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 nonphyscial numerical results, as well as a sound basis for error analysis. Applications to converging-diverging nozzle and blunt-body flow problems demonstarte the promising performance of the overall numerical algorithm.