Invariant-Domain-Preserving High-Order Time Stepping: I. Explicit Runge--Kutta Schemes

We introduce a technique that makes every explicit Runge--Kutta (ERK) time stepping method invariant domain preserving and mass conservative when applied to high-order discretizations of the Cauchy problem associated with systems nonlinear conservation equations. The key idea is at each stage ERK scheme one computes low-order update, both defined from same intermediate stage, then applies nonlinear, limiting operator. main advantage over strong stability (SSP) paradigm more flexibility in choice scheme, thus allowing for less stringent restrictions on step. agnostic space discretization. It can be combined continuous finite elements, discontinuous volume space. Numerical experiments are presented illustrate theory.