long been used as a design principle for solid simulation (e.g. collisions between rigid bodies, mass-spring elastic and damping forces, etc.), yet it has not been widely used for fluid simulation. In fact, semi-Lagrangian advection does not conserve momentum, but is still regularly used as a bread and butter method for fluid simulation. In this paper, we propose a modification to the semi-Lagrangian method in order to make it fully conserve momentum. While methods of this type have been proposed earlier in the computational physics literature, they are not necessarily appropriate for coarse grids, large time steps or inviscid flows, all of which are common in graphics applications. In addition, we show that the commonly used vorticity confinement turbulence model can be modified to exactly conserve momentum as well. We provide a number of examples that illustrate the benefits of this new approach, both in conserving fluid momentum and passively advected scalars such as smoke density. In particular, we show that our new method is amenable to efficient smoke simulation with one time step per frame, whereas the traditional non-conservative semi-Lagrangian method experiences serious artifacts when run with these large time steps, especially when object interaction is considered.

Mass and Momentum Conservation for Fluid Simulation

Kenny Erleben, Marek Misztal, J. Andreas Baerentzen

We present the mathematical foundation of a fluid animation method for unstructured meshes. Key contributions not previously treated are the extension to include diffusion forces and higher order terms of non-linear force approximations. In our discretization we apply a fractional step method to be able to handle advection in a numerically simple Lagrangian approach. Following this a finite element method is used for the remaining terms of the fractional step method. The key to deriving a discretization for the diffusion forces lies in restating the momentum equations in terms of a Newtonian stress tensor. Rather than applying a straightforward temporal finite difference method followed by a projection method to enforce incompressibility as done in the stable fluids method, the last step of the fractional step method is rewritten as an optimization problem to make it easy to incorporate non-linear force terms such as surface tension.

Mathematical Foundation of the Optimization-Based Fluid Animation Method