Reynolds averaged navier-stokes flow computation of RAE2822 airfoil using gas-kinetic BGK Scheme - Ong, Jiunn Chit; Omar, Ashraf Ali E.; Asrar, Waqar (2009)
In this paper, a gas-kinetic solver is developed to solve Reynolds Averaged Navier-Stokes (RANS) equations in two-space dimensions generalized coordinates. The convection flux terms which appear on the left hand side of the RANS equations are discretized by a semi-discrete finite difference method. Then, the resulting inviscid flux functions are approximated by gas-kinetic BGK scheme which is based on the BGK model of the approximate collisional Boltzmann equation. The cell interface values required by the inviscid flux functions are reconstructed to second-order spatial accuracy via the MUSCL (Monotone Upstream-Centered Schemes for Conservation Laws) variable interpolation method coupled with a minmod limiter. As for the diffusion flux terms, they are discretized by a second-order central difference scheme. To account for the turbulence effect, a combined k-ε / k-ω SST (Shear-Stress Transport) two-equation turbulence model is used in the solver. An explicit-type time integration method known as the modified fourth-order Runge-Kutta method is used to march the solution to steady-state. Computation over the RAE2822 airfoil flow corresponding to transonic speed has been solved using the developed gas-kinetic solver. Accuracy of BGK scheme in solving viscous transonic turbulent flow over the airfoil will be examined. Results obtained from the computations are also compared with experimental data and will demonstrate that a very good agreement has been achieved.