Premium
Information flux maximum‐entropy approximation schemes for convection–diffusion problems
Author(s) -
Cyron Christian J.,
Nissen Keijo,
Gravemeier Volker,
Wall Wolfgang A.
Publication year - 2010
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2271
Subject(s) - entropy (arrow of time) , finite element method , mathematics , statistical physics , convection , computational fluid dynamics , mathematical optimization , computer science , mechanics , physics , thermodynamics
The requirement for stabilization or other similar techniques is well known when using the finite element method in computational fluid mechanics. A variety of such techniques has been introduced during the past decades along with different physical interpretations of the stabilization terms employed. In introducing so‐called information flux methods, we developed a new point of view on the problem of numerical instabilities; with respect to Shannon's information theory instabilities are interpreted as a consequence of unadequate observance of the information flux present in fluid mechanics. Here we discuss different approaches to setting up information flux maximum‐entropy approximation schemes based on that idea. The good accuracy of these approximation schemes is demonstrated for convection–diffusion problems by means of several linear, time‐independent one‐ and two‐dimensional numerical examples and comparisons with state‐of‐the‐art stabilized finite element methods. Copyright © 2010 John Wiley & Sons, Ltd.