Maximum Principle Preserving Space and Time Flux Limiting for Diagonally Implicit Runge–Kutta Discretizations of Scalar Convection-diffusion Equations
KAUST DepartmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Extreme Computing Research Center
Embargo End Date2023-08-01
Permanent link to this recordhttp://hdl.handle.net/10754/671359
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AbstractWe 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.
CitationQuezada de Luna, M., & Ketcheson, D. I. (2022). Maximum Principle Preserving Space and Time Flux Limiting for Diagonally Implicit Runge–Kutta Discretizations of Scalar Convection-diffusion Equations. Journal of Scientific Computing, 92(3). https://doi.org/10.1007/s10915-022-01922-8
SponsorsThis work was funded by King Abdullah University of Science and Technology (KAUST) in Thuwal, Saudi Arabia. We are grateful to Prof. Dmitri Kuzmin for important discussions that formed the basis of this work, for providing feedback on drafts of the paper and for suggesting the fixed point iteration (31).
PublisherSpringer Science and Business Media LLC
JournalJournal of Scientific Computing
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