Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-25T18:42:30.591Z Has data issue: false hasContentIssue false
  • English
  • Français

A Multi-Material CCALE-MOF Approach in Cylindrical Geometry

Published online by Cambridge University Press:  03 June 2015

Marie Billaud Friess ,
Jérôme Breil ,
Pierre-Henri Maire  and
Mikhail Shashkov
Marie Billaud Friess
Affiliation:
LUNAM Université, GeM, UMR CNRS 6183, Ecole Centrale Nantes, Université de Nantes, 1 rue de la Noë, BP 92101, 44321 Nantes Cedex 3, France
Jérôme Breil*
Affiliation:
Univ. Bordeaux, CEA, CNRS, CELIA, UMR5107, F-33400 Talence, France
Pierre-Henri Maire
Affiliation:
CEA CESTA, 15 Avenue des Sablières, CS 60001, 33116 Le Barp Cedex, France
Mikhail Shashkov
Affiliation:
Los Alamos National Laboratory, XCP-4, Los Alamos, NM 87545, USA
*
*Corresponding author.Email:breil@celia.u-bordeauxl.fr
Get access

Abstract

In this paper we present recent developments concerning a Cell-Centered Arbitrary Lagrangian Eulerian (CCALE) strategy using the Moment Of Fluid (MOF) interface reconstruction for the numerical simulation of multi-material compressible fluid flows on unstructured grids in cylindrical geometries. Especially, our attention is focused here on the following points. First, we propose a new formulation of the scheme used during the Lagrangian phase in the particular case of axisymmetric geometries. Then, the MOF method is considered for multi-interface reconstruction in cylindrical geometry. Subsequently, a method devoted to the rezoning of polar meshes is detailed. Finally, a generalization of the hybrid remapping to cylindrical geometries is presented. These explorations are validated by mean of several test cases using unstructured grid that clearly illustrate the robustness and accuracy of the new method.

