The conception, gestation, birth and infancy of FCT -- The design of flux-corrected transport (FCT) algorithms for structured grids -- On monotonically integrated large eddy simulation of tubulent flows based on FCT algorithms -- Large scale urban simulations with FCT -- 30 years of FCT -- Algebraic flux corretion I -- Algebraic flux correction II -- Algebraic flux correction III -- Algebraic flux correction IV -- An evaluation of the FCT method for high-speed flows -- Flux-corrected and optimization-based remap.

Many modern high-resolution schemes for Computational Fluid Dynamics trace their origins to the Flux-Corrected Transport (FCT) paradigm. FCT maintains monotonicity using a nonoscillatory low-order scheme to determine the bounds for a constrained high-order approximation. This book begins with historical notes by J.P. Boris and D.L. Book who invented FCT in the early 1970s. The chapters that follow describe the design of fully multidimensional FCT algorithms for structured and unstructured grids, limiting for systems of conservation laws, and the use of FCT as an implicit subgrid scale model. The second edition presents 200 pages of additional material. The main highlights of the three new chapters include: FCT-constrained interpolation for Arbitrary Lagrangian-Eulerian methods, an optimization-based approach to flux correction, and FCT simulations of high-speed flows on overset grids. Addressing students and researchers, as well as CFD practitioners, the book is focused on computational aspects and contains many numerical examples.