A natural element updated Lagrangian approach for modelling fluid structure interactions
DOI:
https://doi.org/10.13052/REMN.16.323-336Keywords:
fluid structure interaction, meshless methods, natural element method, α-shapesAbstract
In this paper we present a novel methodology for the numerical simulation of fluid structure interactions in the presence of free surfaces. It is based on the use of the Natural Element Method (NEM) in an updated Lagrangian framework, together with the integration of the Navier-Stokes equations by employing a Galerkin-characteristics formulation. Tracking of the free-surface is made by employing shape constructors, in particular α- shapes. A theoretical description of the method is made and also some examples of the performance of the technique are included.
Downloads
References
Belytschko T., Lu Y. Y., Gu L., “Element-Free Galerkin Methods”, International Journal for
Numerical Methods in Engineering, 37, 1994, p. 229-256.
Chen Jiun-Shyan, Wu Cheng-Tang, Yoon Sangpil, You Yang, “A stabilized conforming
nodal integration for galerkin mesh-free methods”, International Journal for Numerical
Methods in Engineering, 50, 2001, p. 435-466.
Cueto E., Calvo B., Doblare M., “Modeling three-dimensional piece-wise homogeneous
domains using the α-shape based Natural Element Method”, International Journal for
Numerical Methods in Engineering, 54, 2002, p. 871-897.
Cueto E., Cegoñino J., Calvo B., Doblare M., “On the imposition of essential boundary
conditions in Natural Neighbour Galerkin methods”, Communications in Numerical
Methods in Engineering, vol. 19, n° 5, 2003, p. 361-376.
Cueto E., Doblare M., Gracia L., “Imposing essential boundary conditions in the Natural
Element Method by means of density-scaled alpha-shapes”, International Journal for
Numerical Methods in Engineering, vol. 49, n° 4, 2000, p. 519-546.
Cueto E., Sukumar N., Calvo B., Martinez M. A., Cegoñnino J., Doblare M., “Overview and
recent advances in Natural Neighbour Galerkin methods”, Archives of Computational
Methods in Engineering, vol. 10, n° 4, 2003, p. 307-384.
Donea J., “Arbitrary Lagrangian-Eulerian finite element methods”, Belytschko T.,
Hughes T. J. R., editors, Computer methods for transient analyses, Elsevier-Amsterdam,
, p. 474-516.
Donea J., Huerta A., Finite Element Methods for Flow Problems, John Wiley and sons, 2003.
Duchemin L., Popinet S., Josserand C., Zaleski S., “Jet formation in bubbles bursting at a free
surface”, Physics of Fluids, 14, 2002, p. 3000-3008.
Edelsbrunner H., Muecke E., “Three dimensional alpha shapes”, ACM Transactions on
Graphics, 13, p. 43-72, 1994.
Gonzalez D., Cueto E., Martinez M. A., Doblare M., “Numerical integration in Natural
Neighbour Galerkin methods”, International Journal for Numerical Methods in
Engineering, vol. 60, n° 12, 2004, p. 2077-2104.
Gonzalez D., Cueto E., Doblare M., “Volumetric locking in Natural Neighbour Galerkin
methods”, International Journal for Numerical Methods in Engineering, vol. 61, n° 4,
, p. 11-632.
González D., Cueto E., Chinesca F., Doblaré M., “A Natural Element updated Lagrangian
strategy for free-surface Fluid Dynamics”, Submitted, 2006.
Idelsohn S. R., Oñate E., del Pin F., “The particle finite element method: a powerful tool to
solve incompressible flows with free-surfaces and breaking waves”, International Journal
for Numerical Methods in Engineering, vol. 61, n° 7, 2004, p. 964-989.
Liu W. K., Jun S., Li S., Adee J., Belytschko T., “Reproducing kernel particle methods”,
International Journal for Numerical Methods in Engineering, 38, 1995, p. 1655-1679.
Martin J.C., Moyce W.J., “Part IV. an experimental study of the collapse of liquid columns
on a rigid horizontal plane”, Phil. Tran. R. Soc. London, 244, p. 312, 1952.
Martinez M. A., Cueto E., Alfaro I., Doblare M., Chinesta F., “Updated Lagrangian free
surface flow simulations with Natural Neighbour Galerkin methods”, International
Journal for Numerical Methods in Engineering, vol. 60, n° 13, 2004, p. 2105-2129.
Sibson R., “A Vector Identity for the Dirichlet Tesselation”, Mathematical Proceedings of the
Cambridge Philosophical Society , 87, 1980, p. 151-155.
Sibson R., “A brief description of natural neighbour interpolation”, Interpreting Multivariate
Data, V. Barnett (Editor), John Wiley, 1981, p. 21-36.
Sukumar N., Moran B., Belytschko T., “The Natural Element Method in Solid Mechanics”,
International Journal for Numerical Methods in Engineering, vol. 43, n° 5, 1998, p. 839-
Sukumar N., Moran B., Yu Semenov A., Belikov V. V., “Natural Neighbor Galerkin
Methods”, International Journal for Numerical Methods in Engineering, vol. 50, n° 1,
p. 1-27, 2001.
