• 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}
}

• M. Luna, D. Ketcheson
• Published 17 September 2021
• Computer Science, Mathematics
• ArXiv

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 by an additional limiting step that removes these violations while preserving high order accuracy. The desirable properties of the resulting schemes are demonstrated through several numerical examples.