Marcos Paulo de Carvalho Oliveira¹              Vicente Luiz Scalon¹         Alcides Padilha¹

1 Universidade Estadual Paulista Júlio de Mesquita Filho - UNESP. Bauru, SP, Brasil. E-mail: mpcoliveira@feb.unesp.br, scalon@feb.unesp.br, padilha@feb.unesp.br

RESUMO 

Neste trabalho é realizada uma análise da aplicação e do tempo de execução de um algoritmo numérico desenvolvido para a simulação de escoamento isotérmico de fluido incompressível. No código, emprega-se o algoritmo denominado esquema baseado nas características (CBS – characteristic based split), em que é usado o acoplamento da compressibilidade artificial (AC) para as equações da pressão e velocidades. A discretização foi realizada com o método dos elementos finitos, empregando-se uma malha de elementos bilineares. O programa GNU-Octave foi utilizado para implementar e executar as rotinas. Por meio do problema clássico da cavidade recirculante, foram avaliados resultados para diversos valores do número de Reynolds. Esses resultados mostraram boa concordância quando comparados aos disponíveis na literatura. A análise do tempo de execução das rotinas mostrou ainda que a montagem das matrizes é a etapa que exige maior consumo de tempo da implementação.

Palavras-chave: CBS, compressibilidade artificial, método de elementos finitos, cavidade recirculante, GNU-Octave.

ABSTRACT 

This work intends to analyze the application and execution time of a numerical algorithm that simulates incompressible and isothermal flows. It was used the explicit scheme of the "Characteristic Based Split" (CBS) algorithm and the "Artificial Compressibility" (AC) scheme for coupling pressure-velocity equations. The discretization was done with the finite element method using a bilinear elements grid. The free software GNU-Octave was used for implementation and execution of routines.  The results were analyzed using the classic lid-driven cavity problem. This work shows results for tests with several Reynolds' number. The results for these tests show a good agreement when compared with previous ones obtained from bibliography. The code runtime's analysis shows yet that the matrix's assembly is the part of greater consumption time in the implementation.

Keywords: CBS, artificial compressibility, finite element method, lid-driven cavity, GNU-Octave.

AGRADECIMENTOS 

Os autores agradecem à CAPES pelo suporte financeiro oferecido na forma de bolsa de estudos para o aluno de Pós-Graduação.

REFERÊNCIAS

[1] N. Massarotti, P. Nithiarasu e O.C. Zienkiewicz. "Characteristic-Based-Split (CBS) Algorithm for Incompressible Flow Problems with Heat Transfer". International Journal of Numerical Methods for Heat & Fluid Flow. Vol. 8, pp. 969-990. 1998.

[2] O.C. Zienkiewicz, P. Nithiarasu, R. Codina, M. Vazquez e P. Ortiz. "The Characteristic-Based-Split Procedure: A Efficient and Accurate Algorithm for Fluid Problems". Int. J. Numer. Meth. Fluids. Vol. 31, pp. 359-392. 1999.

[3] O.C. Zienkiewicz e R.L. Taylor. "The Finite Element Method". 5 edition. Butterworth-Heinemann. Oxford, England. 2000.

[4] P. Nithiarasu e O.C. Zienkiewicz. "On Stabilization of the CBS Algorithm: Internal and External Time Steps". Int. J. Numer. Meth. Engng. Vol. 48, pp. 875-880. 2000.

[5] P. Nithiarasu e C.B. Liu. "An artificial compressibility based characteristic based split (CBS) scheme for steady and unsteady turbulent incompressible flows". Comput. Methods Appl. Mech. Engrg. Vol. 195, pp. 2961-2982. 2006.

[6] P. Nithiarasu, J.S. Mathur, P. Weatherill e K. Morgan. "Three-dimensional incompressible flow calculations using the characteristic based split (CBS) scheme". International Journal for Numerical Methods in Fluids. Vol. 44, pp. 1207-1229. 2004.

[7] P. Nithiarasu e O.C. Zienkiewicz. "Analysis of an explicit and matrix free fractional step method for incompressible flows". Comput. Methods Appl. Mech. Engrg. Vol. 195, pp. 5537-5551. 2006.

[8] P. Nithiarasu, N. Massarotti e J.S. Mathur. "Forced convection heat transfer from solder balls on a printed circuit board using the characteristic based split (CBS) scheme".  International Journal for Numerical Methods in Heat & Fluid Flow. Vol. 15, pp. 73-95. 2005.

[9] C.G. Thomas e P. Nithiarasu. "Influences of element size and variable smoothing on inviscid compressible flow solution". International Journal of Numerical Methods for Heat and Fluid Flow. Vol. 15, pp. 420-428. 2005.

[10] U. Ghia, K.N. Ghia e C.T. Shin. "High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method". Journal of Computational Physics. Vol. 48, pp. 387-411. 1982.

[11] E. Erturk. "Lid Driven Cavity Flow". URLs: http://www.cavityflow.com. Acesso em: junho/2007.

[12] John W. Eaton. "GNU Octave". Verbatim copying and distribution is permitted in any medium, provided this notice is preserved. University of Wisconsin. Department of Chemical Engineering. Madison WI 53719. Copyright  1998-2006. URLs: http://www.gnu.org/software/octave/. Acesso em: 13 jun. 2007.

[13] P. Nithiarasu. "An efficient artificial compressibility (AC) scheme based on the characteristic based split (CBS) method for incompressible flows". Int. J. for Numer. Meth. Engng. Vol. 56, pp. 1815-1845. 2003.

Received: July 17, 2007, Accepted: April 27, 2009