Chao, Chien-Chi Three-dimensional free surface simulation. (English) Zbl 1429.76026 Math. Comput. Simul. 81, No. 6, 1161-1176 (2011). Summary: A 3D boundary element method with linear triangular element has been developed for the simulation of the free surface subjected to the surface tension force. A liquid droplet and a liquid jet are chosen to be the studying cases for the free surface simulation. The codes include 3D Laplace’s solver, grid generation, and free surface module for the calculation of surface normal vector, surface curvature, and tangential velocity. Distortion of a droplet has shown the corresponding mode oscillation by specifying a given order of Legendre function for the initial velocity potential. And, the comparison of computational results and the predicted values from the dispersion equation, which serves as the analytical solution for the growth rate, for the temporal instability analysis on a liquid jet shows a very good agreement. This has shown that the proposed model is capable of the complex 3D liquid jet simulation. MSC: 76-10 Mathematical modeling or simulation for problems pertaining to fluid mechanics 76M15 Boundary element methods applied to problems in fluid mechanics 76B45 Capillarity (surface tension) for incompressible inviscid fluids 76D45 Capillarity (surface tension) for incompressible viscous fluids Keywords:3D BEM; liquid droplet; liquid jet; temporal instability analysis; surface tension force PDFBibTeX XMLCite \textit{C.-C. Chao}, Math. Comput. Simul. 81, No. 6, 1161--1176 (2011; Zbl 1429.76026) Full Text: DOI References: [1] Chao, C. C.; Heister, S. D., Contributions of atomization to F-1 engine combustion instabilities, Anal. Bound. Elem., 28, 1045-1053 (2004) [2] Chahine, G. L., A numerical model for three-dimensional bubble dynamics in complex configurations, (Proceedings of the 22nd American Towing Tank Conference (1989)) [3] Chahine, G. L.; Purdue, T. O., Simulation of the three-dimensional behavior of an unsteady large bubble near a structure, (Wang, T. G., A.I.P. Conference Proceedings (1989)), 169-187 [4] Chahine, G. L.; Kalumuck, K. M.; Duraiswami, R., Fluid-structure interaction simulation of bubble dynamics by coupling fluid BEM and structural FEM codes, (Bubble Noise and Cavitation and Multiphase Flow Forum, vol. 109 (1991)), 49-54 [5] Chahine, G. L.R.; Duraiswami, R.; Lakshminarsimha, A. N., Dynamical interactions in a bubble cloud, (Cavitation and Multiphase Flow Forum, vol. 109 (1991)), 49-54 [6] Liggett, J. A.; Liu, P. L.F., The Boundary Integral Equation Method for Porous Media Flow (1983), George Allen and Unwin: George Allen and Unwin London · Zbl 0622.76103 [7] Mansour, N. N., Satellite formation in capillary jet breakup, Phys. Fluids A, 2, 1141-1144 (1990) [8] Oguz, H.; Zeng, J., Axisymmetric and three-dimensional boundary integral simulations of bubble growth from an underwater orifices, Eng. Anal. Bound. Elem., 19, 319-330 (1997) [9] Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P., Numerical Recipes in FORTRAN. The Art of Scientific Computing (1992), Cambridge University Press · Zbl 0778.65002 [10] Rayleigh, W. S., On the instabilities of jets, (Proceedings of the London Mathematical Society, vol. 10 (1878)), 4-6 [11] Spangler, C. A.; Hilbing, J. H.; Heister, S. D., A boundary element method for atomization of a finite liquid jet, Atom. Sprays, 5, 621-638 (1995) [12] Spangler, C. A.; Hibing, J. H.; Heister, S. D., Nonlinear modeling of jet atomization in the wind-induced regime, Phys. Fluids, 7, 964-971 (1995) · Zbl 1023.76571 [13] Yang, H. Q., Asymmetric instability of a liquid jet, Phys. Fluids, 4, 681-689 (1992) · Zbl 0825.76259 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.