A Posteriori Error Estimation Based on Discrepancies in an Entropy Variable

Abstract Spurious entropy is often used as a criterion by which the accuracy of a numerical solution of the Euler equations may be judged. In the case of subcritical, compressible flows, we have been able to develop a mathematical theory relating the observed spurious entropy to its local generation. Moreover, the theory may be expressed in terms of the finite volume residual for the Euler equations and hence related to the theory of adaptive finite element methods. We have analysed the formula for the local generation of the spurious entropy and have shown it to be made up of terms of very simple form for which the effect of mesh quality can be assessed. In order to demonstrate the effectiveness of the theory in the context of adaptive grid generation, the local estimator is coupled with an existing mesh movement algorithm, with much improved results being obtained.