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Ocean Engineering

Computational Techniques for Stabilized Edge-Based Finite Element Simulation of Nonlinear Free-Surface Flows

[+] Author and Article Information
Renato N. Elias

High Performance Computing Centre, Federal University of Rio de Janeiro, P.O. Box 68506, Rio de Janeiro, RJ 21945-970, Brazilrenato@nacad.ufrj.br

Milton A. Gonçalves

High Performance Computing Centre, Federal University of Rio de Janeiro, P.O. Box 68506, Rio de Janeiro, RJ 21945-970, Brazilmilton@nacad.ufrj.br

Alvaro L. G. A. Coutinho

High Performance Computing Centre, Federal University of Rio de Janeiro, P.O. Box 68506, Rio de Janeiro, RJ 21945-970, Brazilalvaro@nacad.ufrj.br

Paulo T. T. Esperança

Department of Naval and Ocean Engineering, Federal University of Rio de Janeiro, P.O. Box 68508, Rio de Janeiro, RJ 21945-970, Brazilptarso@peno.coppe.ufrj.br

Marcos A. D. Martins

 PETROBRAS Research Center, Avenida Horacio Macedo 850, Rio de Janeiro, Brazilmarcos.martins@petrobras.com.br

Marcos D. A. S. Ferreira

 PETROBRAS Research Center, Avenida Horacio Macedo 850, Rio de Janeiro, Brazilmarcos.donato@petrobras.com.br

J. Offshore Mech. Arct. Eng 131(4), 041103 (Sep 08, 2009) (7 pages) doi:10.1115/1.3124136 History: Received August 16, 2008; Revised February 26, 2009; Published September 08, 2009

Free-surface flows occur in several problems in hydrodynamics, such as fuel or water sloshing in tanks, waves breaking in ships, offshore platforms, harbors, and coastal areas. The computation of such highly nonlinear flows is challenging, since free-surfaces commonly present merging, fragmentation, and breaking parts, leading to the use of interface-capturing Eulerian approaches. In such methods the surface between two fluids is captured by the use of a marking function, which is transported in a flow field. In this work we discuss computational techniques for efficient implementation of 3D incompressible streamline-upwind/Petrov–Galerkin (SUPG)/pressure-stabilizing/Petrov–Galerkin finite element methods to cope with free-surface problems with the volume-of-fluid method (Elias, and Coutinho, 2007, “Stabilized Edge-Based Finite Element Simulation of Free-Surface Flows,” Int. J. Numer. Methods Fluids, 54, pp. 965–993). The pure advection equation for the scalar marking function was solved by a fully implicit parallel edge-based SUPG finite element formulation. Global mass conservation is enforced, adding or removing mass proportionally to the absolute value of the normal velocity of the interface. We introduce parallel edge-based data structures, a parallel dynamic deactivation algorithm to solve the marking function equation only in a small region around the interface. The implementation is targeted to distributed memory systems with cache-based processors. The performance and accuracy of the proposed solution method is tested in the simulation of the water impact on a square cylinder and in the propagation of a solitary wave.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 2

Solitary wave propagation from free-surface elevation at t=0 s, t=2 s, t=4 s, t=6 s, t=8 s, and t=10 s.

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Figure 3

Wave impact with a tall structure—model description

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Figure 4

Impact force on the column in the mainstream direction

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Figure 5

Velocity in the x direction

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Figure 6

Snapshots for the simulation of the wave impact with a tall structure: (a) t=0.451 s, (b) t=0.901 s, and (c) t=1.651 s

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Figure 7

Parallel dynamic deactivation region of active entities

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Figure 1

Schematic view of computational domain. L=200 m, h=10 m, d=10 m, and w=0.5 m.

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