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The Diffused Vortex Hydrodynamics Method

Published online by Cambridge University Press:  30 July 2015

Emanuele Rossi ,
Andrea Colagrossi ,
Benjamin Bouscasse  and
Giorgio Graziani
Emanuele Rossi
Affiliation:
Department of Mathematics, University of Rome, Sapienza, Rome, 00185, Italy
Andrea Colagrossi*
Affiliation:
CNR-INSEAN, Marine Technology Research Institute, Rome, 00128, Italy
Benjamin Bouscasse
Affiliation:
CNR-INSEAN, Marine Technology Research Institute, Rome, 00128, Italy
Giorgio Graziani
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Rome, Sapienza, Rome, 00185, Italy
*
*Corresponding author. Email addresses: e-rossi@mat.uniroma1.it (E. Rossi), andrea.colagrossi@cnr.it (A. Colagrossi), benjamin.bouscasse@cnr.it (B. Bouscasse), g.graziani@uniroma1.it (G. Graziani)
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Abstract

A new Particle Vortex Method, called Diffused Vortex Hydrodynamics (DVH), is presented in this paper. The DVH is a meshless method characterized by the use of a regular distribution of points close to a solid surface to perform the vorticity diffusion process in the boundary layer regions. This redistribution avoids excessive clustering or rarefaction of the vortex particles providing robustness and high accuracy to the method. The generation of the regular distribution of points is performed through a packing algorithm which is embedded in the solver. The packing algorithm collocates points regularly around body of arbitrary shape allowing an exact enforcement on the solid surfaces of the no-slip boundary condition. The present method is tested and validated on different problems of increasing complexities up to flows with Reynolds number equal to 100,000 (without using any subgrid-scale turbulence model).

Keywords

Vorticity dynamicsvortex methodparticle methodsmeshless methodsmeshfree methodspacking algorithmdiffused vortex hydrodynamicsbody fitted methodvortex wake
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 2 , August 2015 , pp. 351 - 379
Copyright
Copyright © Global-Science Press 2015 

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References

[1]Barba, L.A., Leonard, A., and Allen, C.B.. Advances in viscous vortex methods-meshless spatial adaption based on radial basis function interpolation. International Journal for Numerical Methods in Fluids, 47(5):387–421, 2005.Google Scholar
[2]Barba, L.A., Leonard, A., and Allen, C.B.. Numerical investigations on the accuracy of the vortex method with and without remeshing. In 16th AIAA Computational Fluid Dynamics Conference, June 2003.Google Scholar
[3]Benson, M.G., Bellamy-Knights, P.G, Gerrard, J.H., and Gladwell, I.. A viscous splitting algorithm applied to low reynolds number flows round a circular cylinder. Journal of Fluids and Structures, 3(5):439–479, 1989.Google Scholar
[4]Chorin, A.. Numerical study of slightly viscous flow. Journal of Fluid Mechanics, 57(04):785–796, 1973.CrossRefGoogle Scholar
[5]Chorin, A.. Vortex sheet approximation of boundary layers. Journal of Computational Physics, 27(3):428–442, 1978.CrossRefGoogle Scholar
[6]Christiansen, I.P.. Numerical simulation of hydrodynamics by the method of point vortices. Journal of Computational Physics, 13(3):363–379, 1973.CrossRefGoogle Scholar
[7]Colagrossi, A., Bouscasse, B., Antuono, M., and Marrone, S.. Particle packing algorithm for SPH schemes. Computer Physics Communications, 183(2):1641–1683, 2012.CrossRefGoogle Scholar
[8]Colagrossi, A., Graziani, G., and Pulvirenti, M.. Particles for fluids: SPH vs vortex methods. Journal of Mathematics and Mechanics of Complex Systems, 2(1):45–70, 2014.Google Scholar
[9]Cottet, G.-H. and Koumoutsakos, P.D.. Vortex Methods: Theory and Practice. Cambridge University Press, University Printing House, Shaftesbury Road, Cambridge, United Kingdom, 2008.Google Scholar
[10]Coutanceau, M. and Bouard, R.. Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. Part 1. Steady flow. Journal of Fluid Mechanics, 79(02):231–256, 1977.CrossRefGoogle Scholar
[11]Edwards, E. and Bridson, R.. A high-order accurate particle-in-cell method. International Journal for Numerical Methods in Engineering, 90(9):1073–1088, 2012.Google Scholar
[12]Eldredge, J.D.. Efficient tools for the simulation of flapping wing flows. AIAA, 85(2005):1–11, 2005.Google Scholar
[13]Graziani, G. and Bassanini, P.. Unsteady viscous flows about bodies: Vorticity release and forces. Meccanica, 37(3):283–303, 2002.Google Scholar
[14]Graziani, G. and Landrini, M.. Application of multipoles expansion technique to two-dimensional nonlinear free-surface flows. Journal of Ship Research, 43(1):1–12, 1999.Google Scholar
[15]Graziani, G., Ranucci, M., and Piva, R.. From a boundary integral formulation to a vortex method for viscous flows. Computational Mechanics, 15(4):301–314, 1995.Google Scholar
[16]Hockney, R.W. and Eastwood, J.W.. Computer Simulation Using Particles. Adam Hilger, Bristol, 1988.Google Scholar
[17]Huang, C.-J. and Huang, M.-J.. A vortex method suitable for long time simulations of flow over body of arbitrary geometry. Computers & Fluids, 74:1–12, 2013.Google Scholar
[18]Koumoutsakos, P. and Leonard, A.. High-resolution simulations of the flow around an impulsively started cylinder using vortex methods. Journal of Fluid Mechanics, 296:1–38, 1995.Google Scholar
[19]Macià, F., Antuono, M., González, L.M., and Colagrossi, A.. Theoretical analysis of the no-slip boundary condition enforcement in SPH methods. Progress of Theoretical Physics, 125(6):1091–1121, 2011.CrossRefGoogle Scholar
[20]Marrone, S., Bouscasse, B., Colagrossi, A., and Antuono, M.. Study of ship wave breaking patterns using 3D parallel SPH simulations. Computers & Fluids, 69(0):54–66, 2012.Google Scholar
[21]Marrone, S., Colagrossi, A., Antuono, M., Colicchio, G., and Graziani, G.. An accurate SPH modeling of viscous flows around bodies at low and moderate reynolds numbers. Journal of Computational Physics, 245(0):456–475, 2013.Google Scholar
[22]Nair, M.T. and Sengupta, T.K.. Unsteady flow past elliptic cylinders. Journal of Fluids and Structures, 11(6):555–595, 1997.Google Scholar
[23]Riccardi, G. and Durante, D.. Elementi di Fluidodinamica. Springer, 2006.Google Scholar
[24]Rossi, E., Colagrossi, A., and Graziani, G.. Numerical simulation of 2D-vorticity dynamics using particle methods. Computers & Mathematics with Applications, 69(12):1484-1503, 2015.Google Scholar
[25]Shadloo, M.S., Zainali, A., Yildiz, M., and Suleman, A.. A robust weakly compressible SPH method and its comparison with an incompressible SPH. International Journal for Numerical Methods in Engineering, 89(8):939–956, 2012.CrossRefGoogle Scholar
[26]Singh, S.P. and Mittal, S.. Flow past a cylinder: Shear layer instability and drag crisis. International Journal for Numerical Methods in Fluids, 47(1):75–98, 2005.CrossRefGoogle Scholar
[27]Dommelen, L. Van and Rundensteiner, E.A.. Fast, adaptive summation of point forces in the two-dimensional poisson equation. Journal of Computational Physics, 83(1):126–147, 1989.Google Scholar