Research Fellows
Flavio Gagliardi
Early Stage Researcher 7 at National Technical University of Athens
Mesh displacement based on Radial Basis Functions (RBF) interpolation is known for its ability to preserve the validity and quality of the mesh, even for large displacements, without being affected by mesh connectivity. However, in the case of large meshes, such as those used in real-world CFD applications, RBF interpolation, in its standard formulation, becomes excessively expensive.
The work proposed a cost reduction technique for mesh displacement based on RBF, by splitting the process into two steps. In the first step, named predictor, a data reduction algorithm that adaptively agglomerates mesh boundary nodes by reducing the RBF interpolation problem size is used. Upon completion of the first step, due to the agglomeration and the fact that the RBF interpolation is applied to the boundary nodes too, the so-displaced boundaries do not match the given displacements; thus, the position of the boundary nodes must be corrected during the second step, named corrector. The latter performs a local deformation based on RBF kernels with local support, to make the boundary conform to the known displacements of its nodes. The proposed method is accelerated by employing the Sparse Approximate Inverse (SPAI) preconditioner based on geometrical considerations and the Fast Multipole Method.
The method and the programmed software are validated on three test cases related to the deformation of CFD meshes inside a duct and a turbine stator row as well as around a car model.
Double elbow duct. RBF sources (spheres) generated by the data reduction algorithm in the predictor step. Colors from blue to red represent small to large displacements . The reference and displaced duct shapes are depicted in gray and blue, respectively. Most RBF sources lie in the area ofhigh spatial gradient of the displacements. The computed sources do not necessarily lie on the mesh surface.
Double elbow duct. Octree used by the data reduction algorithm in the predictor step. The barycenters of the leaf bins are used as RBF sources. The surface mesh nodes are depicted in red.
Relevant Publication:
- Gagliardi, Flavio; Giannakoglou, Kyriakos, C., "A Two-Step Radial Basis Function-Based CFD Mesh Displacement Tool" February 2019