Parallel simulation of multiphase flows using octree adaptivity and the volume-of-fluid method

Gilou Agbaglah; Sébastien Delaux; Daniel Fuster; Jérôme Hoepffner; Christophe Josserand; Stéphane Popinet; Pascal Ray; Ruben Scardovelli; Stéphane Zaleski

doi:10.1016/j.crme.2010.12.006

Parallel simulation of multiphase flows using octree adaptivity and the volume-of-fluid method

Gilou Agbaglah ^1,²; Sébastien Delaux ³; Daniel Fuster ^1,²; Jérôme Hoepffner ^1,²; Christophe Josserand ^1,²; Stéphane Popinet ^1,^2,³; Pascal Ray ^1,²; Ruben Scardovelli ⁴; Stéphane Zaleski ^1,²

¹ Univ. Paris 06, UMR 7190, institut Jean-Le-Rond-d'Alembert, 75005 Paris, France
² CNRS, UMR 7190, institut Jean-Le-Rond-d'Alembert, 75005 Paris, France
³ National Institute of Water and Atmospheric Research, Private Bag 14-901, Wellington, New Zealand
⁴ DIENCA - Lab. di Montecuccolino, Università degli Studi di Bologna, Via dei Colli 16, 40136 Bologna, Italy

Comptes Rendus. Mécanique, High Performance Computing, Volume 339 (2011) no. 2-3, pp. 194-207.

Abstract
Résumé

We describe computations performed using the Gerris code, an open-source software implementing finite volume solvers on an octree adaptive grid together with a piecewise linear volume of fluid interface tracking method. The parallelisation of Gerris is achieved by domain decomposition. We show examples of the capabilities of Gerris on several types of problems. The impact of a droplet on a layer of the same liquid results in the formation of a thin air layer trapped between the droplet and the liquid layer that the adaptive refinement allows to capture. It is followed by the jetting of a thin corolla emerging from below the impacting droplet. The jet atomisation problem is another extremely challenging computational problem, in which a large number of small scales are generated. Finally we show an example of a turbulent jet computation in an equivalent resolution of $6 \times 1024^{3}$ cells. The jet simulation is based on the configuration of the Deepwater Horizon oil leak.

Nous décrivons des simulations réalisées avec le code Gerris, un logiciel libre qui implémente des méthodes de résolution de type volume fini sur un maillage adaptatif hiérarchique octree, et une méthode de suivi en volume avec construction d'interface affine par morceaux. La parallélisation de Gerris est obtenue par une décomposition en domaine. Nous montrons des exemples des capacités de cette approche sur plusieurs types de problèmes. L'impact d'un goutte sur une couche du même liquide provoque la formation d'une mince couche d'aire sous la goutte à l'instant de l'impact qui peut être capturée par la méthode adaptative. Il est suivi par le jaillissement d'une mince corolle par dessous la goutte impactante. Le problème de l'atomization est également un défi important pour le calcul intentsif, dans lequel un grand nombre de structures de petite échelle sont produites. Finalement nous montrons un exemple de simulation de jet turbulent avec une résolution équivalente de $6 \times 1024^{3}$ cellules. Cette configuration est basée sur celle de la fuite de pétrole brut de Deepwater Horizon.

Published online: 2011-01-14

DOI: 10.1016/j.crme.2010.12.006

Keywords: Computer science, Two-phase flow, Parallel computing, Octree, Volume-of-fluid, Droplet impact, Atomisation
Mots-clés : Informatique, Algorithmique, Écoulement diphasique, Calcul parallèle, Octree, Volume de fluid, Impact de goutte, Atomisation

Author's affiliations:

Gilou Agbaglah ^{1, 2}; Sébastien Delaux ³; Daniel Fuster ^{1, 2}; Jérôme Hoepffner ^{1, 2}; Christophe Josserand ^{1, 2}; Stéphane Popinet ^{1, 2, 3}; Pascal Ray ^{1, 2}; Ruben Scardovelli ⁴; Stéphane Zaleski ^{1, 2}

