Moving Mesh Algorithm for Unstructured Grids Based on Interpolation with Radial Basis Functions

Fluid-structure interaction computations typically involve moving boundaries for the flow due to the deformation of the structure. Examples can be found in: flutter simulation of wings, blood flow through veins and stability analysis of bridges and tall buildings subjected to windloads. Because of these moving boundaries a fast and reliable method for deforming the computational grid is needed to be able to perform the unsteady flow computations accurately and efficiently. Structured grids can be deformed by fast and accurate algebraic techniques, but for the meshing of complex domains and grid adaptation the greater flexibility of unstructured grids is required.

For unstructured grids two different mesh movement strategies are known. The first exploits the connectivity of the internal grid points. The connection between the grid points is represented for example by springs or as solid body elasticity. These methods involve solving a system of equations as large as the number of flow points involved and are therefore very expensive. Also special treatment is required for hanging nodes. The other strategy moves each grid point individually based on its position in space and are the so called point-by-point schemes. Hanging nodes are no problem and when radial basis function interpolation is used, a much smaller system, only involving the nodes on the boundary, has to be solved. Also the implementation for partitioned meshes, occuring in parallel flow computations, is straightforward. However, untill now point-by-point schemes are only applied to the boundary nodes of multi-grid blocks [

1

] (the structured interior mesh of the blocks is adapted with algebraic techniques) or the data transfer over the fluid-structure interface [2, 3].

In this paper a new point-by-point mesh movement algorithm based on interpolation with radial basis functions (RBF’s) is developed, which interpolates the displacements of the boundary nodes to the whole flow mesh, instead of over the fluid-structure interface only as is the case in [

2

] and [

3

]. The algorithm is tested with several RBF’s for a variety of problems. The new method can handle large translations, rotations and deformations, depending on the used RBF. The best accuracy and robustness are obtained with the thin plate spline [

3

]. However, when efficiency is more important, the C2 RBF with compact support [

2

] is the best choice. Further research includes comparing the new method with existing methods on accuracy and efficiency and applying it to a real fluid-structure interaction problem.