A Cartesian Grid Finite-Volume Method for the Advection-Diffusion Equation in Irregular Geometries

We present a fully conservative, high-resolution, finite volume algorithm for advection-diffusion equations in irregular geometries. The algorithm uses a Cartesian grid in which some cells are cut by the embedded boundary. A novel feature is the use of a “capacity function” to model the fact that so...

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Bibliographic Details
Published in:Journal of computational physics Vol. 157; no. 1; pp. 143 - 180
Main Authors: Calhoun, Donna, LeVeque, Randall J.
Format: Journal Article
Language:English
Published: United States Elsevier Inc 01.01.2000
Subjects:
ADVECTION
ALGORITHMS
CARTESIAN COORDINATES
CONVERGENCE
DIFFUSION
ENGINEERING
FINITE ELEMENT METHOD
GEOMETRY
MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
MESH GENERATION
Finite-volume
advection-diffusion
Cartesian grid
software
embedded boundary
high-resolution
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary:We present a fully conservative, high-resolution, finite volume algorithm for advection-diffusion equations in irregular geometries. The algorithm uses a Cartesian grid in which some cells are cut by the embedded boundary. A novel feature is the use of a “capacity function” to model the fact that some cells are only partially available to the fluid. The advection portion then uses the explicit wave-propagation methods implemented in CLAWPACK, and is stable for Courant numbers up to 1. Diffusion is modelled with an implicit finite-volume algorithm. Results are shown for several geometries. Convergence is verified and the 1-norm order of accuracy is found to between 1.2 and 2 depending on the geometry and Peclet number. Software is available on the web.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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USDOE
FG03-96ER25292
National Science Foundation (NSF)
ISSN:0021-9991
1090-2716
DOI:10.1006/jcph.1999.6369