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210
Animating sand as a fluid
- ACM Trans. Graph. (Proc. SIGGRAPH
, 2005
"... My thesis presents a physics-based simulation method for animating sand. To allow for efficiently scaling up to large volumes of sand, we abstract away the individual grains and think of the sand as a continuum. In particular we show that an existing water simulator can be turned into a sand simulat ..."
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Cited by 128 (4 self)
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My thesis presents a physics-based simulation method for animating sand. To allow for efficiently scaling up to large volumes of sand, we abstract away the individual grains and think of the sand as a continuum. In particular we show that an existing water simulator can be turned into a sand simulator within frictional regime with only a few small additions to account for inter-grain and boundary friction, yet with visually acceptable result. We also propose an alternative method for simulating fluids. Our core representation is a cloud of particles, which allows for accurate and flexible surface tracking and advection, but we use an auxiliary grid to efficiently enforce boundary conditions and incompressibility. We further address the issue of reconstructing a surface from particle data to render each frame. ii Contents ii
A Fast and Accurate Semi-Lagrangian Particle Level Set Method
- COMPUTERS AND STRUCTURES
, 2004
"... In this paper, we present an efficient semi-Lagrangian based particle level set method for the accurate capturing of interfaces. This method retains the robust topological properties of the level set method without the adverse effects of numerical dissipation. Both the level set method and the p ..."
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Cited by 83 (11 self)
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In this paper, we present an efficient semi-Lagrangian based particle level set method for the accurate capturing of interfaces. This method retains the robust topological properties of the level set method without the adverse effects of numerical dissipation. Both the level set method and the particle level set method typically use high order accurate numerical discretizations in time and space, e.g. TVD RungeKutta and HJ-WENO schemes. We demonstrate that these computationally expensive schemes are not required. Instead, fast, low order accurate numerical schemes suffice. That is, the addition of particles to the level set method not only removes the difficulties associated with numerical diffusion, but also alleviates the need for computationally expensive high order accurate schemes. We use an efficient, first order accurate semi-Lagrangian advection scheme coupled with a first order accurate fast marching method to evolve the level set function. To accurately track the underlying flow characteristics, the particles are evolved with a second order accurate method. Since we avoid complex high order accurate numerical methods, extending the algorithm to arbitrary data structures becomes more feasible, and we show preliminary results obtained with an octree-based adaptive mesh.
A fast variational framework for accurate solid-fluid coupling
- ACM Trans. Graph
, 2007
"... Figure 1: Left: A solid stirring smoke runs at interactive rates, two orders of magnitude faster than previously. Middle: Fully coupled rigid bodies of widely varying density, with flow visualized by marker particles. Right: Interactive manipulation of immersed rigid bodies. Physical simulation has ..."
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Cited by 75 (4 self)
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Figure 1: Left: A solid stirring smoke runs at interactive rates, two orders of magnitude faster than previously. Middle: Fully coupled rigid bodies of widely varying density, with flow visualized by marker particles. Right: Interactive manipulation of immersed rigid bodies. Physical simulation has emerged as a compelling animation tech-nique, yet current approaches to coupling simulations of fluids and solids with irregular boundary geometry are inefficient or cannot handle some relevant scenarios robustly. We propose a new varia-tional approach which allows robust and accurate solution on rela-tively coarse Cartesian grids, allowing possibly orders of magnitude faster simulation. By rephrasing the classical pressure projection step as a kinetic energy minimization, broadly similar to modern approaches to rigid body contact, we permit a robust coupling be-tween fluid and arbitrary solid simulations that always gives a well-posed symmetric positive semi-definite linear system. We provide several examples of efficient fluid-solid interaction and rigid body coupling with sub-grid cell flow. In addition, we extend the frame-work with a new boundary condition for free-surface flow, allowing fluid to separate naturally from solids.
Spatially adaptive techniques for level set methods and incompressible flow
- Comput. Fluids
"... Since the seminal work of [92] on coupling the level set method of [69] to the equations for two-phase incompressible flow, there has been a great deal of interest in this area. That work demonstrated the most powerful aspects of the level set method, i.e. automatic han-dling of topological changes ..."
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Cited by 73 (15 self)
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Since the seminal work of [92] on coupling the level set method of [69] to the equations for two-phase incompressible flow, there has been a great deal of interest in this area. That work demonstrated the most powerful aspects of the level set method, i.e. automatic han-dling of topological changes such as merging and pinching, as well as robust geometric information such as normals and curvature. Interest-ingly, this work also demonstrated the largest weakness of the level set method, i.e. mass or information loss characteristic of most Eulerian capturing techniques. In fact, [92] introduced a partial differential equation for battling this weakness, without which their work would not have been possible. In this paper, we discuss both historical and most recent works focused on improving the computational accuracy of the level set method focusing in part on applications related to in-compressible flow due to both its popularity and stringent accuracy requirements. Thus, we discuss higher order accurate numerical meth-ods such as Hamilton-Jacobi WENO [46], methods for maintaining a signed distance function, hybrid methods such as the particle level set method [27] and the coupled level set volume of fluid method [91], and adaptive gridding techniques such as the octree approach to free surface flows proposed in [56].
