A generalized finite-difference (GFD) ALE scheme for incompressible flows around moving solid bodies on hybrid meshfree–Cartesian grids

A scheme using the mesh-free generalized finite differencing (GFD) on flows past moving bodies is proposed. The aim is to devise a method to simulate flow past an immersed moving body that avoids the intensive remeshing of the computational domain and minimizes data interpolation associated with the established computational fluid methodologies; as such procedures are time consuming and are a significant source of error in flow simulation. In the present scheme, the moving body is embedded and enveloped by a cloud of mesh-free nodes, which convects with the motion of the body against a background of Cartesian nodes. The generalized finite-difference (GFD) method with weighted least squares (WLS) approximation is used to discretize the two-dimensional viscous incompressible Navier–Stokes equations at the mesh-free nodes, while standard finite-difference approximations are applied elsewhere. The convecting motion of the mesh-free nodes is treated by the Arbitrary Lagrangian–Eulerian (ALE) formulation of the flow equations, which are solved by a second-order Crank–Nicolson based projection method. The proposed numerical scheme was tested on a number of problems including the decaying-vortex flow, external flows past moving bodies and body-driven flows in enclosures.