By R.D. Richtmyer

ISBN-10: 3540071393

ISBN-13: 9783540071396

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**Additional resources for 4th Int'l Conference on Numerical Methods in Fluid Dynamics**

**Example text**

The obtained Lax-Wendroff scheme, on the other hand, is more accurate in smooth parts of the solution, but near discontinuities, numerical dispersion generates oscillations also reducing the accuracy. A successful approach to suppress these oscillations is to apply flux limiters [LeVeque (1997); LeVeque (1998); Fogarthy and LeVeque (1999); Langseth and LeVeque (2000)]. 5 Conservative wave propagation algorithm Another possibility to increase the accuracy on smooth solutions is conservative wave propagation algorithm [Bale et al.

1) The entropy maximum postulate yields that the hyper-surface S = S(U, V, M ) in the thermodynamic configuration space should have the property that it lies everywhere below its tangent planes. 3) U,M and ∂2S ∂2S − ∂U 2 ∂V 2 ∂2S ∂U ∂V 2 ≥ 0. 4) April 17, 2008 10:42 World Scientific Book - 9in x 6in BerEngMaug Local Phase Equilibrium and Jump Relations at Moving Discontinuities 33 The stability criteria can be reformulated in the energy representation U = U (S, V, M ). Whereas the entropy is maximum, the energy is minimum; thus the concavity of the entropy surface is replaced by convexity of energy surface.

93) where the scalar driving force fS is introduced fS = −[W − N · T · (F · N)]. 67) are fulfilled; no hypothesis of small strain or quasi-statics has been envisaged [Maugin (2000)]. 96) F F is the deformation gradient, T is the first Piola-Kirchhoff stress tensor, L = K−W is the Lagrangian density of energy per unit reference volume, K is the kinetic energy density, and S is the entropy density per unit reference volume. Here (in thermoelasticity), b satisfies the equation of balance of pseudomomentum (we discard material inhomogeneities and external body forces for the sake of simplicity; cf.

### 4th Int'l Conference on Numerical Methods in Fluid Dynamics by R.D. Richtmyer

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