Developing of Numerical Solution Algorithms for Analysis of External Flows Around Cylinder

Kamiar ZAMZAMIAN, Seyyed Hadi TAHERI
2.177 622


Incompressible flows are an indispensable part of research issues in the area of aerodynamic and hydrodynamic. The main solution for incompressible Navier-Stocks equations are the spinfunction and initial variables methods, which is divided into two main categories including pressure based and artificial compressibility methods. In pressure based method, governing nonlinear equation are separated and then pressure Poisson equation based on momentum and continuity is formed. In this method, velocity and pressure fields are calculated by solving the momentum and pressure Poisson equations respectively. Considering a constant density through the incompressible flow is resulted in the absence of derivative termsin the continuity equation which causes a problem in integrating. In order to overcome these problems artificial compressibility method is utilized which adds an artificial derivative term in continuity equations, then the velocity and pressure fields are coupled. In this research, the effectiveness of pressure based and artificial compressibility methods are compared to analyze the external flows characteristics, in various Reynolds number. Developed approaches are validated by comparing previous researches. Simulation results indicate that artificial compressibility method base on characteristics gives more accurate solutions than pressure based method.


Artificial Compressibility, Pressure Based, Navier-Stoks Equations, External Flow, Finite Volume

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A.K.,Hofman, S.T., Chiang, “Computational fluid dynamics for engineers”, Vol.1, Mc Graw-Hill, New York, PP.590, (1994).

F.H., Harlow, J.E., Welch, “Numerical calculation of time dependent viscous incompressible flow of fluid with free surface,physics”, vol. 8, pp.2182-2194, (1965).

S.V., Ptanakar,D.B., Spalding, “A calculation procedure for heat, mass and momentum transfer in three dimension parabolic flows”,Int.J Heat Mass, Vol. 15, Issue 10, pp. 1787– 1806, 1972.

J.P. van Doormaal, G.D. Raithby,“Enhancement of the SIMPLE method forpredictingincompressible fluid flow”, Numer. Heat Transfer, vol. 7 pp. 147–163, (1984).

P.F. Galpin, G.D. Raithby, “Numerical solution of problems in incompressible fluid flow: treatment of the temperature-velocity coupling”, Numerical HeatTransfer, vol.10, pp. 105– 129, (1986).

Y. Jiang, A.J. Przekwas, “Implicit pressure-based incompressible Navier–Stokes equations solver for unstructured meshes”, AIAA 940305, (1994).

Y. Jiang, Y.G. Lai, A.J. Przekwas, “3D simulation of complex flows at all flow speeds with an implicit multi-domain approach”, AIAA, 93-3124, (1993).

N.S. Reddy, K.,Rajagopal, P.H.,Veena, V.K.,Pravin, “A Pressure based Solver for an Incompressible Laminar Newtonian Fluids”, International Journal of Fluids Engineering, Vol. 5, Number 1, pp. 21-28, (2013).

Z.J., Chen, S.V.,Marella, A.J.,Przekwas, “A Finite Volume Method of Pressure-Based Coupled Solver for Incompressible/Compressible Flows”, 47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition 5 -, Orlando, Florida, (2009).

Z. J. Chen, A. J. Przekwas, “A coupled pressure-based computational method for incompressible/compressible flows”, Journal of Computational Physics, Volume 229 Issue 24, pp. 9150-9165, (2010).

A.J.,Chorin, “A Numerical Method for Solving Incompressible Viscous flowproblems”, Journal of Computational Physics, Vol. 2, pp. 12-26, (1967).

K., Siong, C.Y., Zhao, “Numerical Study of Steady/unsteady Flow and Heat Transfer in PorousMedia Using a Characteristics-Based Matrix-Free Implicit FV Method on Unstructured Grids”,International Journal of Heat and Fluid Flow, Vol. 25, pp. 1015-1033, (2004).

E. Shapiro, D. Drikakis,“Artificial compressibility, characteristics-based schemes for variable density, incompressible, multi-species flows. Part II. Multigrid implementation and numerical tests”, Journal of Computational Physics, Vol. 210, pp. 608-631, (2005).

K.Zamzamian, S.A.,Razavi, “Multidimensional upwinding for incompressible flows based on characteristics”, J. Comput. Phys. Vol. 227, pp. 8699–8713, (2008).

V.Esfahanian , P.Akbarzadeh, “The Jameson’s numerical method for solving the incompressible viscous and inviscid flows by means of artificial compressibility and preconditioning method”, Applied Mathematics and Computation, Vol. 206, pp. 651–661, (2008).

A.Crivellini, V. D’Alessandro, F.Bassi, “Assessment of a high-order discontinuous Galerkin method for incompressible three-dimensional Navier–Stokes equations: Benchmark results for the flow past a sphere up to Re = 500”, Computers & Fluids, Vol. 86,pp. 442–458, (2013).

J., Kim, D., Kim, H., Choi, “An immersed-boundary finite-volume method for simulations of flow in complex geometries”, Journal of Computational Physics, Vol. 171 Issue 1, pp. 132 – 150, (2001).