An improved limiter for multidimensional flux-corrected transport, NASA

An improved prescription is given for limiting (‘correcting’) the high-order °uxes in multidimensional, °ux{corrected transport (FCT) algorithms. These °uxes are designed to reduce the numerical error in positive-deflnite, monotone solutions to the hydrodynamics equations. The role of the limiter is to ensure that the desirable positivity and monotonicity properties of the low-order solutions are not lost in the quest to minimize the numerical error. It is shown that Zalesak’s (1979) formulation of a limiter for multidimensional FCT preserves positivity but not monotonicity. The introduction of a prelimiting step into his prescription, based on the original positive and monotone limiter of Boris and Book (1973), is proposed and is shown to improve signiflcantly the performance of multidimensional FCT algorithms