an:06063865
Zbl 1244.76104
Young, D. L.; Lin, Y. C.; Fan, C. M.; Chiu, C. L.
The method of fundamental solutions for solving incompressible Navier-Stokes problems
EN
Eng. Anal. Bound. Elem. 33, No. 8-9, 1031-1044 (2009).
00250908
2009
j
76M28 76D05 65M80
Navier-Stokes equations; meshless numerical method; method of fundamental solutions; method of particular solutions; Eulerian-Lagrangian method; operator-splitting method
Summary: A novel meshless numerical procedure based on the method of fundamental solutions (MFS) is proposed to solve the primitive variables formulation of the Navier-Stokes equations. The MFS is a meshless method since it is free from the mesh generation and numerical integration. We will transform the Navier-Stokes equations into simple advection-diffusion and Poisson differential operators via the operator-splitting scheme or the so-called projection method, instead of directly using the more complicated fundamental solutions (Stokeslets) of the unsteady Stokes equations. The resultant velocity advection-diffusion equations and the pressure Poisson equation are then calculated by using the MFS together with the Eulerian-Lagrangian method (ELM) and the method of particular solutions (MPS). The proposed meshless numerical scheme is a first attempt to apply the MFS for solving the Navier-Stokes equations in the moderate-Reynolds-number flow regimes. The lid-driven cavity flows at the Reynolds numbers up to 3200 for two-dimensional (2D) and 1000 for three-dimensional (3D) are chosen to validate the present algorithm. Through further simulating the flows in the 2D circular cavity with an eccentric rotating cylinder and in the 3D cube with a fixed sphere inside, we are able to demonstrate the advantages and flexibility of the proposed meshless method in the irregular geometry and multi-dimensional flows, even though very coarse node points are used in this study as compared with other mesh-dependent numerical schemes.