A novel discretization and numerical solver for non-fourier diffusion

Tao Xue, Haozhe Su, Chengguizi Han, Chenfanfu Jiang, Mridul Aanjaneya

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Article number178
JournalACM Transactions on Graphics
Volume39
Issue number6
DOIs
StatePublished - Nov 26 2020

All Science Journal Classification (ASJC) codes

  • Computer Graphics and Computer-Aided Design

Keywords

  • C-F diffusion
  • MPM
  • convection-diffusion
  • fick's law
  • incompressble flow
  • multigrid solver
  • non-fourier

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