Abstract: In this work a detailed study of the numerical entropy production for both low and high order central schemes is carried out. Our data suggest that the 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 behaviour of the local error, and therefore it can be used as an a posteriori error indicator. 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 behaviour of such high order schemes.
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