Flux-Corrected Transport looks at forty

• A 40-year retrospective on Flux-Corrected Transport (FCT) is given.
• FCT captures the physics of convection; formal mathematical accuracy is secondary.
• Evolution of FCT is related to the rapid evolution of high-performance computers.
• Real-world applications and their validation shaped the development of FCT.
• Monotone Integrated Large Eddy Simulation, FCT’s turbulence, “model” is explained.

This year, 2013, marks the 40th anniversary of the journal article “Flux-Corrected Transport I. SHASTA, A Fluid Transport Algorithm That Works” by Jay Boris and David Book [1]. Flux-Corrected Transport (FCT) removed a serious roadblock to advances in Computational Fluid Dynamics (CFD) by enabling the accurate treatment of strong, time-dependent shock problems in blast, reactive-flow, and combustion physics, and in aerodynamics and astrophysics. Steep gradients in conserved fluid variables could now be convected across a computational grid without the appearance of spurious oscillations and physically impossible negative values. The nonlinear “flux-correction” algorithm introduced in FCT imposes the physical properties of conservation, locality, causality, and monotonicity on the numerical solutions for convection without adding a great deal of numerical diffusion. This article shows that implementing these physical properties in solving the continuity equation through high-resolution FCT also results in a serviceable Large-Eddy Simulation treatment of turbulent flows without need for additional “subgrid turbulence models.” We have named this simplified approach Monotone Integrated Large Eddy Simulation (MILES).