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
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accurate adaptive advection algebraic algorithm antidiffusive fluxes applied approach approximation Boris boundary boundary conditions bounds calculations cell characteristic choice coefficients components Computational conservation construction contributions convective correction corresponding coupled defined density depends described difference diffusion direction discontinuities discretization dissipation dynamics edge effects equations error Euler equations example FCT algorithm FEM-FCT FEM-TVD finite element flow fluid flux limiter Flux-Corrected follows fully function geometry given global grid grid point high order fluxes implementation implicit initial iterative laws linear low-order mass matrix mesh method MILES multidimensional negative node nonlinear Note numerical obtained operator original particular performed physical positive possible present pressure problem represented resolved scalar scales schemes shock simulation solution solved solvers space step structure techniques tion transport turbulent typically upwind values variables vector velocity wave