research-article

A novel discretization and numerical solver for non-fourier diffusion

Authors:

Chengguizi Han,

Chenfanfu Jiang,

Mridul AanjaneyaAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 39, Issue 6

Article No.: 178, Pages 1 - 14

https://doi.org/10.1145/3414685.3417863

Published: 27 November 2020 Publication History

Abstract

We introduce the C-F diffusion model [Anderson and Tamma 2006; Xue et al. 2018] to computer graphics for diffusion-driven problems that has several attractive properties: (a) it fundamentally explains diffusion from the perspective of the non-equilibrium statistical mechanical Boltzmann Transport Equation, (b) it allows for a finite propagation speed for diffusion, in contrast to the widely employed Fick's/Fourier's law, and (c) it can capture some of the most characteristic visual aspects of diffusion-driven physics, such as hydrogel swelling, limited diffusive domain for smoke flow, snowflake and dendrite formation, that span from Fourier-type to non-Fourier-type diffusive phenomena. We propose a unified convection-diffusion formulation using this model that treats both the diffusive quantity and its associated flux as the primary unknowns, and that recovers the traditional Fourier-type diffusion as a limiting case. We design a novel semi-implicit discretization for this formulation on staggered MAC grids and a geometric Multigrid-preconditioned Conjugate Gradients solver for efficient numerical solution. To highlight the efficacy of our method, we demonstrate end-to-end examples of elastic porous media simulated with the Material Point Method (MPM), and diffusion-driven Eulerian incompressible fluids.

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Cited By

Wu TXue TZhang X(2025)Thermal contact analysis of cracked through-silicon via structures in integrated circuitsInternational Journal of Heat and Mass Transfer10.1016/j.ijheatmasstransfer.2024.126576239(126576)Online publication date: Apr-2025
https://doi.org/10.1016/j.ijheatmasstransfer.2024.126576
Tu ZLi CZhao ZLiu LWang CWang CQin H(2024)A Unified MPM Framework Supporting Phase-field Models and Elastic-viscoplastic Phase TransitionACM Transactions on Graphics10.1145/363804743:2(1-19)Online publication date: 3-Jan-2024
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Xue TZhang X(2024)Stabilized state-based peridynamics for elasticity emanating from constrained LagrangianEuropean Journal of Mechanics - A/Solids10.1016/j.euromechsol.2023.105127103(105127)Online publication date: Jan-2024
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Index Terms

A novel discretization and numerical solver for non-fourier diffusion
1. Computing methodologies
  1. Computer graphics
    1. Animation
      1. Physical simulation

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 39, Issue 6

December 2020

1605 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/3414685

Editor:
Karol Myszkowski
MPI Informatik

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Copyright © 2020 ACM.

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Published: 27 November 2020

Published in TOG Volume 39, Issue 6

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Cited By

Wu TXue TZhang X(2025)Thermal contact analysis of cracked through-silicon via structures in integrated circuitsInternational Journal of Heat and Mass Transfer10.1016/j.ijheatmasstransfer.2024.126576239(126576)Online publication date: Apr-2025
https://doi.org/10.1016/j.ijheatmasstransfer.2024.126576
Tu ZLi CZhao ZLiu LWang CWang CQin H(2024)A Unified MPM Framework Supporting Phase-field Models and Elastic-viscoplastic Phase TransitionACM Transactions on Graphics10.1145/363804743:2(1-19)Online publication date: 3-Jan-2024
https://dl.acm.org/doi/10.1145/3638047
Xue TZhang X(2024)Stabilized state-based peridynamics for elasticity emanating from constrained LagrangianEuropean Journal of Mechanics - A/Solids10.1016/j.euromechsol.2023.105127103(105127)Online publication date: Jan-2024
https://doi.org/10.1016/j.euromechsol.2023.105127
Wang XXu YLiu SRen BKosinka JTelea AWang JSong CChang JLi CZhang JBan X(2024)Physics-based fluid simulation in computer graphics: Survey, research trends, and challengesComputational Visual Media10.1007/s41095-023-0368-y10:5(803-858)Online publication date: 27-Apr-2024
https://doi.org/10.1007/s41095-023-0368-y
Su HLi XXue TJiang CAanjaneya M(2023)A Generalized Constitutive Model for Versatile MPM Simulation and Inverse Learning with Differentiable PhysicsProceedings of the ACM on Computer Graphics and Interactive Techniques10.1145/36069256:3(1-20)Online publication date: 24-Aug-2023
https://dl.acm.org/doi/10.1145/3606925
Xue TZhang X(2023)A highly efficient semi-implicit two-field modeling for thermal contact problems with non-Fourier effectsInternational Communications in Heat and Mass Transfer10.1016/j.icheatmasstransfer.2023.106924146(106924)Online publication date: Jul-2023
https://doi.org/10.1016/j.icheatmasstransfer.2023.106924
Su HXue THan CAanjaneya M(2022) A ‐ULMPM: An Adaptively Updated Lagrangian Material Point Method for Efficient Physics Simulation without Numerical Fracture Computer Graphics Forum10.1111/cgf.1447741:2(325-341)Online publication date: 24-May-2022
https://doi.org/10.1111/cgf.14477
Herrera JHädrich TPałubicki WBanuti DPirk SMichels D(2021)WeatherscapesACM Transactions on Graphics10.1145/3478513.348053240:6(1-19)Online publication date: 10-Dec-2021
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Su HXue THan CJiang CAanjaneya M(2021)A unified second-order accurate in time MPM formulation for simulating viscoelastic liquids with phase changeACM Transactions on Graphics10.1145/3450626.345982040:4(1-18)Online publication date: 19-Jul-2021
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Han CXue TAanjaneya M(2021)A Lagrangian Particle‐based Formulation for Coupled Simulation of Fracture and Diffusion in Thin MembranesComputer Graphics Forum10.1111/cgf.1440440:7(97-108)Online publication date: 27-Nov-2021
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