Local remeshing for large amplitude grid deformations. (English) Zbl 1193.74037
Summary: Fluid-structure interaction (FSI) modelling can involve large deformations in the fluid domain, which could lead to degenerating mesh quality and numerical inaccuracies or instabilities, if allowed to amplify unchecked. Complete remeshing of the entire domain during the solution process is computationally expensive, and can require interpolation of solution variables between meshes. As an alternative, we investigate a local remeshing algorithm, with two emphases: (a) the identification and remedy of flat, degenerate tetrahedra, and (b) the avoidance of node motion, and hence associated interpolation errors.
Initially, possible topological changes are examined using a dynamic programming algorithm to maximise the minimum local element quality through edge reconnection. In the 3D situation it was found that reconnection improvements tend to be limited to long edges, and those with few (three or four) element neighbours. The remaining degenerate elements are classified into one of four types using three proposed metrics – the minimum edge-to-edge distance (EE), the minimum node-to-edge distance (NE), and the shortest edge length (SE) – and removed according to the best manner for their type. Optimised thresholds for identifying and classifying elements for removal were found to be EE \(<0.18\), NE \(< 0.21\), SE \(< 0.2\).
Initially, possible topological changes are examined using a dynamic programming algorithm to maximise the minimum local element quality through edge reconnection. In the 3D situation it was found that reconnection improvements tend to be limited to long edges, and those with few (three or four) element neighbours. The remaining degenerate elements are classified into one of four types using three proposed metrics – the minimum edge-to-edge distance (EE), the minimum node-to-edge distance (NE), and the shortest edge length (SE) – and removed according to the best manner for their type. Optimised thresholds for identifying and classifying elements for removal were found to be EE \(<0.18\), NE \(< 0.21\), SE \(< 0.2\).
MSC:
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |
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