Aerodynamic Computations Using the Convective-Upstream Split-Pressure Scheme with Local Preconditioning

The implementation of the convective-upstream-split-pressure (CUSP) approach to numerical dissipation is presented for an approximately factored algorithm in conjunction with time-derivative local preconditioning. An inexpensive  ux limiter is used to blend the lowand high-order CUSP dissipation to capture shocks without oscillations. The resulting algorithm is applied to several subsonic and transonic turbulent aerodynamic  ows and compared with results computed using the matrix dissipation scheme. Grid convergence studies are used to assess global errors. The results show the CUSP scheme to be very effective in providing good shock capturing, low numerical dissipation in boundary layers, and low numerical errors. For the  ow regimes studied, accuracy is not signiŽ cantly compromised when the limiter is based on the pressure variable only, leading to signiŽ cant savings in computational expense. For freestream Mach numbers below 0.2, the convergence rate and accuracy of the solver are signiŽ cantly improved by preconditioning the CUSP scheme. Overall, the CUSP scheme provides accuracy similar to that of matrix dissipation at a reduced computational cost.