An implicit upwind algorithm for computing turbulent flows on unstructured grids

Abstract

An implicit, Navier-Stokes solution algorithm is presented for the computation of turbulent flow on unstructured grids. The inviscid fluxes are computed using an upwind algorithm and the solution is advanced in time using a backward-Euler time-stepping scheme. At each time step, the linear system of equations is approximately solved with a point-implicit relaxation scheme. This methodology provides a viable and robust algorithm for computing turbulent flows on unstructured meshes. Results are shown for subsonic flow over a NACA 0012 airfoil and for transonic flow over an RAE 2822 airfoil exhibiting a strong upper-surface shock. In addition, results are shown for 3- and 4-element airfoil configurations. For the calculations, two 1-equation turbulence models are utilized. For the NACA 0012 airfoil a pressure distribution and force data are compared with other computational results as well as with the experiment. Comparisons of computed pressure distributions and velocity profiles with experimental data are shown for the RAE airfoil and for the 3-element configuration. For the 4-element case, comparisons of surface pressure distributions with the experiment are made. In general, the agreement between the computations and the experiment is good.