A Radial Basis Function–Based Ghost Cell Method for Complex Rigid or Flexible Moving Boundary Flows

Abstract

A radial basis function (RBF)-based ghost cell method is presented to simulate flows around a rigid or flexible moving hydrofoil on a Cartesian grid. A compactly supported radial basis function (CSRBF) is introduced to the ghost cell immersed boundary method to treat the complex flexible boundaries in the fluid. The results indicate that this RBF representation method can accurately track tempo-spatially varied interfaces and avoid the identification failure encountered in original RBF. In addition, an interface cell interpolation method is developed to treat the irregular boundaries such as sharp points and thin boundaries. Solution quality is improved by constructing the interface cells along the local irregular boundaries, instead of the ghost cells. To validate the proposed method, uniform flows around stationary and pitching hydrofoils are simulated. Then, a flexible hydrofoil undulating in the fluid is simulated. Good agreements are obtained by comparing the present results with the reference results. Furthermore, the relationship between the oscillation frequency and the force coefficient is studied. Also, generation mechanism of the thrust force is explained.