Minimizing Errors in Flux-Corrected Transport Algorithms.
NAVAL RESEARCH LAB WASHINGTON D C
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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.
- Theoretical Mathematics
- Fluid Mechanics