A versatile sharp boundary ghost-node method for moving rigid boundary fluid flow with meshless nodes distribution

Abstract

A sharp boundary ghost-node method (GNM) is developed to solve the moving boundary fluid flow in a meshless local radial basis function (LRBF) framework. The background Euler fluid node is the mesh-less scattered node based on LRBF rather than the conventional Cartesian grid or unstructured mesh. The present approach (LRBF-GNM) can flexibly treat the steady boundary with the body-fitted nodes and tackle the moving boundary using the ghost-node method. The key idea of GNM is to project the information of fluid nodes into the ghost nodes by considering the boundary conditions of immersed boundary on Lagrangian nodes, and the influence of immersed boundary on the fluid can be explicitly added during the projection. There are some free parameters that should be determined before computing the virtual forcing source term acted only on the ghost nodes. The distribution of the ghost nodes, the projection strategy and the distribution of the image nodes should be treated carefully to balance the penetrability of streamlines over the immersed boundary, the numerical stability and the thickness of the diffusion boundary. A definition of sharp boundary is introduced to estimate the influences of the above free parameters on the immersed boundary. According to the numerical tests for a static boundary, the optimal parameters for GNM to precisely treat the immersed boundary are summarized. The fluid flow over steady and moving rigid boundaries and the vortex-induced vibration (VIV) are conducted and their solutions agree well with published numerical solutions and experimental measurements.