Operator Splitting Algorithms for Free Surface Flows: Application to Extrusion Processes
We investigate the benefits of operator splitting methods in the context of computational fluid dynamics. In particular, we exploit their capacity at handling free surface flows and a large variety of physical phenomena in a flexible way. A mathematical a
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Operator Splitting Algorithms for Free Surface Flows: Application to Extrusion Processes Andrea Bonito, Alexandre Caboussat, and Marco Picasso
Abstract We investigate the benefits of operator splitting methods in the context of computational fluid dynamics. In particular, we exploit their capacity at handling free surface flows and a large variety of physical phenomena in a flexible way. A mathematical and computational framework is presented for the numerical simulation of free surface flows, where the operator splitting strategy allows to separate inertial effects from the other effects. The method of characteristics on a fine structured grid is put forward to accurately approximate the inertial effects while continuous piecewise polynomial finite element associated with a coarser subdivision made of simplices is advocated for the other effects. In addition, the splitting strategy also allows modularity, and in a straightforward manner rheological model change for the fluid. We will emphasize this flexibility by treating Newtonian flows, visco-elastic flows, multi-phase, and multi-density immiscible incompressible Newtonian flows. The numerical framework is thoroughly presented; the test case of the filling of a cylindrical tube with potential die swell in an extrusion process is taken as the main illustration of the advantages of operator splitting.
A. Bonito () Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA e-mail: [email protected] A. Caboussat Haute Ecole de Gestion de Genève, University of Applied Sciences Western Switzerland (HES-SO), Rue de la Tambourine 17, 1227 Carouge, Switzerland e-mail: [email protected] M. Picasso MATHICSE, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland e-mail: [email protected]
© Springer International Publishing Switzerland 2016 R. Glowinski et al. (eds.), Splitting Methods in Communication, Imaging, Science, and Engineering, Scientific Computation, DOI 10.1007/978-3-319-41589-5_21
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1 Introduction Complex free surface phenomena involving multi-phase Newtonian and/or NonNewtonian flows are nowadays a topic of active research in many fields of physics, engineering, and bioengineering. Numerous mathematical models and associated numerical approximations for complex liquid-gas free surfaces problems are also available. The purpose of this chapter is to present a comprehensive review of a computational methodology developed in the group of Jacques Rappaz at Ecole polytechnique fédérale de Lausanne (EPFL), called cfsFlow and commercialized by a spinoff company of EPFL named Ycoor Systems S.A. [40]. Originally proposed for two-dimensional cases by Maronnier, Picasso, and Rappaz [25], it evolved to handle three-dimensional flows [26], account for surrounding compressible gas [11, 12] and surface tension [8], allow complex rheology [6], include space adaptive interface tracking [9], and recently integrate multi-phase fluids [19]. Besides the typical fluid flows applications, it is
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