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

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.

Keywords

• convection-diffusion-reaction equations
• algebraic flux correction
• discrete maximum principle
• linearity preservation