# Eigenvalues and Eigenvectors for 3-D TVD Finite Volume Solver

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 March 13, 2000, 15:01 Re: Eigenvalues and Eigenvectors for 3-D TVD Finite Volume Solver #2 Patrick Godon Guest   Posts: n/a Hi Axel, There is a series of (3-three) papers of J.S. Hestaven and David Gottlieb in SIAM journal of Scientific Computing about a method for the compressible Navier-Stokes equations in general curvilinear system of coordinates. There they treat the boundary conditions on the characteristics of the flow, and therefore they have to linearize the equations and solve the eigenvalues and eigenvectors of the system (characteristics) in a general system of coordinates (like yours). This is similar to what you are talking about. The references I have are as follows: J. S. Hesthaven and D. Gottlieb, 1996, SIAM J. Sci. Comput. vol.17, no.3, p.579 ("A stable penalty method for the compressible NS eqs: I. Open boundary conditions"). J. S. Hesthaven, (preprint) - probably 1996 or 1997 in SIAM J. Sci.Comput., ("A stable penatly...: II. One dimensional domain decomposition schemes"). J. S. Hesthaven (preprint) 1997(?), in SIAM J. Sci. Comput. , ("A stable ..: III multidimensional domain decomposition schemes"). PG

 March 14, 2000, 04:06 Re: Eigenvalues and Eigenvectors for 3-D TVD Finite Volume Solver #3 B O Bamkole Guest   Posts: n/a See the papers by Peter A. Gnoffo describing Program LAURA (LANGLEY AEROTHERMODYNAMIC UPWIND RELAXATION ALGORITHM). He gives the eigenvalues/eigenvectors not only for the flow of perfect gases but chemically-reacting flows. 1. For Perfect gases, see Gnoffo, P.A " An Upwind-Biased, Point Implicit Relaxation Algorithm for Viscous, Compressible Perfect Gas Flows", NASA TP-2953, 1990. This probably has more than you need as he also gives a form for the viscous matrices. 2. In case U are interested for chemically-reacting flows see F. M Cheatwood, & Gnoffo, P.A "User's manual for the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) " NASA TM 4674.

 April 2, 2000, 17:42 Re: Eigenvalues and Eigenvectors for 3-D TVD Finite Volume Solver #4 Chih-Hao Chang Guest   Posts: n/a A general form of this eigensystem can be found in Vinokur, M., "An Analysis of Finite-Difference and Finite- Volume formulation of Conservation Laws," Journal of Computational Physics, Vol. 81, pp.1-52, 1989