¹ Univ. Paris 06, UMR 7190, institut Jean-Le-Rond-d'Alembert, 75005 Paris, France
² CNRS, UMR 7190, institut Jean-Le-Rond-d'Alembert, 75005 Paris, France
³ National Institute of Water and Atmospheric Research, Private Bag 14-901, Wellington, New Zealand
⁴ DIENCA - Lab. di Montecuccolino, Università degli Studi di Bologna, Via dei Colli 16, 40136 Bologna, Italy

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     author = {Gilou Agbaglah and S\'ebastien Delaux and Daniel Fuster and J\'er\^ome Hoepffner and Christophe Josserand and St\'ephane Popinet and Pascal Ray and Ruben Scardovelli and St\'ephane Zaleski},
     title = {Parallel simulation of multiphase flows using octree adaptivity and the volume-of-fluid method},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {194--207},
     publisher = {Elsevier},
     volume = {339},
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     year = {2011},
     doi = {10.1016/j.crme.2010.12.006},
     language = {en},
}

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Gilou Agbaglah; Sébastien Delaux; Daniel Fuster; Jérôme Hoepffner; Christophe Josserand; Stéphane Popinet; Pascal Ray; Ruben Scardovelli; Stéphane Zaleski. Parallel simulation of multiphase flows using octree adaptivity and the volume-of-fluid method. Comptes Rendus. Mécanique, High Performance Computing, Volume 339 (2011) no. 2-3, pp. 194-207. doi : 10.1016/j.crme.2010.12.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.12.006/

References
Cited by

[1] D. Fuster; G. Agbaglah; C. Josserand; S. Popinet; S. Zaleski Numerical simulation of droplets, bubbles and waves: state of the art, Fluid Dynam. Res., Volume 41 (2009), p. 065001

[2] S. Popinet An accurate adaptive solver for surface-tension-driven interfacial flows, J. Comput. Phys., Volume 228 (2009) no. 16, pp. 5838-5866

[3] M. Sussman; A.S. Almgren; J.B. Bell; P. Colella; L.H. Howell; M.L. Welcome An adaptive level set approach for incompressible two-phase flows, J. Comput. Phys., Volume 148 (1999), pp. 81-124

[4] R. Lebas; T. Menard; P.A. Beau; A. Berlemont; F.X. Demoulin Numerical simulation of primary break-up and atomization: DNS and modelling study, Int. J. Multiphase Flow, Volume 35 (2009), pp. 247-260

[5] S. Popinet Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries, J. Comput. Phys., Volume 190 (2003) no. 2, pp. 572-600

[6] G. Agresar; J.J. Linderman; G. Tryggvason; K.G. Powell An adaptive, Cartesian, front-tracking method for the motion, deformation and adhesion of circulating cells, J. Comput. Phys., Volume 43 (1998), pp. 346-380

[7] F. Gibou; L. Chen; D. Nguyen; S. Banerjee A level set based sharp interface method for the multiphase incompressible Navier–Stokes equations with phase change, J. Comput. Phys., Volume 222 (2007), pp. 536-555

[8] S. Popinet The Gerris flow solver, 2010 http://gfs.sf.net

[9] G. Tryggvason, R. Scardovelli, S. Zaleski, Direct Numerical Simulations of Gas–Liquid Multiphase Flows, Cambridge University Press, 2011, in press.

[10] E. Aulisa; S. Manservisi; R. Scardovelli; S. Zaleski Interface reconstruction with least-squares fit and split advection in three-dimensional Cartesian geometry, J. Comput. Phys., Volume 225 (2007), pp. 2301-2319

[11] J. Li Calcul d'interface affine par morceaux, C. R. Acad. Sci. Paris Sér. IIb (Paris), Volume 320 (1995), pp. 391-396

[12] R. Scardovelli; S. Zaleski Interface reconstruction with least-square fit and split Lagrangian–Eulerian advection, Int J. Numer. Meth. Fluids, Volume 41 (2003), pp. 251-274

