Parametrized maximum principle preserving flux limiters for high order schemes solving multi-dimensional scalar hyperbolic conservation laws

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Department of Mathematical Sciences


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.

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Journal of Scientific Computing