Maximum Principle Preserving Space and Time Flux Limiting for Diagonally Implicit Runge–Kutta Discretizations of Scalar Convection-diffusion Equations

We provide a framework for high-order discretizations of nonlinear scalar convection-diffusion equations that satisfy discrete maximum principle. The resulting schemes can have arbitrarily high order accuracy in time and space, be stable maximum-principle-preserving (MPP) with no step size restriction. are based on two-tiered limiting strategy, starting limiter-based method may small oscillations or maximum-principle violations, followed by an additional removes these violations while preserving accuracy. desirable properties the demonstrated through several numerical examples.