Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2017-04-19Preprint Posting Date
2016-10-02Online Publication Date
2017-04-19Print Publication Date
2018-01Permanent link to this record
http://hdl.handle.net/10754/623303
Metadata
Show full item recordAbstract
We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to study positivity preservation for a class of TVD semi-discretizations of 1D scalar hyperbolic conservation laws. This technique is a generalization of the approach suggested in Khalsaraei (J Comput Appl Math 235(1): 137–143, 2010). We give more relaxed conditions on the time-step for positivity preservation for slope-limited semi-discretizations integrated in time with explicit Runge–Kutta methods. We show that the step-size restrictions derived are sharp in a certain sense, and that many higher-order explicit Runge–Kutta methods, including the classical 4th-order method and all non-confluent methods with a negative Butcher coefficient, cannot generally maintain positivity for these semi-discretizations under any positive step size. We also apply the proposed technique to centered finite difference discretizations of scalar hyperbolic and parabolic problems.Citation
Fekete I, Ketcheson DI, Lóczi L (2017) Positivity for Convective Semi-discretizations. Journal of Scientific Computing. Available: http://dx.doi.org/10.1007/s10915-017-0432-9.Sponsors
This work was supported by the King Abdullah University of Science and Technology (KAUST), 4700 Thuwal, 23955-6900, Saudi Arabia. The first author was also supported by the Tempus Public Foundation. The third author was also supported by the Department of Numerical Analysis, Eötvös Loránd University, and the Department of Differential Equations, Budapest University of Technology and Economics, Hungary.Publisher
Springer NatureJournal
Journal of Scientific ComputingarXiv
1610.00228Additional Links
http://link.springer.com/article/10.1007/s10915-017-0432-9ae974a485f413a2113503eed53cd6c53
10.1007/s10915-017-0432-9