Flux-corrected transport for scalar hyperbolic conservation laws and convection-diffusion equations by using linear programming

Flux-corrected transport (FCT) is one of the flux limiter methods. Unlike total variation diminishing methods, obtaining known FCT formulas for computing limiters not quite transparent, and their transformation obvious when original differential operator changes. We propose a novel formal mathematical approach to design correction weighted hybrid difference schemes by using linear programming. The scheme combination monotone high order scheme. determination maximal antidiffusive fluxes treated as an optimization problem with objective function. To obtain constraints problem, inequalities that are valid applied numerical solution nonlinear reduced iterative programming problems. A nontrivial approximate corresponding can be required limiters. present scalar hyperbolic conservation laws convection-diffusion equations. designed flux-corrected yields entropy solutions. Numerical results presented.