EFFICIENT CELL-VERTEX UPWIND SCHEME FOR THE 2-DIMENSIONAL EULER EQUATIONS

The accuracy and efficiency of a cell-vertex upwind scheme are investi gated. Upwinding is achieved by an unequal distribution of the transfo rmed flux balances to the vertices of a computational cell. The equati ons are rotated with respect to the local velocity vector to determine the upwinding directions. Fourth differences background dissipation i s added to ensure convergence, and time integration is performed using a five-stage Runge-Kutta scheme. The background dissipation is scaled by the appropriate eigenvalues, and convergence toward steady state i s accelerated by employing upwind implicit residual smoothing and mult igrid. The scheme is second order accurate in space at steady state, a nd it yields very accurate results on significantly coarse meshes. Thu s its efficiency is competitive with that of central-differencing sche mes using multigrid acceleration.