Results 1  10
of
17
Matching Fluid Simulation Elements to Surface Geometry and Topology
"... Figure 1: Sphere Splash. Coupling an explicit surface tracker to a Voronoi simulation mesh built from pressure points sampled in a geometryaware fashion lets us capture very fine details in this sphere splash animation that uses only 314K tetrahedra. We introduce an Eulerian liquid simulation frame ..."
Abstract

Cited by 35 (7 self)
 Add to MetaCart
Figure 1: Sphere Splash. Coupling an explicit surface tracker to a Voronoi simulation mesh built from pressure points sampled in a geometryaware fashion lets us capture very fine details in this sphere splash animation that uses only 314K tetrahedra. We introduce an Eulerian liquid simulation framework based on the Voronoi diagram of a potentially unorganized collection of pressure samples. Constructing the simulation mesh in this way allows us to place samples anywhere in the computational domain; we exploit this by choosing samples that accurately capture the geometry and topology of the liquid surface. When combined with highresolution explicit surface tracking this allows us to simulate nearly arbitrarily thin features, while eliminating noise and other artifacts that arise when there is a resolution mismatch between the simulation and the surface—and allowing a precise inclusion of surface tension based directly on and at the same resolution as the surface mesh. In addition, we present a simplified Voronoi/Delaunay mesh velocity interpolation scheme, and a direct extension of embedded free surfaces and solid boundaries to Voronoi meshes.
HOT: HodgeOptimized Triangulations
 ACM Trans. Graph
, 2011
"... We introduce Hodgeoptimized triangulations (HOT), a family of wellshaped primaldual pairs of complexes designed for fast and accurate computations in computer graphics. Previous work most commonly employs barycentric or circumcentric duals; while barycentric duals guarantee that the dual of each ..."
Abstract

Cited by 17 (4 self)
 Add to MetaCart
We introduce Hodgeoptimized triangulations (HOT), a family of wellshaped primaldual pairs of complexes designed for fast and accurate computations in computer graphics. Previous work most commonly employs barycentric or circumcentric duals; while barycentric duals guarantee that the dual of each simplex lies within the simplex, circumcentric duals are often preferred due to the induced orthogonality between primal and dual complexes. We instead promote the use of weighted duals (“power diagrams”). They allow greater flexibility in the location of dual vertices while keeping primaldual orthogonality, thus providing a valuable extension to the usual choices of dual by only adding one additional scalar per primal vertex. Furthermore, we introduce a family of functionals on pairs of complexes that we derive from bounds on the errors induced by diagonal Hodge stars, commonly used in discrete computations. The minimizers of these functionals, called HOT meshes, are shown to be generalizations of Centroidal Voronoi Tesselations and Optimal Delaunay Triangulations, and to provide increased accuracy and flexibility for a variety of computational purposes.
Mass and Momentum Conservation for Fluid Simulation
, 2011
"... Momentum conservation has long been used as a design principle for solid simulation (e.g. collisions between rigid bodies, massspring elastic and damping forces, etc.), yet it has not been widely used for fluid simulation. In fact, semiLagrangian advection does not conserve momentum, but is still ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
Momentum conservation has long been used as a design principle for solid simulation (e.g. collisions between rigid bodies, massspring elastic and damping forces, etc.), yet it has not been widely used for fluid simulation. In fact, semiLagrangian 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 semiLagrangian 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 nonconservative semiLagrangian method experiences serious artifacts when run with these large time steps, especially when object interaction is considered.
MultiFLIP for Energetic TwoPhase Fluid Simulation
"... Fig. 1: The “glugging ” effect of water pouring through a spout cannot be reproduced with singlephase liquid simulation. Physicallybased liquid animations often ignore the influence of air, giving up interesting behaviour. We present a new method which treats both ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
Fig. 1: The “glugging ” effect of water pouring through a spout cannot be reproduced with singlephase liquid simulation. Physicallybased liquid animations often ignore the influence of air, giving up interesting behaviour. We present a new method which treats both
An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids
"... We present a novel method for discretizing a multitude of moving and overlapping Cartesian grids each with an independently chosen cell size to address adaptivity. Advection is handled with first and second order accurate semiLagrangian schemes in order to alleviate any time step restriction associ ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
(Show Context)
We present a novel method for discretizing a multitude of moving and overlapping Cartesian grids each with an independently chosen cell size to address adaptivity. Advection is handled with first and second order accurate semiLagrangian schemes in order to alleviate any time step restriction associated with small grid cell sizes. Likewise, an implicit temporal discretization is used for the parabolic terms, such as the heat equation and NavierStokes viscosity. The most intricate aspect of any such discretization is the method used in order to solve the elliptic equation for the NavierStokes pressure or that resulting from the temporal discretization of parabolic terms. We address this by first removing any degrees of freedom which duplicately cover spatial regions due to overlapping grids, and then providing a discretization for the remaining degrees of freedom adjacent to these regions. We observe that a robust second order accurate symmetric positive definite readily preconditioned discretization can be obtained by constructing a local Voronoi region on the fly for each degree of freedom in question in order to obtain both its stencil (logically connected neighbors) and stencil weights. We independently demonstrate each aspect of our approach on test problems in order to show efficacy and convergence before finally addressing a number of common test cases for incompressible flow with potentially moving solid bodies. 1.
