Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-22T19:32:53.157Z Has data issue: false hasContentIssue false
  • English
  • Français

Local Error Analysis and Comparison of the Swept- and Intersection-Based Remapping Methods

Published online by Cambridge University Press:  07 February 2017

Matej Klima ,
Milan Kucharik  and
Mikhail Shashkov
Matej Klima*
Affiliation:
Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Brehova 7, Praha 1, 115 19, Czech Republic
Milan Kucharik*
Affiliation:
Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Brehova 7, Praha 1, 115 19, Czech Republic
Mikhail Shashkov*
Affiliation:
XCP-4 Group, MS-F644, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
*
*Corresponding author.Email addresses:[email protected] (M. Klima), [email protected] (M. Kucharik), [email protected] (M. Shashkov)
*Corresponding author.Email addresses:[email protected] (M. Klima), [email protected] (M. Kucharik), [email protected] (M. Shashkov)
*Corresponding author.Email addresses:[email protected] (M. Klima), [email protected] (M. Kucharik), [email protected] (M. Shashkov)
Get access

Abstract

In this paper, the numerical error of two widely used methods for remapping of discrete quantities from one computational mesh to another is investigated. We compare the intuitive, but resource intensive method utilizing intersections of computational cells with the faster and simpler swept-region-based method. Both algorithms are formally second order accurate, however, they are known to produce slightly different quantity profiles in practical applications. The second-order estimate of the error formula is constructed algebraically for both algorithms so that their local accuracy can be evaluated. This general estimate is then used to assess the dependence of the performance of both methods on parameters such as the second derivatives of the remapped distribution, mesh geometry or mesh movement. Due to the complexity of such analysis, it is performed on a set of simplified elementary mesh patterns such as cell corner expansion, rotation or shear. On selected numerical tests it is demonstrated that the swept-based method can distort a symmetric quantity distribution more substantially than the intersection-based approach when the computational mesh moves in an unsuitable direction.

Keywords

Conservative interpolationremappingnumerical error analysisswept regionspolygon intersections
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 2 , February 2017 , pp. 526 - 558
Copyright
Copyright © Global-Science Press 2017 

