Implicit Formulation for SPH-based Viscous Fluids

Tetsuya Takahashi, Yoshinori Dobashi, Issei Fujishiro, Tomoyuki Nishita, Ming C. Lin

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

We propose a stable and efficient particle-based method for simulating highly viscous fluids that can generate coiling and buckling phenomena and handle variable viscosity. In contrast to previous methods that use explicit integration, our method uses an implicit formulation to improve the robustness of viscosity integration, therefore enabling use of larger time steps and higher viscosities. We use Smoothed Particle Hydrodynamics to solve the full form of viscosity, constructing a sparse linear system with a symmetric positive definite matrix, while exploiting the variational principle that automatically enforces the boundary condition on free surfaces. We also propose a new method for extracting coefficients of the matrix contributed by second-ring neighbor particles to efficiently solve the linear system using a conjugate gradient solver. Several examples demonstrate the robustness and efficiency of our implicit formulation over previous methods and illustrate the versatility of our method.

Original languageEnglish
Pages (from-to)493-502
Number of pages10
JournalComputer Graphics Forum
Volume34
Issue number2
DOIs
Publication statusPublished - 2015 May 1

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Viscosity
Fluids
Linear systems
Buckling
Hydrodynamics
Boundary conditions

ASJC Scopus subject areas

  • Computer Networks and Communications

Cite this

Takahashi, T., Dobashi, Y., Fujishiro, I., Nishita, T., & Lin, M. C. (2015). Implicit Formulation for SPH-based Viscous Fluids. Computer Graphics Forum, 34(2), 493-502. https://doi.org/10.1111/cgf.12578

Implicit Formulation for SPH-based Viscous Fluids. / Takahashi, Tetsuya; Dobashi, Yoshinori; Fujishiro, Issei; Nishita, Tomoyuki; Lin, Ming C.

In: Computer Graphics Forum, Vol. 34, No. 2, 01.05.2015, p. 493-502.

Research output: Contribution to journalArticle

Takahashi, T, Dobashi, Y, Fujishiro, I, Nishita, T & Lin, MC 2015, 'Implicit Formulation for SPH-based Viscous Fluids', Computer Graphics Forum, vol. 34, no. 2, pp. 493-502. https://doi.org/10.1111/cgf.12578
Takahashi, Tetsuya ; Dobashi, Yoshinori ; Fujishiro, Issei ; Nishita, Tomoyuki ; Lin, Ming C. / Implicit Formulation for SPH-based Viscous Fluids. In: Computer Graphics Forum. 2015 ; Vol. 34, No. 2. pp. 493-502.
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