Efficient Cell-Vertex Upwind Scheme for the Two-Dimensional Equations

Abstract

The accuracy and efficiency of a cell-vertex upwind scheme are in- vestigated. Upwinding is acheived by an unequal distribution of the transformed flux balances to the vertices of a computational cell. The equations are rotated with respect to the local velocity vector to determine the upwinding directions. Fourth differences back- ground dissipation is added to ensure convergence, and time integra- tion is performed using a five-stage Runge-Kutta scheme. The back- ground dissipation is scaled by the appropriate eigenvalues, and convergence toward steady state is accelerated by employing upwind implicit residual smoothing and multigrid. The scheme is second order accurate in space at steady state, and it yields very accurate re- sults on significantly coarse meshes. Thus its efficiency is com- petitative with that of central-differencing schemes using multigrid acceleration.