Arbitrary Lagrangian-Eulerian (ALE) Method for Moving-Boundary Problems

An (ALE) method [1] for solving time-dependent incompressible Navier-Stokes equations is developed. In this method, the pressure is defined at the center of a control volume, while the Cartesian velocity components at its corners. The projection method is used for temporal discretisation and the pressure Poisson equation is solved iteratively with an efficient multigrid method. Solutions of both steady and unsteady problems established the favourable accuracy and efficiency of the present method.

Flow Passing a Cylinder


Fig. 1. Stream lines of flow passing a cylinder (Re = 39).

Flow Around airfoil NACA0012

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Fig. 2. Stream lines of flow around airfoil NACA0012 at Re = 1000 under attack angle 34 degree. Time t = 5 at left and t = 25 at right. Click here to see a movie.


[1] Li J., Hesse M., Ziegler J. and Woods A. W., 2005,
An Arbitrary Lagrangian Eulerian Method for Moving-Boundary Problems and Its Application to Jumping Over Water, J. Comp. Phys., 208, p.289-314.