A Cell-Centered, Finite-Volume Upwind Scheme with Global Conservation

Abstract

A finite-volume, conservative upwind scheme has been developed, based on the flux-difference splitting method. Pseudo-compressibility is introduced to the continuity equation. The cell-centered is adopted, i. e., nodes for flow variables were placed at the center of each grid cell. With this combination of the scheme and the node-cell layout, the global conservation property has been derived in a straightforward manner.
The scheme was applied to two types of flows. First the flow past a circular cylinder was computed using the O-grid at the Reynolds number R_e =40. The integrated momentum and mass fluxes at inner and outer boundaries agreed up to more than 9 significant figures after 1, 000 time steps. Thus the global conservation property was confirmed. The computed drag coefficient value agreed well with other computed values. The same flow was computed using the H-grid. The drag coefficient value thus obtained differed very little from the O-grid value.
The flow past a flat plate with a point of mapping singularity was computed at an attack angle of 30 degrees. It was confirmed that the global conservation property of the present scheme is not affected by the presence of mapping singularities.