×

zbMATH — the first resource for mathematics

A new surface-tension formulation for multi-phase SPH using a reproducing divergence approximation. (English) Zbl 1346.76161
Summary: In this paper, we propose a new surface-tension formulation for multi-phase smoothed particle hydrodynamics (SPH). To obtain a stable and accurate scheme for surface curvature, a new reproducing divergence approximation without the need for a matrix inversion is derived. Furthermore, we introduce a density-weighted color-gradient formulation to reflect the reality of an asymmetrically distributed surface-tension force. We validate our method with analytic solutions and demonstrate convergence for different cases. Furthermore, we show that our formulation can handle phase interfaces with density and viscosity ratios of up to 1000 and 100, respectively. Finally, complex three-dimensional simulations including breakup of an interface demonstrate the capabilities of our method.

MSC:
76M28 Particle methods and lattice-gas methods
76Txx Multiphase and multicomponent flows
Software:
PPM
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Brackbill, J.U.; Kothe, D.B.; Zemach, C., A continuum method for modeling surface tension, J. comput. phys., 100, 2, 335-354, (1992) · Zbl 0775.76110
[2] Chen, J.K.; Beraun, J.E.; Carney, T.C., A corrective smoothed particle method for boundary value problems in heat conduction, Int. J. numer. methods eng., 46, 2, 231-252, (1999) · Zbl 0941.65104
[3] Español, P.; Revenga, M., Smoothed dissipative particle dynamics, Phys. rev. E, 67, 2, 026705, (2003)
[4] Fitzgibbon, A.; Pilu, M.; Fisher, R.B., Direct least square Fitting of ellipses, IEEE trans. pattern anal. machine intell., 21, 476-480, (1999)
[5] Hongbin, J.; Xin, D., On criterions for smoothed particle hydrodynamics kernels in stable field, J. comput. phys., 202, 2, 699-709, (2005) · Zbl 1061.76067
[6] Hu, X.Y.; Adams, N.A., A multi-phase SPH method for macroscopic and mesoscopic flows, J. comput. phys., 213, 2, 844-861, (2006) · Zbl 1136.76419
[7] Hu, X.Y.; Adams, N.A., Angular-momentum conservative smoothed particle dynamics for incompressible viscous flows, Phys. fluids, 18, 10, 101702, (2006)
[8] Hu, X.Y.; Adams, N.A., An incompressible multi-phase SPH method, J. comput. phys., 227, 1, 264-278, (2007) · Zbl 1126.76045
[9] Li, J.; Renardy, Y.Y.; Renardy, M., Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method, Phys. fluids, 12, 2, 269-282, (2000) · Zbl 1149.76454
[10] Monaghan, J.J., Smoothed particle hydrodynamics, Rep. prog. phys., 68, 8, 1703-1759, (2005)
[11] Morris, J.P., Simulating surface tension with smoothed particle hydrodynamics, Int. J. numer. methods fluids, 33, 3, 333-353, (2000) · Zbl 0985.76072
[12] Morris, J.P.; Fox, P.J.; Zhu, Y., Modeling low Reynolds number incompressible flows using SPH, J. comput. phys., 136, 1, 214-226, (1997) · Zbl 0889.76066
[13] Nugent, S.; Posch, H.A., Liquid drops and surface tension with smoothed particle applied mechanics, Phys. rev. E, 62, 4, (2000)
[14] Randles, P.W.; Libersky, L.D., Smoothed particle hydrodynamics: some recent improvements and applications, Comput. methods appl. mech. eng., 139, 1-4, 375-408, (1996) · Zbl 0896.73075
[15] Sbalzarini, I.F.; Walther, J.H.; Bergdorf, M.; Hieber, S.E.; Kotsalis, E.M.; Koumoutsakos, P., PPM - a highly efficient parallel particle-mesh library for the simulation of continuum systems, J. comput. phys., 215, 2, 566-588, (2006) · Zbl 1173.76398
[16] Tartakovsky, A.M.; Meakin, P., Modeling of surface tension and contact angles with smoothed particle hydrodynamics, Phys. rev. E, 72, 2, (2005)
[17] Taylor, G.I., The formation of emulsions in definable fields of flow, Proc. roy. soc. London ser. A, 501-523, (1934)
[18] Zhu, Y.; Fox, P.J., Smoothed particle hydrodynamics model for diffusion through porous media, Transport porous media, 43, 3, 441-471, (2001)
[19] J. Biddiscombe, D. Graham, P. Maruzewski, Interactive visualization and exploration of SPH data, in: Proceedings of 2nd SPHERIC international workshop, Madrid (Spain), May 2007, pp. 47-50.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.