Evaluation of Two High-Order Weighted Essentially Nonoscillatory Schemes

Abstract

Two fifth-order spatial weighted essentially nonoscillatory schemes for the convective terms were added to the OVERFLOW 2 implicit overset Navier-Stokes flow solver. The method used to incorporate the schemes is similar to a monotone upstream-centered scheme for conservation laws and requires no modification of the viscous terms, transport equations, or turbulence models in the code. The new flux calculation schemes were applied to problems involving vortex convection, strong shocks, and large scale unsteady flows. The weighted essentially nonoscillatory schemes were found to have much lower numerical dissipation/dispersion than traditional third-order spatial monotone upstream-centered schemes for conservation laws. Both weighted essentially nonoscillatory schemes were . numerically robust over a wide range of Mach numbers when solved using the existing implicit schemes within OVERFLOW 2. The weighted essentially nonoscillatory schemes also provided improved numerical accuracy over traditional third-order spatial monotone upstream-centered schemes for conservation laws on the same computational grid for all the applications examined here. The weighted essentially nonoscillatory schemes are 10-30% more expensive than the third-order spatial monotone upstream-centered schemes for conservation laws depending on choice of implicit solver.