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Multi-material pressure relaxation methods for Lagrangian hydrodynamics. (English) Zbl 1290.76138
Summary: In Arbitrary Lagrangian-Eulerian (ALE) methods for hydrodynamics with several materials, multiple-material Lagrangian cells invariably arise when the flow field is remapped onto a new mesh. One must close the system of equations for multi-material cells; this, in effect, constitutes a model – either explicit or implicit – for the sub-scale dynamics. We discuss several different multi-material closure model algorithms for Lagrangian hydrodynamics under the assumption of a single velocity for 1D, multiple-material cells. Russian researchers at the All-Russian Research Institute of Experimental Physics (VNIIEF) have developed several models, which we describe in some detail; recent work by US researchers was developed independent of the details of these models. This work contains a comparison of these different approaches, which we believe is unique in the literature. We compare these methods on two standard test problems and discuss the results.

##### MSC:
 76N15 Gas dynamics (general theory) 76T99 Multiphase and multicomponent flows 76M20 Finite difference methods applied to problems in fluid mechanics
##### Keywords:
compressible flow; Lagrangian methods; closure models
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##### References:
 [1] Barlow A. A new Lagrangian scheme for multimaterial cells. In: Proceedings of European congress on computational methods in applied sciences and engineering. ECCOMAS computational fluid dynamics conference; 2001. p. 235-94. [2] Després, B.; Lagoutière, F., Numerical resolution of a two-component compressible fluid model with interfaces, Prog Comput Fluid Dyn, 7, 295-310, (2007) · Zbl 1152.76443 [3] Shashkov, M. J., Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes, Int J Numer Meth Fl, 56, 1497-1504, (2008) · Zbl 1151.76026 [4] Managan RA, Miller DS. Mixed zone volume fraction updates. Tech. Rep. LLNL-PRES-416884; Livermore National Laboratory; 2009. . [5] Kamm, J. R.; Shashkov, M. J., A pressure relaxation closure model for one-dimensional, two-material Lagrangian hydrodynamics based on the Riemann problem, Commun Comput Phys, 7, 927-976, (2010) · Zbl 1364.76134 [6] Bondarenko, Y. A.; Yanilkin, Y. V., Computation of thermodynamical parameters of the mixed cells in gasdynamics, VANT (Mathematical Modeling of Physical Processes), 4, 12-25, (2000), [in Russian] [7] Delov, V. I.; Sadchikov, V. V., Comparison of several models for computation of thermodynamical parameters for heterogeneous Lagrangian cells, VANT (Mathematical Modeling of Physical Processes), 1, 57-70, (2005), [in Russian] [8] Goncharov, E. A.; Yanilkin, Y. V., New method for computations of thermodynamical states of the materials in the mixed cells, VANT (Mathematical Modeling of Physical Processes), 3, 16-30, (2004), [in Russian] [9] Goncharov, E. A.; Kolobyanin, V. Y.; Yanilkin, Y. V., A closure model for Lagrangian gasdynamics in mixed cells based on the assumption of equal constituent velocities, VANT (Mathematical Modeling of Physical Processes), 4, 100-105, (2006), [in Russian] [10] Kamm, J. R.; Shashkov, M. J.; Rider, W. J., A new pressure relaxation closure model for one-dimensional two-material Lagrangian hydrodynamics, Eur Phys J Web Conf, (2011) · Zbl 1429.76088 [11] Drake, R. P., Hydrodynamic instabilities in astrophysics and in laboratory high-energy-density systems, Plasma Phys Contr F, 47, B419-B440, (2005) [12] Bakhrakh, S. M.; Spiridonov, V. F.; Shanin, A. A., A method for computing gas-dynamic flows of inhomogeneous medium in Lagrangian-Eulerian coordinates, DAN SSR, 276, 4, 829-833, (1984), [in Russian; translated in Sov Phys Doklady 1984;29:443-5] [13] Benson, D. J., Computational methods in Lagrangian and Eulerian hydrocodes, Comput Method Appl Mech Eng, 99, 23, 235, (1992) · Zbl 0763.73052 [14] Weseloh WN, Clancy SP, Painter JW. PAGOSA Physics Manual. Tech. Rep. LA-14225-M; Los Alamos National Laboratory; 2010. [15] Zharova, G. V.; Yanilkin, Y. V., The EGAK code mixed cell pressure equilibration algorithm, VANT (Mathematical Modeling of Physical Processes), 3, 77-81, (1993), [in Russian] [16] Yanilkin YV. Study and implementation of multi-material pressure relaxation methods for Lagrangian hydrodynamics. Tech. Rep. LA-UR-10-06664; Los Alamos National Laboratory; 2010. [17] Goncharov, E. A.; Kolobyanin, V. Y.; Yanilkin, Y. V., On the way of finding artificial viscosities for materials in mixed cells, VANT (Mathematical Modeling of Physical Processes), 2, 15-29, (2010), [in Russian]
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