A semi-torsional spring analogy model for updating unstructured meshes in 3D moving domains

Computational modeling in deforming 3D domains requires a method for updating the computational mesh/grid as the domains deform, while maintaining mesh/grid quality. One popular technique, known as the spring analogy, is based on elastic deformation of element edges where element edges are modeled a...

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Bibliographic Details
Published in:Finite elements in analysis and design 2005-06, Vol.41 (11), p.1118-1139
Main Authors: Zeng, Dehong, Ethier, C. Ross
Format: Article
Language:English
Subjects:
Analogies
Boundary displacement
Computation
Computational techniques
Deformation
Deforming domains
Exact sciences and technology
Finite element method
Finite-element and galerkin methods
Fundamental areas of phenomenology (including applications)
Mathematical methods in physics
Mathematical models
Measurement and testing methods
Mesh quality
Numerical modeling
Physics
Solid mechanics
Springs (elastic)
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Three dimensional
Two dimensional
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Summary:Computational modeling in deforming 3D domains requires a method for updating the computational mesh/grid as the domains deform, while maintaining mesh/grid quality. One popular technique, known as the spring analogy, is based on elastic deformation of element edges where element edges are modeled as springs producing forces to propagate boundary displacements into the interior of a mesh. Unfortunately, existing spring analogy formulations have problems with maintaining element quality for realistic 3D problems, especially during large deformations. Here, we present a semi-torsional spring analogy model based on a consistent definition of the edge stiffness that avoids mis-shaped elements. The model is applicable to both 2D and 3D fully unstructured meshes, and includes a computationally efficient means of incorporating geometric information about element shape so as to allow element deformation while penalizing formation of mis-shaped elements, with little restriction on the magnitude of mesh deformation. Extensive numerical testing in 2D and 3D showed that the algorithm preserves mesh quality even under severe deformations. We conclude that the semi-torsional technique presented here is an improvement over existing spring-based mesh updating schemes.
ISSN:0168-874X
1872-6925
DOI:10.1016/j.finel.2005.01.003