A two–step radial basis function-based CFD mesh displacement tool

Abstract

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 Computational Fluid Dynamics (CFD) applications, RBF interpolation, in its standard formulation, becomes excessively expensive. This paper proposes 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 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.