• Corpus ID: 237563040

Maximum principle preserving space and time flux limiting for Diagonally Implicit Runge-Kutta discretizations of scalar convection-diffusion equations

@article{Luna2021MaximumPP,
  title={Maximum principle preserving space and time flux limiting for Diagonally Implicit Runge-Kutta discretizations of scalar convection-diffusion equations},
  author={Manuel Quezada de Luna and David I. Ketcheson},
  journal={ArXiv},
  year={2021},
  volume={abs/2109.08272}
}
We provide a framework for high-order discretizations of nonlinear scalar convection-diffusion equations that satisfy a discrete maximum principle. The resulting schemes can have arbitrarily high order accuracy in time and space, and can be stable and maximum-principle-preserving (MPP) with no step size restriction. The schemes are based on a two-tiered limiting strategy, starting with a high-order limiter-based method that may have small oscillations or maximum-principle violations, followed… 
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