Article ID Journal Published Year Pages File Type
522988 Journal of Computational Physics 2006 19 Pages PDF
Abstract

The algebraic flux correction (AFC) paradigm is extended to finite element discretizations with a consistent mass matrix. It is shown how to render an implicit Galerkin scheme positivity-preserving and remove excessive artificial diffusion in regions where the solution is sufficiently smooth. To this end, the original discrete operators are modified in a mass-conserving fashion so as to enforce the algebraic constraints to be satisfied by the numerical solution. A node-oriented limiting strategy is employed to control the raw antidiffusive fluxes which consist of a convective part and a contribution of the consistent mass matrix. The former offsets the artificial diffusion due to ‘upwinding’ of the spatial differential operator and lends itself to an upwind-biased flux limiting. The latter eliminates the error induced by mass lumping and calls for the use of a symmetric flux limiter. The concept of a target flux and a new definition of upper/lower bounds make it possible to combine the advantages of algebraic FCT and TVD schemes introduced previously by the author and his coworkers. Unlike other high-resolution schemes for unstructured meshes, the new algorithm reduces to a consistent (high-order) Galerkin scheme in smooth regions and is designed to provide an optimal treatment of both stationary and time-dependent problems. Its performance is illustrated by application to the linear advection equation for a number of 1D and 2D configurations.

Related Topics
Physical Sciences and Engineering Computer Science Computer Science Applications
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