[13] E. Aulisa; S. Manservisi; R. Scardovelli; S. Zaleski A geometrical area-preserving volume of fluid advection method, J. Comput. Phys., Volume 192 (2003), pp. 355-364

[14] M.M. Francois; S.J. Cummins; E.D. Dendy; D.B. Kothe; J.M. Sicilian; M.W. Williams A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework, J. Comput. Phys., Volume 213 (2006) no. 1, pp. 141-173

[15] S. Popinet The GNU triangulated surface library, 2010 http://gts.sf.net

[16] R. Diekmann; R. Preis; F. Schlimbach; C. Walshaw Shape-optimized mesh partitioning and load balancing for parallel adaptive FEM, Parallel Comput., Volume 26 (2000) no. 12, pp. 1555-1581

[17] J.E. Boillat Load balancing and Poisson equation in a graph, Concurrency: Practice and Experience, Volume 2 (1990) no. 4, pp. 289-313

[18] Y.F. Hu; R.J. Blake; D.R. Emerson An optimal migration algorithm for dynamic load balancing, Concurrency: Practice and Experience, Volume 10 (1998) no. 6, pp. 467-483

[19] J.K. Johnson, D. Bickson, D. Dolev, Fixing convergence of Gaussian belief propagation, in: IEEE International Symposium on Information Theory (ISIT) 2009.

[20] H. Kellerer; U. Pferschy; D. Pisinger Knapsack Problems, Springer-Verlag, 2004

[21] S. Popinet Atomisation of a pulsed liquid jet, 2009 http://gfs.sourceforge.net/examples/examples/atomisation.html

[22] D. Fuster; A. Bagué; T. Boeck; L. Le Moyne; A. Leboissetier; S. Popinet; P. Ray; R. Scardovelli; S. Zaleski Simulation of primary atomization with an octree adaptive mesh refinement and VOF method, Int. J. Multiphase Flow, Volume 35 (2009) no. 6, pp. 550-565

[23] J.L. Zable Splatter during ink jet printing, IBM J. Res. Development, Volume 21 (1977) no. 4, pp. 315-320

[24] P. Einsenklam Atomisation of liquid fuel for combustion, J. Inst. Fuel, Volume 0 (1961), pp. 130-143

[25] O. Planchon; E. Mouche A physical model for the action of raindrop erosion on soil microtopography, Soil Sci. Soc. Am. J., Volume 74 (2010), pp. 1092-1103

[26] S.T. Thoroddsen; T.G. Etoh; K. Takehara Air entrapment under an impacting drop, J. Fluid Mech., Volume 478 (2003), pp. 125-134

[27] V. Mehdi-Nejad; J. Mostaghimi; S. Chandra Air bubble entrapment under an impacting droplet, Phys. Fluids, Volume 15 (2003) no. 1, pp. 173-183

[28] C. Josserand; S. Zaleski Droplet splashing on a thin liquid film, Phys. Fluids, Volume 15 (2003), p. 1650

[29] S. Mandre; M. Mani; M.P. Brenner Precursors to splashing of liquid droplets on a solid surface, Phys. Rev. Lett., Volume 102 (2009), p. 134502

[30] S.D. Howison; J.R. Ockendon; J.M. Oliver; R. Purvis; F.T. Smith Droplet impact on a thin fluid layer, J. Fluid. Mech., Volume 542 (2005), pp. 1-23

[31] F. Ben Rayana, Étude des instabilités interfaciales liquide-gaz en atomisation assistée et tailles de gouttes, PhD thesis, Institut National Polytechnique de Grenoble, 2007.

[32] T. Boeck; S. Zaleski Viscous versus inviscid instability of two-phase mixing layers with continuous velocity profile, Phys. Fluids, Volume 17 (2005), p. 032106

[33] P. Marmottant; E. Villermaux On spray formation, J. Fluid Mech., Volume 498 (2004), pp. 73-111

[34] T.J. Crone; M. Tolstoy Magnitude of the 2010 Gulf of Mexico oil leak, Science, Volume 330 (2010) no. 6004, p. 634

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