An improved second moment method for solution of pure advection problems

The second moment numerical method (SMM) of Egan and Mahoney [Numerical mod eling of advection and diffusion of urban area source pollutant. Journal of Applied Meteorology 1972; 11: 312-322] is adapted to solve for the pure ad vection transport equation in a variety of flow fields. SMM eliminates nume rical diffusion by employing a procedure that takes into account the first and second moments of mass distribution in each grid element. For pure tran slational flow fields, the method is conservative, positive definite and sh ape-preserving. In rotational and/or shear flows, the accuracy of SMM is si gnificantly reduced. Two improvements are presented to make the SMM applica ble to a wider range of flow problems. It is shown that the improved SMM (I SMM) is less diffusive and more shape-preserving than the SMM in rotational and/or deformational flows. The ISMM can also be used to solve for a color function in compressible flow fields. The computational efficiency of this method is compared with that of other methods and, for a given accuracy, i t is shown that ISMM is a cost-effective, non-diffusive and shape-preservin g method. Copyright (C) 2000 John Wiley & Sons, Ltd.