An operator splitting algorithm for the three-dimensional advection-diffusion equation

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...

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Bibliographic Details
Published in:International journal for numerical methods in fluids Vol. 28; no. 3; pp. 461 - 476
Main Authors: Khan, Liaqat Ali, Liu, Philip L.-F.
Format: Journal Article
Language:English
Published: Sussex John Wiley & Sons, Ltd 15.09.1998
Wiley
Subjects:
advection-diffusion equation
Algorithms
Computational methods
Computational methods in fluid dynamics
Computer simulation
Differentiation (calculus)
Exact sciences and technology
Finite element method
Fluid dynamics
Functions
Fundamental areas of phenomenology (including applications)
Holly and Preissmann scheme
Interpolation
Mathematical operators
method of characteristics
operator splitting algorithm
Physics
Problem solving
Method of characteristics
Finite element method
Algorithms
Three dimensional flow
Computational fluid dynamics
Digital simulation
Operator splitting
Advection diffusion equation
Velocity distribution
Comparative study
ISSN:0271-2091, 1097-0363
Online Access:Get full text
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Summary: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.
Bibliography:ark:/67375/WNG-7V6PLPXL-3
ArticleID:FLD723
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ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0271-2091
1097-0363
DOI:10.1002/(SICI)1097-0363(19980915)28:3<461::AID-FLD723>3.0.CO;2-H