Month: May 2015

A Stream Function Solver for Liquid Simulations

Ryoichi Ando, Nils Thuerey, Chris Wojtan

This paper presents a liquid simulation technique that enforces the incompressibility condition using a stream function solve instead of a pressure projection. Previous methods have used stream function techniques for the simulation of detailed single-phase flows, but a formulation for liquid simulation has proved elusive in part due to the free surface boundary conditions. In this paper, we introduce a stream function approach to liquid simulations with novel boundary conditions for free surfaces, solid obstacles, and solid-fluid coupling. Although our approach increases the dimension of the linear system necessary to enforce incompressibility, it provides interesting and surprising benefits. First, the resulting flow is guaranteed to be divergence-free regardless of the accuracy of the solve. Second, our free-surface boundary conditions guarantee divergence-free motion even in the un-simulated air phase, which enables two-phase flow simulation by only computing a single phase. We implemented this method using a variant of FLIP simulation which only samples particles within a narrow band of the liquid surface, and we illustrate the effectiveness of our method for detailed two-phase flow simulations with complex boundaries, detailed bubble interactions, and two-way solid-fluid coupling.

A Stream Function Solver for Liquid Simulations

Double Bubbles Sans Toil and Trouble: Discrete Circulation-Preserving Vortex Sheets for Soap Films and Foams

Fang Da, Christopher Batty, Chris Wojtan, Eitan Grinspun

Simulating the delightful dynamics of soap films, bubbles, and foams has traditionally required the use of a fully three-dimensional many-phase Navier-Stokes solver, even though their visual appearance is completely dominated by the thin liquid surface. We depart from earlier work on soap bubbles and foams by noting that their dynamics are naturally described by a Lagrangian vortex sheet model in which circulation is the primary variable. This leads us to derive a novel circulation-preserving surface-only discretization of foam dynamics driven by surface tension on a non-manifold triangle mesh. We represent the surface using a mesh-based multimaterial surface tracker which supports complex bubble topology changes, and evolve the surface according to the ambient air flow induced by a scalar circulation field stored on the mesh. Surface tension forces give rise to a simple update rule for circulation, even at non-manifold Plateau borders, based on a discrete measure of signed scalar mean curvature. We further incorporate vertex constraints to enable the interaction of soap films with wires. The result is a method that is at once simple, robust, and efficient, yet able to capture an array of soap films behaviors including foam rearrangement, catenoid collapse, blowing bubbles, and double bubbles being pulled apart.

Double Bubbles Sans Toil and Trouble: Discrete Circulation-Preserving Vortex Sheets for Soap Films and Foams

Subspace Condensation: Full Space Adaptivity for Subspace Deformations

Yun Teng, Mark Meyer, Tony DeRose, Theodore Kim

Subspace deformable body simulations can be very fast, but can behave unrealistically when behaviors outside the prescribed subspace, such as novel external collisions, are encountered. We address this limitation by presenting a fast, flexible new method that allows full space computation to be activated in the neighborhood of novel events while the rest of the body still computes in a subspace. We achieve this using a method we call subspace condensation, a variant on the classic static condensation precomputation. However, instead of a precomputation, we use the speed of subspace methods to perform the condensation at every frame. This approach allows the full space regions to be specified arbitrarily at runtime, and forms a natural two-way coupling with the subspace regions. While condensation is usually only applicable to linear materials, the speed of our technique enables its application to non-linear materials as well. We show the effectiveness of our approach by applying it to a variety of articulated character scenarios.

Subspace Condensation: Full Space Adaptivity for Subspace Deformations

Restoring the Missing Vortices in Advection-Projection Fluid Solvers

Xinxin Zhang, Robert Bridson, Chen Greif

Most visual effects fluid solvers use a time-splitting approach where velocity is first advected in the flow, then projected to be incompressible with pressure. Even if a highly accurate advection scheme is used, the self-advection step typically transfers some kinetic energy from divergence-free modes into divergent modes, which are then projected out by pressure, losing energy noticeably for large time steps. Instead of taking smaller time steps or using significantly more complex time integration, we propose a new scheme called IVOCK (Integrated Vorticity of Convective Kinematics) which cheaply captures much of what is lost in self-advection by identifying it as a violation of the vorticity equation. We measure vorticity on the grid before and after advection, taking into account vortex stretching, and use a cheap multigrid V-cycle approximation to a vector potential whose curl will correct the vorticity error. IVOCK works independently of the advection scheme (we present examples with various semi-Lagrangian methods and FLIP), works independently of how boundary conditions are applied (it just corrects error in advection, leaving pressure etc.\ to take care of boundaries and other forces), and other solver parameters (we provide smoke, fire, and water examples). For 10~25% extra computation time per step much larger steps can be used, while producing detailed vorticial structures and convincing turbulence that are lost without correction.

Restoring the Missing Vortices in Advection-Projection Fluid Solvers

Power particles: An incompressible fluid solver based on power diagrams

Fernando de Goes, Corentin Wallez, Jin Huang, Dmitry Pavlov, Mathieu Desbrun

This paper introduces a new particle-based approach to incompressible fluid simulation. We depart from previous Lagrangian methods by considering fluid particles no longer purely as material points, but also as volumetric parcels that partition the fluid domain. The fluid motion is described as a time series of well-shaped power diagrams (hence the name power particles), offering evenly spaced particles and accurate pressure computations. As a result, we circumvent the typical excess damping arising from kernel-based evaluations of internal forces or density without having recourse to auxiliary Eulerian grids. The versatility of our solver is demonstrated by the simulation of multiphase flows and free surfaces.

Power Particles: An incompressible fluid solver based on power diagrams