Large-scale fluid simulation using velocity-vorticity domain decomposition

Golas, Abhinav; Narain, Rahul; Sewall, Jason; Krajcevski, Pavel; Dubey, Pradeep; Lin, Ming C.

doi:10.1145/2366145.2366167

Cited by 57 publications

(36 citation statements)

References 50 publications

(38 reference statements)

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“…[Gamito et al 1995;Selle et al 2005], vortex sheets [Pfaff et al 2012;Brochu et al 2012], or with tightly coupled rigid bodies [Vines et al 2014]. These methods focus on single-phase fluid simulation, but the algorithm of Golas et al [2012] uses a grid vortex-particle hybrid and can simulate liquids by resorting to a pressure-based solve near the free surface and solid boundaries. Bridson et al [2007] use an analytically computed stream function, making heavy use of the fact that the resulting velocity is guaranteed to be divergence-free.…”

Section: Related Workmentioning

confidence: 99%

A stream function solver for liquid simulations

2015

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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 solidfluid 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.

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Section: Related Workmentioning

confidence: 99%

A stream function solver for liquid simulations

2015

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“…Incorporating these ideas into our solver ensures accurate pressure solutions and avoids voxelization artifacts. While we focus on adaptive approaches for Eulerian methods, Lagrangian SPH and vortex methods have also been applied in the context of adaptivity [Adams et al 2007;Golas et al 2012;Solenthaler and Gross 2011;Takahashi and Lin 2016].…”

Section: Related Workmentioning

confidence: 99%

Power diagrams and sparse paged grids for high resolution adaptive liquids

et al. 2017

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Fig. 1. (Left)Water filling a river bed surrounded by a canyon, with effective resolution 512 2 × 1024. Three refinement levels are used, based on proximity to the terrain. (Right) Sources inject water into a container and collide to form a thin sheet, with effective resolution 512 3 . Adaptivity pattern shown on background.We present an efficient and scalable octree-inspired fluid simulation framework with the flexibility to leverage adaptivity in any part of the computational domain, even when resolution transitions reach the free surface. Our methodology ensures symmetry, definiteness and second order accuracy of the discrete Poisson operator, and eliminates numerical and visual artifacts of prior octree schemes. This is achieved by adapting the operators acting on the octree's simulation variables to reflect the structure and connectivity of a power diagram, which recovers primal-dual mesh orthogonality and eliminates problematic T-junction configurations. We show how such operators can be efficiently implemented using a pyramid of sparsely populated uniform grids, enhancing the regularity of operations and facilitating parallelization. A novel scheme is proposed for encoding the topology of the power diagram in the neighborhood of each octree cell, allowing us to locally reconstruct it on the fly via a lookup table, rather than resorting to costly explicit meshing. The pressure Poisson equation is solved via a highly efficient, matrix-free multigrid preconditioner for Conjugate Gradient, adapted to the power diagram discretization. We use another sparsely † M. Aanjaneya and M. Gao are joint first authors. * M. Aanjaneya was with the University of Wisconsin -Madison during this work. This work was supported in part by National Science Foundation grants IIS-1253598, CCF-1423064, CCF-1533885 and by the Natural Sciences and Engineering Research Council of Canada under grant RGPIN-04360-2014. The authors are grateful to Nathan Mitchell for his indispensable help with modeling and rendering of examples. C. Batty would like to thank Ted Ying for carrying out preliminary explorations on quadtrees. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. populated uniform grid for high resolution interface tracking with a narrow band level set representation. Using the recently introduced SPGrid data structure, sparse uniform grids in both the power diagram discretization and our narrow band level set can be compactly stored and efficiently updated via streaming operations. Additionally, we present enhancem...

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“…Golas et al [2012] used a hybrid approach: a vortex particle method handles the large interior of the flow domain, and this is coupled to a regular grid-based simulator applied on a narrow band around the liquid interface or solid boundaries. In the context of deep ocean waves, Keeler and Bridson [2014] achieved a surfaceonly discretization by combining the El Topo surface tracker with the solution of a specific boundary integral equation derived under a potential flow assumption.…”

Section: Vortex-based Fluidsmentioning

confidence: 99%

Double bubbles sans toil and trouble

Batty

Wojtan

et al. 2015

ACM Trans. Graph.

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Figure 1: A variety of dynamic foam, film, and bubble scenarios captured by our method. Left: A small foam rearranges and settles to equilibrium. Center: A snapshot of an evolving catenoid soap film joining two circular wires, an instant before the film pinches apart. Right: A bubble with a wire constricting its mid-section gradually squeezes to one side. AbstractSimulating the delightful dynamics of soap films, bubbles, and foams has traditionally required the use of a fully three-dimensional manyphase 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.

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Large-scale fluid simulation using velocity-vorticity domain decomposition

Cited by 57 publications

References 50 publications

A stream function solver for liquid simulations

A stream function solver for liquid simulations

Power diagrams and sparse paged grids for high resolution adaptive liquids

Double bubbles sans toil and trouble

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