GEOMETRIC CONSERVATION LAW OF THE FINITE-VOLUME METHOD FOR THE SIMPLER ALGORITHM AND A PROPOSED UPWIND SCHEME

The geometric conservation law for the diffusive terms is Shyy and Vu's explanation of the geometric conservation law for the convective terms. The finite-volume method for the SIMPLER algorithm using a staggered grid system with curvilinear coordinates is revisited on the physical domain. The classical three-point, second-order upwind (CSOU) scheme for the convective terms and the classical central-difference (CA) scheme for the diffusive terms are found to introduce false flux error on a generalized grid system. Higher-order schemes [an upwind (PSOU) scheme for the convective terms and a higher-order (HA) scheme for the diffusive terms] without this error are proposed in order to check the influence of false flux error in these classical schemes. Comparison of the errors of the present numerical experiments shows that satisfaction of the present geometric conservation law for the diffusive as well as the convective terms is more important in reducing error than is canceling the false fluxes. If the present law is satisfied, the proposed PSOU and HA schemes are feasible, and a combination of the PSOU and CA schemes is also satisfactory. The method composed of the CSOU and CA schemes is also adequate if the law is satisfied and an adaptive grid system is employed.