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Simulation of anisotropic diffusion processes in fluids with smoothed particle hydrodynamics
Author(s) -
TranDuc Thien,
Bertevas Erwan,
PhanThien Nhan,
Khoo Boo Cheong
Publication year - 2016
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4238
Subject(s) - isotropy , anisotropy , discretization , smoothed particle hydrodynamics , anisotropic diffusion , diffusion , coordinate system , classical mechanics , physics , scaling , tensor (intrinsic definition) , mathematical analysis , statistical physics , mathematics , geometry , mechanics , optics , thermodynamics
Summary Anisotropic diffusion phenomenon in fluids is simulated using smoothed particle hydrodynamics (SPH). A new SPH approximation for diffusion operator, named anisotropic SPH approximation for anisotropic diffusion (ASPHAD), is derived. Basic idea of the derivation is that anisotropic diffusion operator is first approximated by an integral in a coordinate system in which it is isotropic. The coordinate transformation is a combination of a coordinate rotation and a scaling in accordance with diffusion tensor. Then, inverse coordinate transformation and particle discretization are applied to the integral to achieve ASPHAD. Noting that weight function used in the integral approximation has anisotropic smoothing length, which becomes isotropic under the inverse transformation. ASPHAD is general and unique for both isotropic and anisotropic diffusions with either constant or variable diffusing coefficients. ASPHAD was numerically examined in some cases of isotropic and anisotropic diffusions of a contaminant in fluid, and the simulation results are very consistent with corresponding analytical solutions. Copyright © 2016 John Wiley & Sons, Ltd.