A linearity preserving algebraic flux correction scheme of upwind type satisfying the discrete maximum principle on arbitrary meshes

• ID: 2804, RIV: 10404479
• ISSN: 1439-7358, ISBN: 978-3-319-96414-0
• source: Numerical Mathematics and Advanced Applications ENUMATH 2017
• keywords: convection-diffusion-reaction equations; algebraic flux correction; discrete maximum principle; linearity preservation
• authors: Petr Knobloch
• authors from KNM: Knobloch Petr

Abstract

Various choices of limiters in the framework of algebraic flux correction (AFC) schemes applied to the numerical solution of scalar steady-state convection-diffusion-reaction equations are discussed. A new limiter of upwind type is proposed for which the AFC scheme satisfies the discrete maximum principle and linearity preservation property on arbitrary meshes.