A local domain-free discretization method for simulation of incompressible flows over moving bodies

Abstract

This paper presents a local domain-free discretization (DFD) method for the simulation of unsteady flows over moving bodies governed by the incompressible Navier-Stokes equations. The discretization strategy of DFD is that the discrete form of partial differential equations at an interior point may involve some points outside the solution domain. All the mesh points are classified as interior points, exterior dependent points and exterior independent points. The functional values at the exterior dependent points are updated at each time step by the approximate form of solution near the boundary. When the body is moving, only the status of points is changed and the mesh can stay fixed. The issue of 'freshly cleared nodes/cells' encountered in usual sharp interface methods does not pose any particular difficulty in the presented method. The Galerkin finite-element approximation is used for spatial discretization, and the discrete equations are integrated in time via a dual-time-stepping scheme based on artificial compressibility. In order to validate the present method for moving-boundary flow problems, two groups of flow phenomena have been simulated: (1) flows over a fixed circular cylinder, a harmonic in-line oscillating cylinder in fluid at rest and a transversely oscillating cylinder in uniform flow; (2) flows over a pure pitching airfoil, a heaving-pitching airfoil and a deforming airfoil. The predictions show good agreement with the published numerical results or experimental data. © 2010 John Wiley & Sons, Ltd.