Flux-Corrected Transport: Principles, Algorithms, and Applications

Addressing students and researchers as well as practitioners of scientific computing, this book describes the state of the art in the development of high-resolution schemes based on the Flux-Corrected Transport (FCT) paradigm. Intended for readers who have a solid background in Computational Fluid Dynamics, the book begins with a historical note by D.L. Book. Review articles then describe various algorithmic aspects (efficient implementation of the proposed high-resolution schemes, choice of parameters and other practical tips). The topics addressed in the book and its main highlights include: the derivation and analysis of classical FCT schemes emphasizing the physical and mathematical constraints as well as flux limiting for hyperbolic systems; its generalization to implicit time-stepping and finite element discretizations on unstructured meshes; applications to Monotonically Integrated Large Eddy Simulation (MILES) of turbulent flows and for designing alternative high-resolution schemes. Further material concerns clipping and terracing, the use of characteristic variables in multidimensions and the discussions on prelimiting/steepening, 'failsafe' adjustment, and iterative flux correction. Many numerical examples are presented as academic test problems and large-scale applications alike. TOC:The Conception, Gestation, Birth and Infancy of FCT.- On the Design of Flux-Corrected Transport Algorithms.- 30 Years of FCT: Status and Directions; On Monotonically Integrated Large Eddy Simulation of Turbulent Flows Based on FCT Algorithms.- Large Scale Urban Simulation with FCT.- Algebraic Flux Correction I. Scalar Conservation Laws.- Algebraic Flux Correction II. Compressible Euler Equations.- Algebraic Flux Correction III. Incompressible Flow Problems