The Design of Flux-Corrected Transport (FCT) Algorithms for Structured Grids

Abstract

A given flux-corrected transport (FCT) algorithm consists of three components: (1) a high order algorithm to which it reduces in smooth parts of the flow field; (2) a low order algorithm to which it reduces in parts of the flow devoid of smoothness; and (3) a flux limiter which calculates the weights assigned to the high and low order algorithms, in flux form, in the various regions of the flow field. In this dissertation, we describe a set of design principles that significantly enhance the accuracy and robustness of FCT algorithms by enhancing the accuracy and robustness of each of the three components individually. These principles include the use of very high order spatial operators in the design of the high order fluxes, the use of non-clipping flux limiters, the appropriate choice of constraint variables in the critical flux-limiting step, and the implementation of a “failsafe” flux-limiting strategy. We show via standard test problems the kind of algorithm performance one can expect if these design principles are adhered to. We give examples of applications of these design principles in several areas of physics. Finally, we compare the performance of these enhanced algorithms with that of other recent front-capturing methods.