Multigrid computation of flow past airfoil using k-ε turbulence model

A method for calculating compressible turbulent flows around an airfoil is presented. A modified low-Reynolds-number k-ε turbulence mode is used in the method to predict turbulent flows. The model is incorporated in a Navier-Stokes flow solver that is based on the cell-centered finite-volume method and Runge-Kutta multistage time-stepping scheme. Linear upwinding is used to specify the far-field boundary conditions for the turbulence transport equations. A limited amount of nonlinear numerical dissipation is introduced to ensure stable and converged results, but care is taken to ensure that the artificial viscosity is much smaller than the physical viscosity. Multigrid algorithm, implicit residual smoothing and local time stepping are used to achieve faster convergence of numerical solutions. Computational results for flows around a NACA 0012 airfoil are presented and discussed. Pressure distribution on the airfoil surface is compared with the corresponding measurement and good agreement is observed. Techniques that are used for solving the k and ε equations for stable and fast convergence are also presented and discussed.