Mesh Morphing and Smoothing by Means of Radial Basis Functions (RBF)

Abstract

Radial Basis Functions (RBF) mesh morphing, its theoretical basis, its numerical implementation, and its use for the solution of industrial problems, mainly in Computer Aided Engineering (CAE), are introduced. RBF theory is presented showing the mathematical framework for a basic RBF fit, its MathCAD implementation, and its usage. The equations required for a 2D case comparing RBF smoothing and pseudosolid smoothing based on Finite Elements Method (FEM) structural solution are given; RBF exhibits excellent performance and produces high quality meshes even for very large deformations. The industrial application of RBF morphing to Computational Fluid Dynamics (CFD) is covered presenting the RBF Morph software, its implementation, and a description of its working principles and performance. Practical examples include: physical problems that use CFD, shape parameterisation strategy, and modelling guidelines for setting-up a well posed RBF problem. Future directions explored are: transient shape evolution, fluid structure interaction modelling, and shape parameterization in multi-physics, multi-objective design optimization.