Title
Parametrized maximum principle preserving flux limiters for high order schemes solving multi-dimensional scalar hyperbolic conservation laws
Document Type
Article
Publication Date
1-1-2014
Abstract
In this paper, we will extend the strict maximum principle preserving flux limiting technique developed for one dimensional scalar hyperbolic conservation laws to the two-dimensional scalar problems. The parametrized flux limiters and their determination from decoupling maximum principle preserving constraint is presented in a compact way for two-dimensional problems. With the compact fashion that the decoupling is carried out, the technique can be easily applied to high order finite difference and finite volume schemes for multi-dimensional scalar hyperbolic problems. For the two-dimensional problem, the successively defined flux limiters are developed for the multi-stage total-variation- diminishing Runge-Kutta time-discretization to improve the efficiency of computation. The high order schemes with successive flux limiters provide high order approximation and maintain strict maximum principle with mild Courant-Friedrichs-Lewy constraint. Two dimensional numerical evidence is given to demonstrate the capability of the proposed approach. © 2013 Springer Science+Business Media New York.
Publication Title
Journal of Scientific Computing
Recommended Citation
Liang, C.,
&
Xu, Z.
(2014).
Parametrized maximum principle preserving flux limiters for high order schemes solving multi-dimensional scalar hyperbolic conservation laws.
Journal of Scientific Computing,
58(1), 41-60.
http://doi.org/10.1007/s10915-013-9724-x
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/4947