An unconditionally stable MacCormack method
, 2006
"... The back and forth error compensation and correction (BFECC) method advects the solution forward and then backward in time. The result is compared to the original data to estimate the error. Although inappropriate for parabolic and other nonreversible partial differential equations, it is useful for ..."
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Cited by 64 (16 self)
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The back and forth error compensation and correction (BFECC) method advects the solution forward and then backward in time. The result is compared to the original data to estimate the error. Although inappropriate for parabolic and other nonreversible partial differential equations, it is useful for often troublesome advection terms. The error estimate is used to correct the data before advection raising the method to second order accuracy, even though each individual step is only first order accurate. In this paper, we rewrite the MacCormack method to illustrate that it estimates the error in the same exact fashion as BFECC. The difference is that the MacCormack method uses this error estimate to correct the already computed forward advected data. Thus, it does not require the third advection step in BFECC reducing the cost of the method while still obtaining second order accuracy in space and time. Recent work replaced each of the three BFECC advection steps with a simple first order accurate unconditionally stable semi-Lagrangian method yielding a second order accurate unconditionally stable BFECC scheme. We use a similar approach to create a second order accurate unconditionally stable MacCormack method.
Multiple interacting liquids
- ACM Trans. Graph
, 2006
"... Copyright © 2006 by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for commercial advantage and that copies bear this notice and ..."
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Cited by 61 (6 self)
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Copyright © 2006 by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for 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, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee.
Glift: Generic, efficient, random-access GPU data structures
- IN PROC. OF SIGGRAPH ’05
, 2005
"... This paper presents Glift, an abstraction and generic template library for defining complex, random-access graphics processor (GPU) data structures. Like modern CPU data structure libraries, Glift enables GPU programmers to separate algorithms from data structure definitions; thereby greatly simplif ..."
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Cited by 61 (7 self)
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This paper presents Glift, an abstraction and generic template library for defining complex, random-access graphics processor (GPU) data structures. Like modern CPU data structure libraries, Glift enables GPU programmers to separate algorithms from data structure definitions; thereby greatly simplifying algorithmic development and enabling reusable and interchangeable data structures. We characterize a large body of previously published GPU data structures in terms of our abstraction and present several new GPU data structures. The structures, a stack, quadtree, and octree, are explained using simple Glift concepts and implemented using reusable Glift components. We also describe two applications of these structures not previously demonstrated on GPUs: adaptive shadow maps and octree 3D paint. Lastly, we show that our example Glift data structures perform comparably to handwritten implementations while requiring only a fraction of the programming effort.
Animating Gases with Hybrid Meshes
, 2005
"... This paper presents a method for animating gases on unstructured tetrahedral meshes to efficiently model the interaction of fluids with irregularly shaped obstacles. Because our discretization scheme parallels that of the standard staggered grid mesh, we are able to combine tetrahedral cells with re ..."
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Cited by 57 (2 self)
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This paper presents a method for animating gases on unstructured tetrahedral meshes to efficiently model the interaction of fluids with irregularly shaped obstacles. Because our discretization scheme parallels that of the standard staggered grid mesh, we are able to combine tetrahedral cells with regular hexahedral cells in a single mesh. This hybrid mesh offers both accuracy near obstacles and efficiency in open regions.
An accurate adaptive solver for surface-tension-driven interfacial flows
- Journal of Computational Physics
, 2009
"... flows ..."
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Hierarchical RLE level set: A compact and versatile deformable surface representation
, 2006
"... This article introduces the Hierarchical Run-Length Encoded (H-RLE) Level Set data structure. This novel data structure combines the best features of the DT-Grid (of Nielsen and Museth [2004]) and the RLE Sparse Level Set (of Houston et al. [2004]) to provide both optimal efficiency and extreme vers ..."
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Cited by 49 (9 self)
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This article introduces the Hierarchical Run-Length Encoded (H-RLE) Level Set data structure. This novel data structure combines the best features of the DT-Grid (of Nielsen and Museth [2004]) and the RLE Sparse Level Set (of Houston et al. [2004]) to provide both optimal efficiency and extreme versatility. In brief, the H-RLE level set employs an RLE in a dimensionally recursive fashion. The RLE scheme allows the compact storage of sequential nonnarrowband regions while the dimensionally recursive encoding along each axis efficiently compacts nonnarrowband planes and volumes. Consequently, this new structure can store and process level sets with effective voxel resolutions exceeding 500030003000 (45 billion voxels) on commodity PCs with only 1 GB of memory. This article, besides introducing the H-RLE level set data structure and its efficient core algorithms, also describes numerous applications that have benefited from our use of this structure: our unified implicit object representation, efficient and robust mesh to level set conversion, rapid ray tracing, level set metamorphosis, collision detection, and fully sparse fluid simulation (including RLE vector and matrix representations.) Our comparisons of the popular octree level set and Peng level set structures to the H-RLE level set indicate that the latter is superior in both narrowband sequential access speed and overall memory usage
