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

  • Authors:

  • C. S. Chew;K. S. Yeo;C. Shu

  • Affiliations:

  • The Institute of High Performance Computing (IHPC), CFD Division, The Capricorn, Singapore Science Park II, Singapore, Singapore;Department of Mechanical Engineering, National University of Singapore, Singapore, Singapore;Department of Mechanical Engineering, National University of Singapore, Singapore, Singapore

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2006

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Abstract

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.