Keywords

76M1076N1565K10Cell-centered schemeLagrangian hydrodynamicsALEMOF interface reconstructionRezoning algorithmpolar mesheshybrid remappingaxisymmetric geometries
Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 2 , February 2014 , pp. 330 - 364
Copyright
Copyright © Global Science Press Limited 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Ahn, H.T., Shashkov, M.J.: Multi-material interface reconstruction on generalized polyhedral meshes, J. Comput. Phys., 226(2):2096–2132, 2007.Google Scholar
[2]Anbarlooei, H.R., Mazaheri, K.: ‘Moment of fluid’ interface reconstruction method in axisym-metric coordinates, Int. J. Numer. Meth. Biomed. Engng., 27(10):1640–1651, 2011.Google Scholar
[3]Barlow, A.J.: A compatible finite element multi-material ALE hydrodynamics algorithm, Int. J. Numer. Meth. Fluids, 56(8):953–964, 2008.Google Scholar
[4]Barlow, A.J., Roe, P.L.: A cell centred Lagrangian Godunov scheme for shock hydrodynamics, Comput. Fluids, 46(1):133–136, 2011.Google Scholar
[5]Barth, T. J. and Jespersen, D. C.: The design and application of upwind schemes on unstructured meshes, 27th Aerospace Sciences Meeting, Reno, Nevada, AIAA paper 89–0366, 1989.Google Scholar
[6]Benson, D. J.: Computational methods in Lagrangian and Eulerian hydrocodes, Comp. Meth. in Appl. Mech. and Eng., 99:235–394, 1992.Google Scholar
[7]Berndt, M., Breil, J., Galera, S., Kucharik, M., Maire, P.-H., Shashkov, M.: Two-step hybrid conservative remapping for multi-material arbitrary Lagrangian-Eulerian methods, J. Comput. Phys., 230(17):6664–6687, 2011.Google Scholar
[8]Botsis, J. and Deville, M.: Mécanique des milieux continus : une introduction, Presses Polytechniques et Universitaires Romandes, 2006.Google Scholar
[9]Breil, J., Galera, S., Maire, P.-H.: Multi-material ALE computation in Inertial Confinement Fusion CHIC, Comput. Fluids, 46(1):161–167, 2011.Google Scholar
[10]Breil, J., Galera, S., Maire, P.-H.: A two-dimensional VOF interface reconstruction in a multimaterial cell-centered ALE scheme, Int. J. Numer. Meth. Fluids, 65(11-12):1351–1364, 2011.Google Scholar
[11]Del, S.Pino: Metric-based mesh adaptation for 2D Lagrangian compressible flows, J. Comput. Phys., 230:17931821, 2011.Google Scholar
[12]Carré, G., Del Pino, S., Després, B.: A cell-centered Lagrangian hydrodynamics scheme on general unstructured meshes in arbitrary dimension, J. Comput. Phys., 228(14):5160–5183, 2009.Google Scholar
[13]Dyadechko, V., Shashkov, M.: Reconstruction of Multi-material Interfaces from Moment Data, J. Comput. Phys., 227(11):5361–5384, 2008.Google Scholar
[14]Dukowicz, J. K.: A general, non-iterative Riemann solver for Godunov’s method, J. Comput. Phys., 61(1):119–137, 1985.Google Scholar
[15]Galera, S., Breil, J. and Maire, P.-H.: A 2Dunstructured multi-material Cell-Centered Arbitrary Lagrangian-Eulerian (CCALE) scheme using MOF interface reconstruction, Comput. Fluids, 46(1):237–244, 2011.Google Scholar
[16]Galera, S., Maire, P.-H. and Breil, J.: A two-dimensional unstructured cell-centered multimaterial ALE scheme using VOF interface reconstruction, J. Comput. Phys., 229(16):5755–5787, 2010.Google Scholar
[17]Haas, J.-F., Sturtevant, B.: Interaction of weak shock wave with cylindrical and spherical gas inhomogeneities, J. Fluid. Mech., 181:41–76, 1987.Google Scholar
[18]Hadjadj, A., Kudryavtsev, A.: Computation and flow visualization in high-speed aerodynamics, Journal of Turbulence, 6(161), 2005.Google Scholar
[19]Hirt, C.W., Amsden, A., and Cook, J.L.: An arbitrary Lagrangian-Eulerian computing method for all flow speeds, J. Comput. Phys., 14:227–253, 1974.Google Scholar
[20]Kamm, J.R., Timmes, F.X.: On efficient generation of numerically robust Sedov solutions,Technical Report LA-UR-07-2849, Los Alamos National Laboratory, 2007.Google Scholar
[21]Knupp, P.: Achieving finite element mesh quality via optimization of the Jacobian matrix norm and associated quantities. Part I– a framework for surface mesh optimization, Int. J. Numer. Meth. Engng, 48:401–420, 2000.Google Scholar
[22]Kucharik, M., Breil, J., Galera, S., Maire, P.-H., Berndt, M., Shashkov, M.: Hybrid remap for multi-material ALE, Comput. Fluids, 46(1):293–297, 2011.Google Scholar
[23]Kucharik, M., Garimella, R.V., Schofield, S.P., Shashkov, M.J.: A comparative study of interface reconstruction methods for multi-material ALE simulations, J. Comput. Phys., 229(7):2432–2452, 2010.CrossRefGoogle Scholar
[24]Loube, R.re, Maire, P.-H., Shashkov, M., Breil, J., Galera, S.: ReALE: A reconnection-based arbitrary-Lagrangian-Eulerian method, J. Comput. Phys., 229(12):4724–4761, 2010.Google Scholar
[25]Maire, P.-H.: A high-order cell-centered Lagrangian scheme for compressible fluid flows in two-dimensional cylindrical geometry, J. Comput. Phys., 228(18):6882–6915, 2009.Google Scholar
[26]Maire, P.-H.: A high-order cell-centered Lagrangian scheme for two-dimensional compressible fluid flows on unstructured meshes, J. Comput. Phys., 228(7):2391–2425, 2009.Google Scholar
[27]Maire, P.-H., Abgrall, R., Breil, J., Ovadia, J.: A cell-centered Lagrangian scheme for two-dimensional compressible flow problems, SIAM Journal of Scientific Computing, 29(4):1781–1824, 2007.Google Scholar
[28]Maire, P.-H.: Contribution to the numerical modeling of Inertial Confinement Fusion, Habilitation à Diriger des Recherches, Bordeaux University, 2011; Available at: http://tel.archives-ouvertes.fr/docs/00/58/97/58/PDF/hdr_main.pdf.Google Scholar
[29]Margolin, L. G., Shashkov, M.: Second-order sign-preserving conservative interpolation (remapping) on general grids, J. Comput. Phys., 184(1):266–298, 2003.Google Scholar
[30]Mirtich, B.: Fast and Accurate Computation of Polygonal Mass Properties, Journal of Graphics Tools, 1:31–50, 1996.Google Scholar
[31]Sedov, L.I.: Similarity and Dimensional Methods in Mechanics, Academic Press, New York, NY, 1959.Google Scholar
[32]Shashkov, M.: Closure models for multidimensional cells in arbitrary Lagrangian-Eulerian hydrocodes, Int. J. Numer. Meth. Fluids 56:1497–1504, 2008.Google Scholar
[33]Vachal, P., Maire, P.-H.: Discretizations for weighted condition number smoothing on general unstructured meshes, Comput. Fluids, 46(1):479–485, 2011.Google Scholar
[34]Vachal, P., Garimella, R.V., Shashkov, M.J.: Untangling of 2D meshes in ALE simulations, J. Comput. Phys., 196:627–644, 2004.Google Scholar
[35]Winslow, A.M.: Equipotential Zoning of Two-Dimensional Meshes, Lawrence Livermore National Laboratory, UCRL-7312, 1963.Google Scholar
[36]Youngs, D.L.: Time dependent multi-material flow with large fluid distortion, Numerical Methods for Fluid Dynamics, Morton, K.W. and Baine, M.J., 273–285, 1982.Google Scholar
[37]Youngs, D. L.: Multi-mode implosion in cylindrical 3D geometry, 11th International Workshop on the Physics of Compressible Turbulent Mixing (IWPCTM11), Santa Fe, 2008.Google Scholar