Implicit weighted essentially nonoscillatory schemes for the compressible Navier-Stokes equations

A class of lower-upper symmetric Gauss-Seidel implicit weighted essentially nonoscillatory (ENO) schemes for solving the two- and three-dimensional compressible Navier-Stokes equations with pointwise version of Baldwin-Barth one-equation turbulence model is presented (Baldwin, B. S., and Barth, T. J., "A One-Equation Turbulence Transport Model for High Reynolds Number Wall Bounded Flows," AIAA Paper 91-0610,1991). A weighted ENO (WENO) spatial operator is employed for inviscid fluxes and central differencing for viscous fluxes. A numerical flux of the WENO scheme in flux limiter form is adopted, which consists of first-order and high-order fluxes and allows for a more flexible choice of first-order dissipative methods. The computations are performed for the two-dimensional turbulent flows over NACA 0012 and Royal Aircraft Establishment 2822 airfoil and the three-dimensional turbulent flow over an ONERA M6 wing. The present solutions are compared with experimental data and other computational results and exhibit good agreement.