Bound-preserving Flux Limiting for High-Order Explicit Runge–Kutta Time Discretizations of Hyperbolic Conservation Laws

We introduce a general framework for enforcing local or global maximum principles in high-order space-time discretizations of scalar hyperbolic conservation law. begin with sufficient conditions space discretization to be bound preserving (BP) and satisfy semi-discrete principle. Next, we propose monolithic convex (GMC) flux limiter which has the structure flux-corrected transport (FCT) algorithm but is applicable spatial semi-discretizations ensures BP property fully discrete scheme strong stability (SSP) Runge–Kutta time discretizations. To circumvent order barrier SSP integrators, constrain intermediate stages and/or final stage RK method using GMC-type limiters. In this work, our theoretical numerical studies are restricted explicit schemes provably sufficiently small steps. The new GMC limiting offers possibility relaxing bounds inequality constraints achieve higher accuracy at cost more stringent step restrictions. ability presented limiters recognize undershoots/overshoots, as well smooth solutions, verified numerically three representative methods combined weighted essentially nonoscillatory (WENO) finite volume linear nonlinear test problems 1D. context, enforce prove preservation advection equation.