An ALE Based Hybrid Meshfree Local RBF-Cartesian FD scheme for Incompressible flow around moving boundaries

Abstract

A solution scheme is presented to simulate incompressible viscous flow around moving boundaries using hybrid meshfree-Cartesian grid. The presented solution approach avoids intensive re-meshing and enhances computational efficiency by combining the advantages of both meshfree and mesh-based methods for flow around moving objects. The scheme employs a body conformal meshfree nodal cloud around the solid object which convects with the moving solid boundary. On the outer side, meshfree nodal cloud is surrounded and partially overlapped by a stationary Cartesian grid. Navier Strokes equations in Arbitrary-Lagrangian-Eulerian (ALE) formulations are solved over moving nodal cloud using meshfree local Radial Basis Functions in finite difference Mode (RBF-FD). Eulerian form of flow equations are solved over static Cartesian grid using conventional finite difference scheme. Meshfree nodes can efficiently adapt to the moving boundary without necessitating re-meshing. Use of finite difference method over Cartesian grid allows faster computing and improves computational efficiency. Variation in computation time has been studied with corresponding change in size of meshfree and Cartesian grids. Significant reduction in computation time is achieved by reducing the size of meshfree cloud. The solution scheme is validated by simulating two dimensional flows around vibrating cylindrical objects. For this purpose, forced as well as vortex induced cylindrical vibration cases are investigated and solutions are compared with computational and experimental results available in literature.