RBFs-MSA Hybrid Method for Mesh Deformation

Abstract

Simulating unsteady flow phenomena involving moving boundaries is a challenging task, one key requirement of which is a reliable and fast algorithm to deform the computational mesh. Radial basis functions (RBFs) interpolation is a very simple and robust method to deform the mesh. However, the number of operations and the requirement of memory storage will be increased rapidly as the number of grid nodes increases, which limits the application of RBFs to three-dimensional (3D) moving mesh. Moving submesh approach (MSA) is an efficient method, but its robustness depends on the method used to deform the background mesh. A hybrid method which combines the benefits of MSA and RBFs interpolation, which is called RBFs-MSA, has been presented. This hybrid method is proved to be robust and efficient via several numerical examples. From the aspect of the quality of deforming meshes, this hybrid method is comparable with the RBFs interpolation; from the aspect of computing efficiency, one test case shows that RBFs-MSA is about two orders of magnitude faster than RBFs interpolation. For these benefits of RBFs-MSA, the new method is suitable for unsteady flow simulation which refers to boundaries movement.