By Fayssal Benkhaldoun, Roland Vilsmeier

Benkhaldoun F., Vilsmeier R. (eds.) Finite Volumes for complicated functions II (Hermes technology guides, 1999)(ISBN 2746200570)

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**Extra info for Finite Volumes for Complex Applications II**

**Example text**

We indeed have : P r o p o s i t i o n 2. z) The first order system (6) is hyperbolic in the phase space R and A ( u ) : R + M ~ ~ ( R admits P) the following three real eigenvalues : v - c, v , v + c, c2 = ( y p + yepe)lp, (14) + + where the eigenvalue v has an order of multiplicity ( n n v 1). i i ) Under standard thermodynamic assumptions, the fields associated with the eigenualues v f c are genuinely nonlinear. iii) The fields associated with the eigenvalue u are linearly degenerate. Their Riemann invariants are given by v and ( P ~ e ) .

H. I. Accurate Solution Algorithms for Incompressible Flows, 33rd Aerospace Sciences Meeting and Exhibit, January 9-12, 1995, Reno, NV [Rid 95/2 Rider and W. , Kothe, Stretching and Tearing Interface Tracking Methods, 12th AIAA CFD Conference, June 20, 1995, San Diego. Paper number AIAA-95-1717 [Rid 981 Rider, W. J . and Kothe, D. , Reconstructing Volume Tracking, Journal of Computational Physics, 141, 112-152, 1998 [Sch 981 Schneider, T, Botta, N , Geratz, K. J . html [Set 961 Sethian, J. , Smereka, P.

COT= cpi + aTf, where a? 2. Hyperbolic systems Considering now the non-commuting linear hyperbolic system the formal extension of the residual distribution discretization (3) is xi where the fluctuation @T is now a vector whose expression is aT= KiUi with Ki being now an inflow matrix expressed as Ki = Atni,e,and where is a distribution matrix. The design criteria for distribution matrices are the same as for distributioncoefficients for the scalar advection equation, plus the additional requirement of invariance under a similarity transformation, i.