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Congruence Approximations for Entrophy Endowed Hyperbolic SystemsBuilding upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.
Document ID
Document Type
Preprint (Draft being sent to journal)
Barth, Timothy J. (NASA Ames Research Center Moffett Field, CA United States)
Saini, Subhash
Date Acquired
August 20, 2013
Publication Date
January 1, 1998
Subject Category
Numerical Analysis
Funding Number(s)
PROJECT: RTOP 519-40-12
Distribution Limits
Work of the US Gov. Public Use Permitted.