Abstract
We present a fluid particle model based on the Voronoi tessellation that allows one to represent an inviscid fluid in a Lagrangian description. The discrete model has all the required symmetries and structure of the continuum equations and can be understood as a linearly consistent discretization of Euler’s equations. Although the model is purely inviscid, we observe that the probability distribution of the accelerations of the Voronoi fluid particles shows the presence of tails at large accelerations, what is compatible with experimental Lagrangian turbulence observations.
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References
Frisch U., Turbulence (Cambridge University Press, 1995)
G. Falkovich K. Gawedzki M. Vergassola (2001) ArticleTitleParticles and fields in fluid turbulence Rev. Mod. Phys. 73 913 Occurrence Handle10.1103/RevModPhys.73.913 Occurrence Handle2001RvMP...73..913F Occurrence Handle2003f:76066
A.L. Porta G.A. Voth A.M. Crawford J. Alexander E Bodenshatz (2001) ArticleTitleFluid particle accelerations in fully developed turbulence Nature 409 1017 Occurrence Handle2001Natur.409.1017L
L.D. Landau and E.M. Lifshitz, Fluid Mechanics (Pergamon Press, 1959)
J.J. Monaghan (2002) ArticleTitleSph compressible turbulence Mon. Not. R Astron. Soc. 335 IssueID3 843–852 Occurrence Handle10.1046/j.1365-8711.2002.05678.x Occurrence Handle2002MNRAS.335..843M
J.J. Monaghan D. Price (2001) ArticleTitleVariational principles for relativistic smoothed particle hydrodynamics Mon. Not. R Astron. Soc. 328 IssueID3 381–392 Occurrence Handle2001MNRAS.328..381M
Lamb H., Hydrodynamics, 6th ed. (Cambridge University Press, 1932)
G.A. Kuz’min (1983) ArticleTitleIdeal incompressible hydrodynamics in terms of the vortex momentum density Phys. Let. 96A 88–90 Occurrence Handle1983PhLA...96...88K
V.I. Osledets (1989) ArticleTitleOn a new way of writing the Navier Stokes equation: The Hamiltonian formalism Russ. Math. Surveys 44 210–211
P. Español M. Serrano H.C. Öttinger (1999) ArticleTitleThermodynamically admissible form for discrete hydrodynamics Phys. Rev. Lett. 83 4542 Occurrence Handle1999PhRvL..83.4542E
P. Español M. Revenga (2003) ArticleTitleSmoothed dissipative particle dynamics Phys. Rev. E 67 026705 Occurrence Handle2003PhRvE..67b6705E
M. Serrano P. Español (2001) ArticleTitleThermodynamically consistent mesoscopic fluid particle model Phys. Rev. E 64 046115 Occurrence Handle10.1103/PhysRevE.64.046115 Occurrence Handle2001PhRvE..64d6115S
Wenneker I., Segal A., and Wesseling P., Computation of compressible flows on unstructured staggered grids, (2000) in ECCOMAS 2000 (Barcelona), E. Onate, G. Bugeda and B. Suarez
S. Friedlander and A. Lipton-Lifschitz, Localized instabilities in fluids, Handbook of Mathematical Fluid Dynamics, 2003 – math.uic.edu
N. Mordant J. Delour E. Léveque A. Arnéodo J.F Pinton (2002) ArticleTitleLong time correlations in Lagrangian dynamics: A key to intermittency in turbulence Phys. Rev. Lett. 89 254501–1 Occurrence Handle10.1103/PhysRevLett.89.254502 Occurrence Handle2002PhRvL..89y4502M
J.D. Weeks D. Chandler H.C. Andersen (1971) ArticleTitleThe Role of Repulsive Forces in Determining the Equilibrium of Simple Liquids J Chem. Phys. 54 5237 Occurrence Handle10.1063/1.1674820
L. Onsager (1949) ArticleTitleStatistical hydrodynamics Nuovo Cimento VI 280–287 Occurrence Handle12,60f
G.L. Eyink (1994) ArticleTitleEnergy dissipation without viscosity in ideal hydromechanics, Fourier analysis and local energy transfer Physica D 78 222–240 Occurrence Handle10.1016/0167-2789(94)90117-1 Occurrence Handle1994PhyD...78..222E Occurrence Handle0817.76011 Occurrence Handle95m:76020
N. Mordant P. Metz O. Michel J.-F. Pinton (2001) ArticleTitleMeasurement of Lagrangian velocity in fully developed turbulence Phys. Rev Lett. 87 214501–1 Occurrence Handle10.1103/PhysRevLett.87.214501 Occurrence Handle2001PhRvL..87u4501M
E.G. Flekkøy P.V. Coveney (1999) ArticleTitleFrom molecular to dissipative particle dynamics Phys. Rev. Lett. 83 1775 Occurrence Handle1999PhRvL..83.1775F
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Serrano, M., Español, P. & Zúñiga, I. Voronoi Fluid Particle Model for Euler Equations. J Stat Phys 121, 133–147 (2005). https://doi.org/10.1007/s10955-005-8414-y
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DOI: https://doi.org/10.1007/s10955-005-8414-y