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Consistent shepard interpolation for SPH-based fluid animation

Published: 08 November 2019 Publication History

Abstract

We present a novel technique to correct errors introduced by the discretization of a fluid body when animating it with smoothed particle hydrodynamics (SPH). Our approach is based on the Shepard correction, which reduces the interpolation errors from irregularly spaced data. With Shepard correction, the smoothing kernel function is normalized using the weighted sum of the kernel function values in the neighborhood. To compute the correction factor, densities of neighboring particles are needed, which themselves are computed with the uncorrected kernel. This results in an inconsistent formulation and an error-prone correction of the kernel. As a consequence, the density computation may be inaccurate, thus the pressure forces are erroneous and may cause instabilities in the simulation process. We present a consistent formulation by using the corrected densities to compute the exact kernel correction factor and, thereby, increase the accuracy of the simulation. Employing our method, a smooth density distribution is achieved, i.e., the noise in the density field is reduced by orders of magnitude. To show that our method is independent of the SPH variant, we evaluate our technique on weakly compressible SPH and on divergence-free SPH. Incorporating the corrected density into the correction process, the problem cannot be stated explicitly anymore. We propose an efficient and easy-to-implement algorithm to solve the implicit problem by applying the power method. Additionally, we demonstrate how our model can be applied to improve the density distribution on rigid bodies when using a well-known rigid-fluid coupling approach.

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  • (2022)The power particle-in-cell methodACM Transactions on Graphics10.1145/3528223.353006641:4(1-13)Online publication date: 22-Jul-2022
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cover image ACM Transactions on Graphics
ACM Transactions on Graphics  Volume 38, Issue 6
December 2019
1292 pages
ISSN:0730-0301
EISSN:1557-7368
DOI:10.1145/3355089
Issue’s Table of Contents
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 the author(s) 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 [email protected].

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Publication History

Published: 08 November 2019
Published in TOG Volume 38, Issue 6

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Author Tags

  1. physically based animation
  2. smoothed particle hydrodynamics

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Cited By

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  • (2024)A Dual-Particle Approach for Incompressible SPH FluidsACM Transactions on Graphics10.1145/364988843:3(1-18)Online publication date: 9-Apr-2024
  • (2023)A comparison of linear consistent correction methods for first-order SPH derivativesProceedings of the ACM on Computer Graphics and Interactive Techniques10.1145/36069336:3(1-20)Online publication date: 24-Aug-2023
  • (2022)The power particle-in-cell methodACM Transactions on Graphics10.1145/3528223.353006641:4(1-13)Online publication date: 22-Jul-2022
  • (2021)Fast Corotated Elastic SPH Solids with Implicit Zero-Energy Mode ControlProceedings of the ACM on Computer Graphics and Interactive Techniques10.1145/34801424:3(1-21)Online publication date: 27-Sep-2021
  • (2021)Two‐step Temporal Interpolation Network Using Forward Advection for Efficient Smoke SimulationComputer Graphics Forum10.1111/cgf.14263840:2(355-365)Online publication date: 4-Jun-2021
  • (2020)A moving least square reproducing kernel particle method for unified multiphase continuum simulationACM Transactions on Graphics10.1145/3414685.341780939:6(1-15)Online publication date: 27-Nov-2020
  • (2020)Efficient 2D simulation on moving 3D surfacesProceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation10.1111/cgf.14098(1-12)Online publication date: 6-Oct-2020
  • (2019)Numerical Linear Algebra for physically-based Fluid AnimationsSIGGRAPH Asia 2019 Doctoral Consortium10.1145/3366344.3366445(1-4)Online publication date: 17-Nov-2019

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