Weak-Strong uniqueness for compressible Navier-Stokes system with degenerate viscosity coefficient and vacuum in one dimension

We prove weak-strong uniqueness results for the compressible Navier-Stokes system with degenerate viscosity coefficient and with vacuum in one dimension. In other words, we give conditions on the weak solution constructed in \cite{Jiu} so that it is unique. The novelty consists in dealing with initial density $\rho_0$ which contains vacuum. To do this we use the notion of relative entropy developed recently by Germain, Feireisl et al and Mellet and Vasseur (see \cite{PG,Fei,15}) combined with a new formulation of the compressible system (\cite{cras,CPAM,CPAM1,para}) (more precisely we introduce a new effective velocity which makes the system parabolic on the density and hyperbolic on this velocity).Comment: arXiv admin note: text overlap with arXiv:1411.550

Transonic cascade flow calculations using non-periodic C-type grids

A new kind of C-type grid is proposed for turbomachinery flow calculations. This grid is nonperiodic on the wake and results in minimum skewness for cascades with high turning and large camber. Euler and Reynolds averaged Navier-Stokes equations are discretized on this type of grid using a finite volume approach. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. Jameson's explicit Runge-Kutta scheme is adopted for the integration in time, and computational efficiency is achieved through accelerating strategies such as multigriding and residual smoothing. A detailed numerical study was performed for a turbine rotor and for a vane. A grid dependence analysis is presented and the effect of artificial dissipation is also investigated. Comparison of calculations with experiments clearly demonstrates the advantage of the proposed grid