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Compact finite volume methods for the diffusion equationAn approach to treating initial-boundary value problems by finite volume methods is described, in which the parallel between differential and difference arguments is closely maintained. By using intrinsic geometrical properties of the volume elements, it is possible to describe discrete versions of the div, curl, and grad operators which lead, using summation-by-parts techniques, to familiar energy equations as well as the div curl = 0 and curl grad = 0 identities. For the diffusion equation, these operators describe compact schemes whose convergence is assured by the energy equations and which yield both the potential and the flux vector with second order accuracy. A simplified potential form is especially useful for obtaining numerical results by multigrid and alternating direction implicit (ADI) methods. The treatment of general curvilinear coordinates is shown to result from a specialization of these general results.
Document ID
19900012252
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Rose, Milton E. (North Carolina Agricultural and Technical State Univ. Greensboro, NC, United States)
Date Acquired
September 6, 2013
Publication Date
September 16, 1989
Subject Category
Numerical Analysis
Report/Patent Number
NAS 1.26:186477
NASA-CR-186477
JCP-4406
Accession Number
90N21568
Funding Number(s)
CONTRACT_GRANT: NAG1-812
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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