Mesh deformation using the biharmonic operator

The use of the biharmonic operator for deforming a mesh in an arbitrary–Lagrangian–Eulerian simulation is investigated. The biharmonic operator has the advantage that two conditions can be specified on each boundary of the mesh. This allows both the position and the normal mesh spacing along a bound...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2003-02, Vol.56 (7), p.1007-1021
Main Author: Helenbrook, Brian T.
Format: Article
Language:English
Subjects:
arbitrary-Lagrangian-Eulerian (ALE)
Biharmonic equations
Boundaries
Computer simulation
Deformation
Expenses
Finite element method
Integrity
mesh deformation
mesh movement
Operators
r-adaptation
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Summary:The use of the biharmonic operator for deforming a mesh in an arbitrary–Lagrangian–Eulerian simulation is investigated. The biharmonic operator has the advantage that two conditions can be specified on each boundary of the mesh. This allows both the position and the normal mesh spacing along a boundary to be controlled, which is important for two‐fluid interfaces and periodic boundaries. At these boundaries, we can simultaneously fix the position of the boundary and ensure that the normal mesh spacing is continuous across the boundary. In addition, results for deforming surfaces show that greater surface deformation can be tolerated when using biharmonic equations compared to approaches using second‐order partial differential equations. A final advantage is that with the biharmonic operator, the integrity of a grid in a moving boundary layer can be preserved as the boundary moves. The main disadvantage of the approach is its increased computational expense. Copyright © 2003 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.595