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On the relation between the entropy balance and the numerical solutions of systems of conservation laws
Author(s) -
Grasso F.,
Manna M.,
Meola C.,
Pascarelli A.
Publication year - 1997
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19971015)25:7<825::aid-fld588>3.0.co;2-n
Subject(s) - conservation law , mathematics , entropy (arrow of time) , entropy production , spurious relationship , numerical analysis , maximum entropy thermodynamics , statistical physics , principle of maximum entropy , binary entropy function , mathematical optimization , mathematical analysis , calculus (dental) , physics , medicine , statistics , dentistry , quantum mechanics
This work deals with the relation between the numerical solutions of hyperbolic systems of conservation laws and the associated entropy evolution. An analysis of the continuum problem by means of variational calculus clearly emphasizes the consequences of the adopted reconstruction procedure on the induced entropy balance. A methodology is proposed that allows for a posterior local and global spurious entropy production estimates on the basis of an additional equation representing a discrete approximation to the entropy inequality. The problem of defining a consistent approximation of the numerical entropy flux is also addressed in detail. Properly designed numerical experiments support the analysis and contribute to providing a more comprehensive evaluation of the numerical entropy dynamics. © 1997 John Wiley & Sons, Ltd.