A CCWENO-type High-order Entropy Stable Scheme for Navier-Stokes Equations at High Reynolds Numbers

In view of the oscillation problem that easily occurs during the numerical solution of compressible Navier–Stokes (N–S) equations at high Reynolds (Re) numbers, this paper constructs a high–order Compact Central Weighted Essentially Non–Oscillatory(CCWENO) type entropy–stable scheme. In the spatial direction, this scheme combines the high–order entropy– conservative flux with CCWENO–type reconstruction of the entropy variable in the dissipation term to construct the high–order entropy–stable flux. For the heat flux term and viscous term, a central scheme is adopted for discretization to achieve a low– dissipation effect, thus constructing the high–order numerical flux. Using the method of dimension–by–dimension extension, the scheme is successfully extended to the multi–dimensional case, and it is proven that the reconstructed high–order numerical scheme satisfies the entropy stability property. The good performance of the algorithm is verified through several numerical examples. The numerical results show that this scheme can accurately capture discontinuities, has high resolution and strong numerical stability for the N–S equations at high Re numbers.