A radial basis function for reconstructing complex immersed boundaries in ghost cell method

Abstract

It is important to track and reconstruct the complex immersed boundaries for simulating fluid structure interaction problems in an immersed boundary method (IBM). In this paper, a polynomial radial basis function (PRBF) method is introduced to the ghost cell immersed boundary method for tracking and reconstructing the complex moving boundaries. The body surfaces are fitted with a finite set of sampling points by the PRBF, which is flexible and accurate. The complex or multiple boundaries could be easily represented. A simple treatment is used for identifying the position information about the interfaces on the background grid. Our solver and interface reconstruction method are validated by the case of a cylinder oscillating in the fluid. The accuracy of the present PRBF method is comparable to the analytic function method. In ta flow around an airfoil, the capacity of the proposed method for complex geometries is well demonstrated.