Premium
An element level zero‐divergence finite element approach
Author(s) -
Mack A. N. F.
Publication year - 1994
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.1650190904
Subject(s) - solenoidal vector field , finite element method , divergence (linguistics) , interpolation (computer graphics) , mathematics , element (criminal law) , benchmark (surveying) , zero (linguistics) , mathematical analysis , geometry , physics , classical mechanics , vector field , motion (physics) , linguistics , philosophy , geodesy , political science , law , thermodynamics , geography
Abstract An innovative idea for the solution of viscous incompressible flows, in which the equation for conservation of mass is satisfied at the element level, is termed the solenoidal finite element approach. The term ‘solenoidal’ derives from the fact that the velocity components need to be solenoidal, i.e. to have zero divergence. The difficulty with this idea centres on the construction of a specialized element in which the velocity components are constrained to be solenoidal by the nature of their interpolation functions. If such an element can be constructed, then the pressure is suppressed from the prime solution. This has obvious attractions, although recourse to another novel idea is needed for its eventual retrieval. The validity of these ideas is demonstrated herein by the results for some classical benchmark problems. Where possible, comparisons are made with other results, both from other codes and from the literature.