ON THE RELATION BETWEEN THE ENTROPY BALANCE AND THE NUMERICAL-SOLUTIONS OF SYSTEMS OF CONSERVATION-LAWS

This work deals with the relation between the numerical solutions of h yperbolic systems of conservation laws and the associated entropy evol ution. An analysis of the continuum problem by means of variational ca lculus clearly emphasizes the consequences of the adopted reconstructi on procedure on the induced entropy balance. A methodology is proposed that allows for a posteriori local and global spurious entropy produc tion estimates on the basis of an additional equation representing a d iscrete approximation to the entropy inequality. The problem of defini ng a consistent approximation of the numerical entropy flux is also ad dressed in detail. Properly designed numerical experiments support the analysis and contribute to providing a more comprehensive evaluation of the numerical entropy dynamics. (C) 1997 John Wiley & Sons, Ltd.