On the relation between the entropy balance and the numerical solutions of systems of conservation laws

✍ Scribed by F. Grasso; M. Manna; C. Meola; A. Pascarelli

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 319 KB
• Volume: 25
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/(sici)1097-0363(19971015)25:7<825::aid-fld588>3.0.co;2-n

✦ Synopsis

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 posteriori 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 de®ning a consistent approximation of the numerical entropy ¯ux 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.