Browsing by Author "Batty, Christopher"

Now showing 1 - 5 of 5
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    Divergence-Free and Boundary-Respecting Velocity Interpolation Using Stream Functions
    (ACM, 2019) Chang, Jumyung; Azevedo, Vinicius C.; Batty, Christopher; Batty, Christopher and Huang, Jin
    In grid-based fluid simulation, discrete incompressibility of each cell is enforced by the pressure projection. However, pointwise velocities constructed by interpolating the discrete velocity samples from the staggered grid are not truly divergence-free, resulting in unphysical local volume changes that manifests as particle spreading and clustering.We present a new velocity interpolation method that produces analytically divergence-free velocity fields in 2D using a stream function. The resulting fields are guaranteed to be divergence-free by a simple calculus identity: the curl of any vector field yields a divergence-free vector field. Furthermore, our method works on cut cell grids to produce fields that strictly obey solid boundary conditions. Therefore, no artificial gaps are created between fluid particles and solids, and fluid particles do not trespass into solid regions.
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    Efficient Unified Stokes using a Polynomial Reduced Fluid Model
    (The Eurographics Association, 2020) Panuelos, Jonathan; Goldade, Ryan; Batty, Christopher; Michels, Dominik L.
    Unsteady Stokes solvers, coupling stress and pressure forces, are a key component of accurate free surface simulators for highly viscous fluids. Because of the simultaneous application of stress and pressure terms, this creates a much larger system than the standard decoupled approach. We propose a reduced fluid model wherein interior regions are represented with incompressible polynomial vector fields. Sets of standard grid cells are consolidated into super-cells, each of which are modelled using only 26 degrees of freedom. This reduced model retains desirable behaviour of the full Stokes system with smaller computational cost.
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    Fast and Scalable Solvers for the Fluid Pressure Equations with Separating Solid Boundary Conditions
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Lai, Junyu; Chen, Yangang; Gu, Yu; Batty, Christopher; Wan, Justin W. L.; Panozzo, Daniele and Assarsson, Ulf
    In this paper, we propose and evaluate fast, scalable approaches for solving the linear complementarity problems (LCP) arising from the fluid pressure equations with separating solid boundary conditions. Specifically, we present a policy iteration method, a penalty method, and a modified multigrid method, and demonstrate that each is able to properly handle the desired boundary conditions. Moreover, we compare our proposed methods against existing approaches and show that our solvers are more efficient and exhibit better scaling behavior; that is, the number of iterations required for convergence is essentially independent of grid resolution, and thus they are faster at larger grid resolutions. For example, on a 256 grid our multigrid method was 30 times faster than the prior multigrid method in the literature.
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    A Multilevel Active-Set Preconditioner for Box-Constrained Pressure Poisson Solvers
    (ACM Association for Computing Machinery, 2023) Takahashi, Tetsuya; Batty, Christopher; Wang, Huamin; Ye, Yuting; Victor Zordan
    Efficiently solving large-scale box-constrained convex quadratic programs (QPs) is an important computational challenge in physical simulation.We propose a new multilevel preconditioning scheme based on the active-set method and combine it with modified proportioning with reduced gradient projections (MPRGP) to efficiently solve such QPs arising from pressure Poisson equations with non-negative pressure constraints in fluid animation. Our method employs a purely algebraic multigrid method to ensure the solvability of the coarser level systems and to merge only algebraically-connected components, thereby avoiding performance degradation of the preconditioner. We present a filtering scheme to efficiently apply our multilevel preconditioning only to unconstrained subsystems of the pressure Poisson system while reusing the hierarchy constructed per simulation step. We demonstrate the effectiveness of our method over previous approaches in various examples.
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    Surface-Only Dynamic Deformables using a Boundary Element Method
    (The Eurographics Association and John Wiley & Sons Ltd., 2022) Sugimoto, Ryusuke; Batty, Christopher; Hachisuka, Toshiya; Dominik L. Michels; Soeren Pirk
    We propose a novel surface-only method for simulating dynamic deformables without the need for volumetric meshing or volumetric integral evaluations. While based upon a boundary element method (BEM) for linear elastodynamics, our method goes beyond simple adoption of BEM by addressing several of its key limitations. We alleviate large displacement artifacts due to linear elasticity by extending BEM with a moving reference frame and surface-only fictitious forces, so that it only needs to handle deformations. To reduce memory and computational costs, we present a simple and practical method to compress the series of dense matrices required to simulate propagation of elastic waves over time. Furthermore, we explore a constraint enforcement mechanism and demonstrate the applicability of our method to general computer animation problems, such as frictional contact.