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dc.contributor.authorKuzmin, Dmitri
dc.contributor.authorQuezada de Luna, Manuel
dc.contributor.authorKetcheson, David I.
dc.contributor.authorGrüll, Johanna
dc.date.accessioned2020-09-14T12:50:45Z
dc.date.available2020-09-14T12:50:45Z
dc.date.issued2020-09-02
dc.identifier.urihttp://hdl.handle.net/10754/665132
dc.description.abstractWe 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.
dc.description.sponsorshipThe 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.
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2009.01133
dc.rightsArchived with thanks to arXiv
dc.titleBound-preserving convex limiting for high-order Runge-Kutta time discretizations of hyperbolic conservation laws
dc.typePreprint
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentNumerical Mathematics Group
dc.eprint.versionPre-print
dc.contributor.institutionInstitute of Applied Mathematics (LS III), TU Dortmund University Vogelpothsweg 87, D-44227 Dortmund, Germany.
dc.identifier.arxivid2009.01133
kaust.personQuezada de Luna, Manuel
kaust.personKetcheson, David I.
refterms.dateFOA2020-09-14T12:51:23Z


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