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] Anderson, R. W., Elliott, N. S., and Pember, R. B.. An arbitrary Lagrangian-Eulerian method with adaptive mesh refinement for the solution of the Euler equations. Journal of Computational Physics, 199(2):598–617, 2004.Google Scholar
[2] Barth, T. J.. Numerical methods for gasdynamic systems on unstructured meshes. In Kroner, D., Ohlberger, M., and Rohde, C., editors, An introduction to Recent Developments in Theory and Numerics for Conservation Laws, Proceedings of the International School on Theory and Numerics for Conservation Laws, Berlin, 1997. Lecture Notes in Computational Science and Engineering, Springer. ISBN 3-540-65081-4.Google Scholar
[3] Benson, D. J.. Computational methods in Lagrangian and Eulerian hydrocodes. Computer Methods in Applied Mechanics and Engineering, 99(2-3):235–394, 1992.CrossRefGoogle Scholar
[4] Berndt, M., Breil, J., Galera, S., Kucharik, M., Maire, P.-H., and Shashkov, M.. Two step hybrid remapping (conservative interpolation) for multimaterial arbitrary Lagrangian-Eulerian methods. Journal of Computational Physics, 230(17):6664–6687, 2011.Google Scholar
[5] Burton, D. E., Kenamond, M. A., Morgan, N. R., Carney, T. C., and Shashkov, M. J.. An intersection based ALE scheme (xALE) for cell centered hydrodynamics (CCH). Talk at Multimat 2013, International Conference on Numerical Methods for Multi-Material Fluid Flows, San Francisco, September 2-6, 2013. LA-UR-13-26756.2.Google Scholar
[6] Caramana, E. J., Burton, D. E., Shashkov, M. J., and Whalen, P. P.. The construction of compatible hydrodynamics algorithms utilizing conservation of total energy. Journal of Computational Physics, 146(1):227–262, 1998.Google Scholar
[7] Caramana, E. J. and Shashkov, M. J.. Elimination of artificial grid distortion and hourglass-type motions by means of Lagrangian subzonal masses and pressures. Journal of Computational Physics, 142(2):521–561, 1998.Google Scholar
[8] Caramana, E.J., Shashkov, M.J., and Whalen, P.P.. Formulations of artificial viscosity for multidimensional shock wave computations. Journal of Computational Physics, 144(1):70–97, 1998.Google Scholar
[9] Dukowicz, J. K. and Baumgardner, J. R.. Incremental remapping as a transport/advection algorithm. Journal of Computational Physics, 160(1):318–335, 2000.Google Scholar
[10] Galera, S., Maire, P.-H., and Breil, J.. A two-dimensional unstructured cell-centered multimaterial ALE scheme using VOF interface reconstruction. Journal of Computational Physics, 229(16):5755–5787, 2010.Google Scholar
[11] Hirt, C. W., Amsden, A. A., and Cook, J. L.. An arbitrary Lagrangian-Eulerian computing method for all flow speeds. Journal of Computational Physics, 14(3):227–253, 1974.CrossRefGoogle Scholar
[12] Hoch, Ph.. An arbitrary Lagrangian-Eulerian strategy to solve compressible fluid flows. Technical report, CEA, 2009. HAL: hal-00366858. Available at http://hal.archives-ouvertes.fr/docs/00/36/68/58/PDF/ale2d.pdf.Google Scholar
[13] Kamm, J.R.. Evaluation of the Sedov-von Neumann-Taylor blast wave solution. Technical Report LA-UR-00-6055, Los Alamos National Laboratory, 2000.Google Scholar
[14] Kenamond, M. A. and Burton, D. E.. Exact intersection remapping of multi-material domain-decomposed polygonal meshes. Talk at Multimat 2013, International Conference on Numerical Methods for Multi-Material Fluid Flows, San Francisco, September 2-6, 2013. LA-UR-13-26794.Google Scholar
[15] Kjellgren, P. and Hyvarinen, J.. An arbitrary Lagrangian-Eulerian finite element method. Computational Mechanics, 21(1):81–90, 1998.Google Scholar
[16] Knupp, Patrick M.. Winslow smoothing on two-dimensional unstructured meshes. In Proceedings of the Seventh International Meshing Roundtable, Park City, UT, pages 449–457, 1998.Google Scholar
[17] Kucharik, M.. Arbitrary Lagrangian-Eulerian (ALE) Methods in Plasma Physics. PhD thesis, Czech Technical University in Prague, 2006.Google Scholar
[18] Kucharik, M., Breil, J., Galera, S., Maire, P.-H., Berndt, M., and Shashkov, M.. Hybrid remap for multi-material ALE. Computers & Fluids, 46(1):293–297, 2011.Google Scholar
[19] Kucharik, M. and Shashkov, M.. Flux-based approach for conservative remap of multimaterial quantities in 2D arbitrary Lagrangian-Eulerian simulations. In Fořt, Jaroslav, Fürst, Jiří, Halama, Jan, Herbin, Raphaèl, and Hubert, Florence, editors, Finite Volumes for Complex Applications VI Problems & Perspectives, volume 1 of Springer Proceedings in Mathematics, pages 623–631. Springer, 2011.Google Scholar
[20] Kucharik, M. and Shashkov, M.. One-step hybrid remapping algorithm for multi-material arbitrary Lagrangian-Eulerian methods. Journal of Computational Physics, 231(7):2851–2864, 2012.Google Scholar
[21] Kucharik, M. and Shashkov, M.. Conservative multi-material remap for staggered multimaterial Arbitrary Lagrangian–Eulerian methods. Journal of Computational Physics, 258:268–304, 2014.Google Scholar
[22] Kucharik, M., Shashkov, M., and Wendroff, B.. An efficient linearity-and-bound-preserving remapping method. Journal of Computational Physics, 188(2):462–471, 2003.Google Scholar
[23] Lauritzen, P.H., Erath, Ch., and Mittal, R.. On simplifying ‘incremental remap’-based transport schemes. Journal of Computational Physics, 230(22):7957–7963, 2011.Google Scholar
[24] Loubere, R., Maire, P.-H., Shashkov, M., Breil, J., and Galera, S.. ReALE: A reconnection-based arbitrary-LagrangianEulerian method. Journal of Computational Physics, 229(12):4724–4761, 2010.Google Scholar
[25] Margolin, L. G.. Introduction to “An arbitrary Lagrangian-Eulerian computing method for all flow speeds”. Journal of Computational Physics, 135(2):198–202, 1997.Google Scholar
[26] Margolin, L. G. and Shashkov, M.. Second-order sign-preserving remapping on general grids. Technical Report LA-UR-02-525, Los Alamos National Laboratory, 2002.Google Scholar
[27] Margolin, L. G. and Shashkov, M.. Second-order sign-preserving conservative interpolation (remapping) on general grids. Journal of Computational Physics, 184(1):266–298, 2003.Google Scholar
[28] Mavriplis, D. J.. Revisiting the least-squares procedure for gradient reconstruction on unstructured meshes. In AIAA 2003-3986, 2003. 16th AIAA Computational Fluid Dynamics Conference, June 23-26, Orlando, Florida.CrossRefGoogle Scholar
[29] Peery, J. S. and Carroll, D. E.. Multi-material ALE methods in unstructured grids. Computer Methods in Applied Mechanics and Engineering, 187(3-4):591–619, 2000.Google Scholar
[30] Pember, R. B. and Anderson, R. W.. A comparison of staggered-mesh Lagrange plus remap and cell-centered direct Eulerian Godunov schemes for Eulerian shock hydrodynamics. Technical report, LLNL, 2000. UCRL-JC-139820.Google Scholar
[31] Scovazzi, G., Love, E., and Shashkov, M.. Multi-scale Lagrangian shock hydrodynamics on Q1/P0 finite elements: Theoretical framework and two-dimensional computations. Computer Methods in Applied Mechanics and Engineering, 197(9-12):1056–1079, 2008.CrossRefGoogle Scholar
[32] Sedov, L.I.. Similarity and Dimensional Methods in Mechanics, Tenth Edition. Taylor & Francis, 1993.Google Scholar