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TECHNICAL PAPERS

Numerical Simulation of Transient Free Surface Flows Using a Moving Mesh Technique

[+] Author and Article Information
Laura Battaglia

Centro Internacional de Métodos Computacionales en Ingeniería, Instituto de Desarrollo Tecnológico para Industria Química, Universidad Nacional del Litoral - CONICET, Güemes 3450, 3000-Santa Fe, Argentinalbattaglia@ceride.gov.ar

Jorge D’Elía

Centro Internacional de Métodos Computacionales en Ingeniería, Instituto de Desarrollo Tecnológico para Industria Química, Universidad Nacional del Litoral - CONICET, Güemes 3450, 3000-Santa Fe, Argentinajdelia@intec.unl.edu.ar

Mario Storti

Centro Internacional de Métodos Computacionales en Ingeniería, Instituto de Desarrollo Tecnológico para Industria Química, Universidad Nacional del Litoral - CONICET, Güemes 3450, 3000-Santa Fe, Argentinamstorti@intec.unl.edu.ar

Norberto Nigro

Centro Internacional de Métodos Computacionales en Ingeniería, Instituto de Desarrollo Tecnológico para Industria Química, Universidad Nacional del Litoral - CONICET, Güemes 3450, 3000-Santa Fe, Argentinannigro@intec.unl.edu.ar

J. Appl. Mech 73(6), 1017-1025 (Feb 28, 2006) (9 pages) doi:10.1115/1.2198246 History: Received July 19, 2005; Revised February 28, 2006

In this work, transient free surface flows of a viscous incompressible fluid are numerically solved through parallel computation. Transient free surface flows are boundary-value problems of the moving type that involve geometrical nonlinearities. In contrast to more conventional computational fluid dynamics problems, the computational flow domain is partially bounded by a free surface which is not known a priori, since its shape must be computed as part of the solution. In steady flow the free surface is obtained by an iterative process, but when the free surface evolves with time the problem is more difficult as it generates large distortions in the computational flow domain. The incompressible Navier-Stokes numerical solver is based on the finite element method with equal order elements for pressure and velocity (linear elements), and it uses a streamline upwind/Petrov-Galerkin (SUPG) scheme (Hughes, T. J. R., and Brooks, A. N., 1979, “A Multidimensional Upwind Scheme With no Crosswind Diffusion,” in Finite Element Methods for Convection Dominated Flows, ASME ed., 34. AMD, New York, pp. 19–35, and Brooks, A. N., and Hughes, T. J. R., 1982, “Streamline Upwind/Petrov-Galerkin Formulations for Convection Dominated Flows With Particular Emphasis on the Incompressible Navier-Stokes Equations,” Comput. Methods Appl. Mech. Eng., 32, pp. 199–259) combined with a Pressure-Stabilizing/Petrov-Galerkin (PSPG) one (Tezduyar, T. E., 1992, “Stablized Finite Element Formulations for Incompressible Flow Computations,” Adv. Appl. Mech., 28, pp. 1–44, and Tezduyar, T. E., Mittal, S., Ray, S. E., and Shih, R., 1992, “Incompressible Flow Computations With Stabilized Bilinear and Linear Equal Order Interpolation Velocity-Pressure Elements,” Comput. Methods Appl. Mech. Eng., 95, pp. 221–242). At each time step, the fluid equations are solved with constant pressure and null viscous traction conditions at the free surface and the velocities obtained in this way are used for updating the positions of the surface nodes. Then, a pseudo elastic problem is solved in the fluid domain in order to relocate the interior nodes so as to keep mesh distortion controlled. This has been implemented in the PETSc-FEM code (PETSc-FEM: a general purpose, parallel, multi-physics FEM program. GNU general public license (GPL), http://www.cimec.org.ar/petscfem) by running two parallel instances of the code and exchanging information between them. Some numerical examples are presented.

Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 14

Vorticity and streamlines at time step nt=224. Once the vortices are shed they are transported by the fluid.

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Figure 15

Vorticity and streamlines at time step nt=230. A new vortex forming on the right half.

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Figure 16

PETSc-FEM hooks that exchange information and data for the synchronization of the global execution of the fluid and pseudo elastic solvers

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Figure 17

The master processes of both PETSc-FEM (fluid and mesh-movement) are executed at the same computing node

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Figure 18

The PETSc-FEM parallel runs (fluid and mesh movement) are running in different node sets but their master processes (MPI rank 0) must be the same

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Figure 3

Boundary conditions for the pseudo elastic problem for a mesh movement: nodes can move freely at the solid walls ABCD, GH and IE (slip boundary condition) and non-slip one in portion HFI to prevent large distortions of elements near the tip F of the separator

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Figure 4

Dimensions in m and initial free surface position for the sloshing problem with known solution

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Figure 5

Analytic solution curve and numerical results (dots) calculated for the sloshing problem

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Figure 6

Vertical and horizontal sections of a right vertical cylinder with annular base for a three-dimensional quasi-inviscid sloshing test. Initial free surface and reference axis. Dimensions in m.

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Figure 7

Displacements time evolution for some representative mesh nodes in the tank of annular base

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Figure 8

Filtered nodes movement on the free surface for the 3D cylindrical tank

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Figure 9

Period of movement T versus mesh mean step h for the sloshing 3D test

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Figure 10

Main geometrical dimensions of a truck-like container with a separating wall

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Figure 11

Updated mesh with a pseudo elastic strategy

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Figure 12

Vorticity and streamlines at time step nt=209. A forming vortex is clearly formed on the left wall of the separator near the tip.

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Figure 13

Vorticity and streamlines at time step nt=217. The previously formed vortex has been separated from the wall.

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Figure 1

A flow domain with a free surface discretized by domain-like schemes: Eulerian-type (left) and Lagrangian-type (right) methods

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Figure 2

Notation for the spines-like employed in the mesh movement

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