Effects of spatial order of accuracy on the computation of vortical flowfields

The effect of the order-of-accuracy, used for the spatial discretization, on the resolution of the leading edge vortices over sharp-edged delta wings is investigated. The flowfield is computed using a viscous/inviscid zonal approach. The viscous flow in the vicinity of the wing is computed using the conservative formulation of the compressible, thin-layer Navier-Stokes equations. The leeward-side vortical flowfield and the other flow regions away from the surface are computed as inviscid. The time integration is performed with both an explicit fourth-order Runge-Kutta scheme and an implicit, factorized, iterative scheme. High-order-accurate inviscid fluxes are computed using both a conservative and a non-conservative (primitive variable) formulation. The nonlinear, inviscid terms of the primitive variable form of the governing equations are evaluated with a finite-difference numerical scheme based on the sign of the eigenvalues. High-order, upwind-biased, finite difference formulas are used to evaluate the derivatives of the nonlinear convective terms. Computed results are compared with available experimental data, and comparisons of the flowfield in the vicinity of the vortex cores are presented.