An analysis of finite-difference and finite-volume formulations of conservation laws
type: Item
instance of: scholarly article
title: An analysis of finite-difference and finite-volume formulations of conservation laws
zbMATH Open document ID: 0662.76039
DOI: 10.1016/0021-9991(89)90063-6
author: Marcel Vinokur
published in: Journal of Computational Physics
publication date: 1989-01-01T00:00:00Z
full work available at URL: http://hdl.handle.net/2060/19880020687
review text: Finite-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.
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65N50
zbMATH DE Number: 4083192
zbMATH Keywords: finite-volume formulations
zbMATH Keywords: numerical solution of conservation laws
zbMATH Keywords: coordinate-free formulation
zbMATH Keywords: Navier-Stokes
zbMATH Keywords: Three-dimensional unsteady flows
zbMATH Keywords: time-varying grids
MaRDI profile type: Publication
OpenAlex ID: W2015861747
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description: scientific article; zbMATH DE number 4083192