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Momentum advection on unstructured staggered quadrilateral meshes
Author(s) -
Benson David J.
Publication year - 2008
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2310
Subject(s) - quadrilateral , polygon mesh , finite element method , momentum (technical analysis) , mathematics , eulerian path , computer science , discretization , mathematical optimization , geometry , mathematical analysis , lagrangian , engineering , structural engineering , finance , economics
Abstract The finite element method, as applied to problems in solid mechanics, typically uses a mesh with the velocities at the nodes and the remaining solution variables, including the density, located at the integration points. The arbitrary Lagrangian–Eulerian formulations used in solid mechanics are therefore faced with the challenge of transporting momentum, which is defined in terms of variables located at separate points in space, in a conservative manner. Two types of momentum transport methods have been developed over the years. The first constructs a dual mesh with the nodes as the integration points, a difficult task on an unstructured finite element mesh. The second uses the original mesh and constructs auxiliary variables for transport from which the final velocity may be recovered. An analysis demonstrates how the two methods are related. Simplified implementations of each type—dual mesh and element centered—are developed in detail and their performance is compared to verify the analysis. Copyright © 2008 John Wiley & Sons, Ltd.