An implicit flux-corrected transport algorithm

Abstract

An implicit flux-corrected transport algorithm is developed which gives accurate, non-negative results for Courant numbers c > 1, and retains high accuracy for c < 1. The new algorithm can give a threefold increase in overall speed over existing methods with the same order of accuracy, or give greater accuracy for the same computational effort; the accuracy decreases slowly as c increases beyond unity. The method has been developed for application in discharge physics problems where a high order of accuracy is required for solving the continuity equations for electrons and ions under the influence of dominant space-charge effects. We follow Zalesak's approach by computing both a high-order solution and a low-order solution and then using some flux-limiter to determine what proportion of each solution is used at any given point in space and time [ J. Comput. Phys. 31, 335 (1979)]. For the high-order solution we use a fourth-order time- and space-centred scheme. For the lower-order solution we use upwind differences. The fourth-order scheme presented is more accurate than the REVFCT algorithm proposed by Boris and Book [ J. Comput. Phys. 20, 397 (1976)] and guarantees positive results.