Unsteady Three-Dimensional Thin-Layer Navier Stokes Solutions on Dynamic Blocked Grids.

摘要

An efficient scheme for calculating steady and unsteady solutions on blocked grids for several airfoils and wings is presented. Two algorithms are presented, both of which are based on upwind, finite-volume, flux splitting for the convective terms, and an explicit treatment of the diffusive terms. The first algorithm is based on a flux difference split (FDS) scheme. The two algorithms are compared for steady thin-layer Navier-Stokes solutions on a laminar flat plate, RAE 2822 airfoil, and the ONERA M6 wing. The FDS scheme proved to be superior to the FVS in all cases, due to the excessive numerical dissipation in the FVS scheme. A flat plate laminar boundary layer profile is shown with the FDS scheme correctly modeling the boundary layer (compared to a Blasius solution) with only three grid cells internal to the boundary layer; the FVS scheme was not capable of correctly modeling the boundary layer profile. The FDS algorithm was used to evaluate the scheme for unsteady viscous calculations. The diffusive terms are time-lagged in the solution process and therefore are treated as source terms to the convective terms, which behave as a hyperbolic set of equations. The scheme is second order accurate in space and first order accurate in time due to the explicit treatment of the diffusive terms. A Newton subiteration technique was implemented to allow for larger time step sizes and second order temporal accuracy.