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    Bound-preserving convex limiting for high-order Runge-Kutta time discretizations of hyperbolic conservation laws

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    Type
    Preprint
    Authors
    Kuzmin, Dmitri
    Quezada de Luna, Manuel
    Ketcheson, David I. cc
    Grüll, Johanna
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Numerical Mathematics Group
    Date
    2020-09-02
    Permanent link to this record
    http://hdl.handle.net/10754/665132
    
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    Abstract
    We introduce a general framework for enforcing local or global inequality constraints in high-order time-stepping methods for a scalar hyperbolic conservation law. The proposed methodology blends an arbitrary Runge-Kutta scheme and a bound-preserving (BP) first-order approximation using two kinds of limiting techniques. The first one is a predictor-corrector method that belongs to the family of flux-corrected transport (FCT) algorithms. The second approach constrains the antidiffusive part of a high-order target scheme using a new globalized monolithic convex (GMC) limiter. The flux-corrected approximations are BP under the time step restriction of the forward Euler method in the explicit case and without any time step restrictions in the implicit case. The FCT and GMC limiters can be applied to antidiffusive fluxes of intermediate RK stages and/or of the final solution update. Stagewise limiting ensures the BP property of intermediate cell averages. If the calculation of high-order fluxes involves polynomial reconstructions from BP data, these reconstructions can be constrained using a slope limiter to correct unacceptable input. The BP property of the final solution is guaranteed for all flux-corrected methods. Numerical studies are performed for one-dimensional test problems discretized in space using explicit weighted essentially nonoscillatory (WENO) finite volume schemes.
    Sponsors
    The work of Dmitri Kuzmin and Johanna Grüll was supported by the German Research Association (DFG) under grant KU 1530/23-1. The work of Manuel Quezada de Luna and David I. Ketcheson was funded by King Abdullah University of Science and Technology (KAUST) in Thuwal, Saudi Arabia.
    Publisher
    arXiv
    arXiv
    2009.01133
    Additional Links
    https://arxiv.org/pdf/2009.01133
    Collections
    Preprints; Applied Mathematics and Computational Science Program; Numerical Mathematics Group; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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