Comparison of several spatial discretizations for the Navier-Stokes equations

摘要

Grid convergence studies for subsonic and transonic flows over airfoils are presented in order to compare the accuracy of several spatial discretizations for the compressible Navier-Stokes equations. ^The spatial discretizations include the following treatment of the inviscid fluxes: (1) second-order centered differences with third-order matrix artificial dissipation, (2) second-order convective upstream split pressure scheme (CUSP), (3) third-order upwind-biased differencing with Roe's flux-difference splitting, and (4) fourth-order centered differences with third-order matrix artificial dissipation. ^The first three schemes are combined with second-order differencing for the viscous terms. ^The fourth scheme uses fourth-order differencing for the viscous terms, as well as higher-order approximations near boundaries and for the numerical integration. ^The grid convergence studies indicate that, for subsonic flows, the scheme using higher-order differencing for both viscous and inviscid fluxes is substantially more accurate than the others, producing less than one percent numerical error in drag even on coarse grids. ^For transonic flows, this scheme is again the most accurate, but somewhat finer grids are required to achieve less than one percent error in drag. ^The formulation of the limiter function is shown to be an important consideration in computing transonic flows. ^(Author)