An entropy stable finite volume scheme for the two dimensional Navier–Stokes equations on triangular grids

摘要

We construct a finite volume scheme for the compressible Navier–Stokes equations on triangular grids which are entropy stable at the semi-discrete level. This is achieved by using entropy stable inviscid fluxes constructed in the recently published work titled Entropy Stable Scheme on Two-Dimensional Unstructured Grids for Euler Equations by Ray, Chandrashekar, Fjordholm and Mishra, (2016), and computing viscous fluxes in terms of entropy variables. Wall boundary conditions are also constructed to be entropy stable and are imposed in a weak manner. The resulting scheme is applied to solve several standard viscous test cases, such as flow over a flat-plat, flow past a NACA-0012 airfoil and unsteady flow past a cylinder, to demonstrate its stability and accuracy.