Constructing an Entropy-Stable Upwind Scheme for Compressible Fluid Flow Computations

A relationship between entropy processes and numerical upwinding is examined in the context of computational gasdynamics. A discretized form of the entropy inequality is constructed at the integration point where convection-diffusion modeling occurs in finite volume methods. Conventional upwinding schemes may violate the local form of the second law of thermodynamics, but a modified upwinding scheme uses additional momentum constraints and pressure terms to provide a positive entropy production rate. The second law is seen as an important quantitative measure of nonphysical numerical results, as well as a sound basis for error analysis. Applications to converging-diverging nozzle and blunt-body flow problems demonstrate the promising performance of the overall numerical algorithm

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