Published in Comput. Methods Appl. Mech. Engrg. (2006) 195: 3001–3037
We present a general formulation for incompressible ﬂuid ﬂow analysis using the ﬁnite element method (FEM). The standard Eulerian formulation is described ﬁrst. The necessary stabilization for dealing with convective eﬀects and the incompressibility condition are introduced via the ﬁnite calculus (FIC) method. A simple extension of the ﬂuid ﬂow equations to an arbitrary Lagrangian–Eulerian (ALE) frame adequate for treating ﬂuid–structure interaction problems is brieﬂy presented. A fully Lagrangian formulation called the particle ﬁnite element method (PFEM) is also described. The PFEM is particularly attractive for ﬂuid–structure interaction problems involving large motions of the free surface and breaking waves. Examples of application of the Eulerian, the ALE and the fully lagrangian PFEM formulations are presented. Ó 2005 Elsevier B.V. All rights reserved.
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