A high-order computational method for the highly unsteady, complex vortical flows over delta wings is presented. A sixth-order compact difference scheme with an eighth-order low pass filter is used to solve the Navier-Stokes equations. Two approaches to turbulence modeling are investigated. The first scheme is an implicit LES (ILES) method which exploits the high-order accuracy of the compact difference scheme and uses the discriminating higher-order filter to regularize the flow. The second approach is a new hybrid RANS/ILES method which employs a standard k–ε model in regions where the grid resolution is unable to capture the turbulent behavior, and transitions to the ILES method in the vortical flow region where large scale turbulent structures are resolved. Computational simulations have been performed for a 50° sweep delta wing at 15° angle of attack and a moderate Reynolds number, Re = 2 × 106. Solutions employing the two turbulence models are evaluated on a baseline grid. A fine mesh computation has been performed for the ILES approach to investigate the impact of mesh resolution on this scheme. Computed results are also compared with the limited experimental measurements available. Computations exploring the control of the vortical flows above a swept delta wing by use of a dialectric-barrier-discharge actuator are also presented. With the actuator located near the apex, significant movement of the vortex breakdown location and a dramatic transformation of the shear-layer sub-structures are demonstrated.
High-Order Compact Difference Scheme and Multigrid Method for Solving the 2D Elliptic Problems
