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An operator splitting algorithm for the three‐dimensional advection–diffusion equation
Author(s) -
Khan Liaqat Ali,
Liu Philip L.F.
Publication year - 1998
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/(sici)1097-0363(19980915)28:3<461::aid-fld723>3.0.co;2-h
Subject(s) - advection , convection–diffusion equation , mathematics , interpolation (computer graphics) , diffusion , algorithm , operator (biology) , diffusion equation , computation , hermite interpolation , hermite polynomials , numerical diffusion , mathematical analysis , computer science , physics , mechanics , biochemistry , chemistry , economy , repressor , transcription factor , gene , economics , thermodynamics , service (business) , animation , computer graphics (images)
Operator splitting algorithms are frequently used for solving the advection–diffusion equation, especially to deal with advection dominated transport problems. In this paper an operator splitting algorithm for the three‐dimensional advection–diffusion equation is presented. The algorithm represents a second‐order‐accurate adaptation of the Holly and Preissmann scheme for three‐dimensional problems. The governing equation is split into an advection equation and a diffusion equation, and they are solved by a backward method of characteristics and a finite element method, respectively. The Hermite interpolation function is used for interpolation of concentration in the advection step. The spatial gradients of concentration in the Hermite interpolation are obtained by solving equations for concentration gradients in the advection step. To make the composite algorithm efficient, only three equations for first‐order concentration derivatives are solved in the diffusion step of computation. The higher‐order spatial concentration gradients, necessary to advance the solution in a computational cycle, are obtained by numerical differentiations based on the available information. The simulation characteristics and accuracy of the proposed algorithm are demonstrated by several advection dominated transport problems. © 1998 John Wiley & Sons, Ltd.