Two-level time-marching scheme using splines for solving the advection equation

A new numerical algorithm using quintic splines is developed and analyzed: quintic spline Taylor-series expansion (QSTSE). QSTSE is an Eulerian #ux-based scheme that uses quintic splines to compute space derivatives and Taylor series expansion to march in time. The new scheme is strictly mass conservative and positive de"nite while maintaining high peak retention. The new algorithm is compared against accurate space derivatives (ASD), Galerkin "nite element techniques, and the Bott scheme. The cases presented include classical rotational "elds, deformative "elds, as well as a full-scale aerosol model. Research shows that QSTSE presents signi"cant improvements in speed and oscillation suppression against ASD. Furthermore, QSTSE predicts some of the most accurate results among the schemes tested. ( 2001 Elsevier Science Ltd. All rights reserved.