# INCOMPRESSIBLE FLUID FLOW BY THE MACCORMACK METHOD

### Martins, M. M.; Bressan, J. D.; Button, S. T.;

The laminar incompressible fluid flow by computational numerical simulation often appears in numerical analysis in academic and industrial activities. In order to solve this kind of flow, it is necessary to determine the velocity and pressure fields which are the variables of Navier-Stockes equations[11,15,21]. However, to solve the equations of fluid flow with losses there is no simple equation to carry out velocity and pressure coupling, hence, it is necessary to use a coupling method to obtain velocity and pressure fields consistent[1,2,3]. This work deals with the presentation of a numerical method to calculate velocity and pressure fields to computational numerical simulation of laminar fluid incompressible flow with losses. The Navier-Stockes equations were discretized by the Finite Volume Method[11,15,21], using explicit MacCormack Method in co-localized and structured mesh[11,15,21], where velocity and pressure coupling was made by SIMPLE method[11,21]. The MacCormack method is a two-steps method (predictor-corrector) of second-order accuracy in both space and time and this method is commonly utilized in the resolution of compressible fluids problems. The numerical results of velocity fields were obtained for bi-dimensional case and it was compared with analytical results for parallel plates.

Palavras-chave: incompressible fluid, finite volume method, MacCormack Method, SIMPLE, velocity field.,

Palavras-chave:

DOI: 10.5151/meceng-wccm2012-18480

##### Referências bibliográficas
•  BASIC H., DEMIRDŽIC I.,DŽAFEROVIC E., “Finite volume method for simulation of extrusion processes”. Inter. Journ. for Num. Meth. in Eng. 62(4), 475–494, 2005.
•  CHORIN A.J., “A Numerical Method for Solving Incompressible Viscous Flow Problems”. Journ. of Comp. Phys. 2, 12-26, 1967.
•  CHOW P., CROSS M., PERICLEOUS K., “A Natural Extension of the Conventional Finite Volume Method into Polygonal Unstructured Meshes in CFD Application”. Inter. Journ. of Heat and Mass Trans. 20, 170-183, 1996.
•  DARWISH M., SRAJ I., MOUKALLED F., “A Coupled Finite Volume Solver for the Solution of Incompressible Flow on Unstructured Grids”. Journ. of Comp. Phys., 228, 180-201, 2009.
•  FORT J., FURST J., HALAMA J., KOZEL K., PRAHA, “Numerical Solution of 3D Transonic Flow Through Cascade”. Math. Bohem. 126, 353-361, 2001.
•  Hans P.L., Kent-Andre M., Ragnar W., “Numerical method for incompressible viscous flow”. Adv. Wat. Res. 25, 1125-1146, 2002.
•  INCROPERA F.P., DEWITT D.P., BERGMAN T.L., LAVINE, A.S., “Fundamentos de Transferência de Calor e de Massa”. Editora: LCT. Rio de Janeiro, 200
•  JASAK H. “Error Analysis and Estimation for the Finite Volume Method with Applications to Fluid Flows”. 1996. 394p. Thesis – Department of Mechanical Engineering, Imperial College of Science, Technology and Medicine, London.
•  LIN G.F., LAI J.S., GUO W.D., “Finite Volume Component-wise TVD Schemes for 2D Shallow Water Equations”. Adv. in Water Resour. 26, 861-873, 2003.
•  LOMAX H., PULLIAN T.H., ZINGG D.W., “Fundamentals of Computational Fluid Dynamics”. Editora: Springer, New York, 2003.
•  MALISKA C.R., “Transferência de Calor e Mecânica dos Fluidos Computacional”. Editora: LCT, Rio de Janeiro, 2004.
•  MOMPEAN G., THAIS, L., “Finite Volume Numerical Simulation of Viscoelastic Flows in General Orthogonal Coordinates”. Math. and Comp. in Sim. 80, 2185-2199, 2010.
•  NEOFYTUL P., “A 3rd Order Upwind Finite Volume Method for Generalized Newtonian Fluid Flows”. Adv. in Eng. Soft. 36, 664-680, 2005.
•  PATANKAR S.V., SPALDING D.B., “A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flow”. Inter. Journ. of Heat and Mass Trans. 15, 1787-1806, 1972.
•  PATANKAR S.V., “Numerical heat Transfer and Fluid Flow”. Editora: TaylorAndamp; Francis, London, 1980.
•  PILLER M., STALIO, E., “Finite-Volume Compact Schemes on Staggered Grids”. Journ. of Comp. Phys. 197, 299-340, 2004.
•  PORÍZKOVA P.P., FURST J. HORÁCEK J., KOZEL, K., “Numerical Solution of Unsteady Flows with Low Inlet Mach Numbers”. Math. and Comp. in Sim. 80, 1795-1805, 2010.
•  PORÍZKOVA P.P., KOZEL K., HORÁCEK J., “Simulation of Unsteady Compressible Flow in a Channel with Vibrating Walls-Influence of the Frequency”. Comp. Andamp; Fluids. 46, 404-410, 2011.
•  POTTER, M., WIGGERT, D.C., “Mecânica dos Fluidos”. Editora: Thomson, São Paulo, 2004.
•  RHIE, C.M., CHOW, W.L., “A Numerical Study of the Turbulent Flow Past an Isolated Airfoil with Trailing Edge Separation”. Am. Inst. of Aero. and Astron. 21, 1525-1532, 1983.
•  TANNEHILL J.C., ANDERSON D.A., PLETCHER, R.H. “Computational Fluid Mechanics and Heat Transfer”. Editora: TaylorAndamp;Francis. London, 1997.
•  VIMMR J., “Mathematical Modelling of Compressible Inviscid Fluid Flow Through a Sealing Gap in the Screw Compressor”. Math. and Comp. in Simul. 61, 187-197, 2003.
•  Zdanski, P.S.B., VAZ JR, M., INÁCIO, G.R., “A Finite Volume Approach to Simulation of Polymer Melt Flow in Channels”. Eng. Comp. 25, 233-250, 2008.
##### Como citar:

Martins, M. M.; Bressan, J. D.; Button, S. T.; "INCOMPRESSIBLE FLUID FLOW BY THE MACCORMACK METHOD", p. 1587-1600 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-18480

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