Weighted triangulations for geometry processing
"... In this paper, we investigate the use of weighted triangulations as discrete, augmented approximations of surfaces for digital geometry processing. By incorporating a scalar weight per mesh vertex, we introduce a new notion of discrete metric that defines an orthogonal dual structure for arbitrary t ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
In this paper, we investigate the use of weighted triangulations as discrete, augmented approximations of surfaces for digital geometry processing. By incorporating a scalar weight per mesh vertex, we introduce a new notion of discrete metric that defines an orthogonal dual structure for arbitrary triangle meshes and thus extends weighted Delaunay triangulations to surface meshes. We also present alternative characterizations of this primaldual structure (through combinations of angles, areas, and lengths) and, in the process, uncover closedform expressions of mesh energies that were previously known in implicit form only. Finally, we demonstrate how weighted triangulations provide a faster and more robust approach to a series of geometry processing applications, including the generation of wellcentered meshes, selfsupporting surfaces, and sphere packing.
Detailed Water with Coarse Grids: Combining Surface Meshes and Adaptive Discontinuous Galerkin
"... Figure 1: A simulation in a 25 × 25 × 25 grid generates thin splashes and sheets down to 1/1200 the domain width. We present a new adaptive fluid simulation method that captures a high resolution surface with precise dynamics, without an inefficient fine discretization of the entire fluid volume. P ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Figure 1: A simulation in a 25 × 25 × 25 grid generates thin splashes and sheets down to 1/1200 the domain width. We present a new adaptive fluid simulation method that captures a high resolution surface with precise dynamics, without an inefficient fine discretization of the entire fluid volume. Prior adaptive methods using octrees or unstructured meshes carry large overheads and implementation complexity. We instead stick with coarse regular Cartesian grids, using detailed cut cells at boundaries, and discretize the dynamics with a padaptive Discontinuous Galerkin (DG) method. This retains much of the data structure simplicity of regular grids, more efficiently captures smooth parts of the flow, and offers the flexibility to easily increase resolving power where needed without geometric refinement.
Chimera Grids for Water Simulation
"... Figure 1: Two ships in stormy seas near Longfellow island. We refine the domain near the ships by placing grids in their object spaces to add detail and allow them to propel themselves using their twoway solidfluid coupled propellers. We introduce a new method for large scale water simulation usin ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Figure 1: Two ships in stormy seas near Longfellow island. We refine the domain near the ships by placing grids in their object spaces to add detail and allow them to propel themselves using their twoway solidfluid coupled propellers. We introduce a new method for large scale water simulation using Chimera grid embedding, which discretizes space with overlapping Cartesian grids that translate and rotate in order to decompose the domain into different regions of interest with varying spatial resolutions. Grids can track both fluid features and solid objects, allowing for dynamic spatial adaptivity without remeshing or repartitioning the domain. We solve the inviscid incompressible NavierStokes equations with an arbitraryLagrangianEulerian style semiLagrangian advection scheme and a monolithic SPD Poisson solver. We modify the particle level set method in order to adapt it to Chimera grids including particle treatment across grid boundaries with disparate cell sizes, and strategies to deal with locality in the implementation of the level set and fast marching algorithms. We use a local Voronoi mesh construction to solve for pressure and address a number of issues that arise with the treatment of the velocity near the interface. The resulting method is highly scalable on distributed parallel architectures with minimal communication costs.
in
, 2011
"... Physicallybased liquid animations often ignore the influence of air, giving up interesting behaviour. We present a new method which treats both air and liquid as incompressible, more accurately reproducing the reality observed at scales relevant to computer animation. The Fluid Implicit Particle (F ..."
Abstract
 Add to MetaCart
(Show Context)
Physicallybased liquid animations often ignore the influence of air, giving up interesting behaviour. We present a new method which treats both air and liquid as incompressible, more accurately reproducing the reality observed at scales relevant to computer animation. The Fluid Implicit Particle (FLIP) method, already shown to effectively simulate incompressible fluids with low numerical dissipation, is extended to twophase flow by associating a phase bit with each particle. The liquid surface is reproduced at each time step from the particle positions, which are adjusted to prevent mixing near the surface and to allow for accurate surface tension. The liquid surface is adjusted around smallscale features so they are represented in the gridbased pressure projection, while separate, loosely coupled velocity fields reduce unwanted influence between the phases. The resulting scheme is easy to implement, requires little parameter tuning and is shown to reproduce lively twophase fluid phenomena. ii Preface The entirety of this thesis has been submitted as a paper entitled “MultiFLIP for Energetic TwoPhase Fluid Simulation ” to the journal, ACM Transactions on Graphics. The authors listed on the paper are, in order, Landon Boyd and Robert Bridson. The paper was written by Landon Boyd with minor revisions from Robert Bridson. The research was conducted by Landon Boyd, exploring and extending key ideas proposed by Robert Bridson: two velocity fields, particle bumping and level set adjustment for escaped particles. The MultiFLIP implementation was written by Landon Boyd as an extension to a singlephase fluid solver by Robert Bridson. The formula to estimate 3D face fractions described in section 3.2.1 was contributed by Robert Bridson.