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An analysis of finite-difference and finite-volume formulations of conservation lawsFinite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.
Document ID
19890047284
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Vinokur, Marcel
(Sterling Software, Inc. Palo Alto, CA, United States)
Date Acquired
August 14, 2013
Publication Date
March 1, 1989
Publication Information
Publication: Journal of Computational Physics
Volume: 81
ISSN: 0021-9991
Subject Category
Numerical Analysis
Accession Number
89A34655
Funding Number(s)
CONTRACT_GRANT: NCC2-16
CONTRACT_GRANT: NAS2-11555
Distribution Limits
Public
Copyright
Other

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