Minimizing Errors in Flux-Corrected Transport Algorithms.

摘要

This paper presents an error analysis of numerical algorithms for solving the convective continuity equation using Flux-Corrected Transport techniques (FCT). The goal of the paper is threefold: First, the nature of numerical errors in Eulerian finite-difference solutions to the continuity equation is analyzed. Second, the properties and intrinsic errors of an 'optimal' algorithm are discussed and such an FCT algorithm is demonstrated for a restricted class of problems. This 'optimal' FCT algorithm is applied to a model test problem and the error is monitored for comparison with more generally applicable algorithms. Third, several improved FCT algorithms are developed and judged against both standard flux-uncorrected transport algorithms and the optimal algorithm. These improved FCT algorithms are found to be four to eight times more accurate than standard non-FCT algorithms, nearly twice as accurate as the original SHASTA FCT algorithm, and approach the accuracy of the 'optimal' algorithm.