A minimum entropy principle in the gas dynamics equations

Authors:
Eitan Tadmor
Affiliations:
School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, 69978 Tel-Aviv, Israel and Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, ...
Venue:
Applied Numerical Mathematics
Year:
1986

Citing 1
Cited 1

A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier—Stokes equations and the second law of thermodynamics

Computer Methods in Applied Mechanics and Engineering

A Local Entropy Minimum Principle for Deriving Entropy Preserving Schemes

SIAM Journal on Numerical Analysis

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Abstract

Let u(@?x, t) be a weak solution of the Euler equation, governing the inviscid polytropic gas dynamics; in addition, u(@?x, t) is assumed to respect the usual entropy conditions connected with the conservative Euler equations. We show that such entropy solutions of the gas dynamics equations satisfy a minimum entropy principle, namely, that the spatial minimum of their specific entropy, Ess inf"@?"xS(u(@?x, t)), is an increasing function of time. This principle equally applies to discrete approximations of the Euler equations such as the Godunov-type and Lax-Friedrichs schemes. Our derivation of this minimum principle makes use of the fact that there is a family of generalized entropy functions connected with the conservative Euler equations.