Numerical Entropy Production for Central Schemes

In this work a detailed study of the numerical entropy production for both low- and high-order central schemes is carried out. Our data show that entropy production can be used to signal the presence of shocks. Moreover, once shocked cells have been identified, the spurious entropy production occurring in the remaining cells mimics the behavior of the local error, and therefore it can be used as an a posteriori error indicator. Applications to shock tracking and scheme adaptivity are given. We also investigate numerically the entropic properties of third and fourth order Central WENO schemes. To our knowledge, this is the first study of the entropic behavior of such high-order schemes.