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TECHNICAL PAPERS

A Stable Semi-Implicit Method for Free Surface Flows

[+] Author and Article Information
Cassio M. Oishi

Departamento de Ciências de Computação e Estatística, ICMC,  Universidade de São Paulo, USP, Av. Trabalhador São Carlense, 400, C.P. 668, 13251-900, São Carlos, SP, Braziloishi@icmc.usp.br

José A. Cuminato

Departamento de Ciências de Computação e Estatística, ICMC,  Universidade de São Paulo, USP, Av. Trabalhador São Carlense, 400, C.P. 668, 13251-900, São Carlos, SP, Braziljacumina@icmc.usp.br

Valdemir G. Ferreira

Departamento de Ciências de Computação e Estatística, ICMC,  Universidade de São Paulo, USP, Av. Trabalhador São Carlense, 400, C.P. 668, 13251-900, São Carlos, SP, Brazilpvgf@icmc.usp.br

Murilo F. Tomé

Departamento de Ciências de Computação e Estatística, ICMC,  Universidade de São Paulo, USP, Av. Trabalhador São Carlense, 400, C.P. 668, 13251-900, São Carlos, SP, Brazilmurilo@icmc.usp.br

Antonio Castelo

Departamento de Ciências de Computação e Estatística, ICMC,  Universidade de São Paulo, USP, Av. Trabalhador São Carlense, 400, C.P. 668, 13251-900, São Carlos, SP, Brazilcastelo@icmc.usp.br

Norberto Mangiavacchi

Departamento de Engenharia Mecânica,  Universidade do Estado do Rio de Janeiro, UERJ, Rua Sao Francisco Xavier, 524, 20550-900 Rio de Janeito, RJ, Brazilnorberto@uerj.br

Sean McKee

Department of Mathematics,  University of Strathclyde, Livingstone Tower, Glasgow, UKsmck@maths.strath.ac.uk

J. Appl. Mech 73(6), 940-947 (Dec 30, 2005) (8 pages) doi:10.1115/1.2173672 History: Received June 01, 2005; Revised December 30, 2005

The present work is concerned with a semi-implicit modification of the GENSMAC method for solving the two-dimensional time-dependent incompressible Navier-Stokes equations in primitive variables formulation with a free surface. A projection method is employed to uncouple the velocity components and pressure, thus allowing the solution of each variable separately (a segregated approach). The viscous terms are treated by the implicit backward method in time and a centered second order method in space, and the nonlinear convection terms are explicitly approximated by the high order upwind variable-order nonoscillatory scheme method in space. The boundary conditions at the free surface couple the otherwise segregated velocity and pressure fields. The present work proposes a method that allows the segregated solution of free surface flow problems to be computed by semi-implicit schemes that preserve the stability conditions of the related coupled semi-implicit scheme. The numerical method is applied to both the simulation of free surface and to confined flows. The numerical results demonstrate that the present technique eliminates the parabolic stability restriction required by the original explicit GENSMAC method, and also found in segregated semi-implicit methods with time-lagged boundary conditions. For low Reynolds number flows, the method is robust and very efficient when compared to the original GENSMAC method.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Cell classification. (b) Flow visualization of glucose syrup. For details see (13).

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Figure 2

Cell of the free surface in contact, in its right lateral face, with an empty cell

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Figure 3

Cell on the free surface with two adjacent empty cells

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Figure 4

Geometry and boundaries for the extrudate-swell problem: (a) unsteady state and (b) steady state

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Figure 5

Free surface profile for extrudate swell of a Newtonian jet using F2 formulation at different non-dimensional times: (a) t=6.0, (b) t=12.0, (c) t=18.0 and (d) t=24.6

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