A Third-Order Maximum-Principle-Preserving CWENO Scheme for Two-Dimensional Nonlocal Conservation Laws

arXiv (Cornell University)

Abstract

We present a third-order finite volume central WENO scheme for systems of nonlocal conservation laws in two spatial dimensions. The CWENO reconstruction of the conservative variable provides polynomials that can be evaluated in the entire domain, which is of advantage when approximating the nonlocal terms. Moreover, this method can be augmented with a limiter that preserves the maximum-principle and especially positivity of the solution.

Authors 2

1. Anika Beckers Aachen Chair of Numerical Analysis Institute for Geometry and Applied Mathematics

   RWTH Aachen University

   Affiliation as printed

   Chair of Numerical Analysis , Institute for Geometry and Applied Mathematics , RWTH Aachen University , Im Süsterfeld 2 , 52072 Aachen , Germany,

2. Jan Friedrich

   Technical University of Munich

   Affiliation as printed

   . Munich , Germany,

   Chair of Optimal Control , Department for Mathematics , School of Computation, Information and Technology , Technical University of Munich , Boltzmannstraße 3 , 85748 Garching