Higher-Order Spatial Discretization for Turbulent Aerodynamic Computations

A higher-order spatial discretization is presented for the solution of the thin-layer Navier ‐Stokes equations with application to two-dimensional turbulent aerodynamic e ows. The terms raised to a level of accuracy consistent with third-order global accuracy include the inviscid and viscous e uxes, the metrics of the generalized curvilinear coordinate transformation, the diffusive e uxes in the turbulence model, the numerical boundary schemes, and the numerical integration technique used to calculate forces and moments. Given the presence of grid and e ow singularities, third-order convergence behavior is not expected. The motivation is to reduce the numerical error on a given grid or to reduce the grid density required to achieve specie ed error levels. Results for several grid convergence studies show that this higher-order approach produces a substantial reduction in numerical error in the computation of single- and multielement aerodynamic e ows, both subsonic and transonic. Comparisons with a well-established second-order algorithm demonstrate that signie cant savings in computing expense, typically factors of three to four, can be achieved using the higher-order discretization.