Adaptive reconnection-based arbitrary Lagrangian Eulerian method

Journal of Computational Physics

Volumn 299, Issue , 2015, Pages 902-939

  Bo, Wurigen ^a   Shashkov, Mikhail ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

H Adaptation; R Adaptation; Reconnection based Arbitrary Lagrangian Methods (ReALE)

Indexed keywords

MESH GENERATION; NUMERICAL METHODS;

ARBITRARY LAGRANGIAN EULERIAN; ARBITRARY LAGRANGIAN EULERIAN METHOD; CENTROIDAL VORONOI TESSELLATION; H-ADAPTATION; LAGRANGIAN; LAGRANGIAN METHODS; MONITOR FUNCTIONS; R-ADAPTATION; RECONNECTION-BASED ARBITRARY LAGRANGIAN METHOD; TIME STEP;

LAGRANGE MULTIPLIERS;

EID: 84938906785     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2015.07.032     Document Type: Article

References (51)

1. Alauzet F. High-order methods and mesh adaptation for Euler equations. Int. J. Numer. Methods Fluids 2008, 56(8):1069-1076.
2. Aurenhammer F. Voronoi diagrams - a survey of fundamental geometric data structures. ACM Comput. Surv. 1991, 23(3):345-405.
3. Barth T.J. Numerical methods for gasdynamic systems on unstructured meshes. Lecture Notes in Computational Science and Engineering 1997, 195-284. Springer, Berlin. D. Kroner, M. Ohlberger, C. Rohde (Eds.).
4. Belme Anca, Dervieux Alain, Alauzet Frédéric Time accurate anisotropic goal-oriented mesh adaptation for unsteady flows. J. Comput. Phys. 2012, 231(19):6323-6348.
5. Bo W., Shashkov M. R-Adaptive Reconnection-based Arbitrary Lagrangian Eulerian method - R-ReALE. J. Math. Study 2015, 48(2):125-167.
6. Breil J., Harribey T., Maire P.-H., Shashkov M. A multi-material ReALE method with MOF interface reconstruction. Comput. Fluids 2013, 83:115-125.
7. Budd Chris J., Huang Weizhang, Russell Robert D. Adaptivity with moving grids. Acta Numer. 2009, 18:111-241.
8. Carré G., Del Pino S., Després Bruno, Labourasse Emmanuel A cell-centered Lagrangian hydrodynamics scheme on general unstructured meshes in arbitrary dimension. J. Comput. Phys. 2009, 228(14):5160-5183.
9. Cheng Siu-Wing, Dey Tamal Krishna, Shewchuk Jonathan Richard Delaunay Mesh Generation 2012, CRC Press.
10. Dorfi E.A., Drury L.O'C. Simple adaptive grids for 1-D initial value problems. J. Comput. Phys. 1987, 69:175-195.
11. Du Qiang, Faber Vance, Gunzburger Max Centroidal Voronoi tessellations: applications and algorithms. SIAM Rev. 1999, 41(4):637-676.
12. Du Qiang, Gunzburger Max, Ju Lili Advances in studies and applications of centroidal Voronoi tessellations. Numer. Math., Theory Methods Appl. 2010, 3(2):119-142.
13. Du Qiang, Wang Desheng Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations. Int. J. Numer. Methods Eng. 2003, 56(9):1355-1373.
14. Du Qiang, Wang Desheng Recent progress in robust and quality Delaunay mesh generation. J. Comput. Appl. Math. 2006, 195(1):8-23.
15. Dukowicz John K., Kodis John W. Accurate conservative remapping (rezoning) for arbitrary Lagrangian-Eulerian computations. SIAM J. Sci. Stat. Comput. 1987, 8(3):305-321.
16. Frey Pascal Jean, Marechal Jean Fast adaptive quadtree mesh generation. 7th International Meshing Roundtable 1998, 211-224. Citeseer.
17. Gersho Allen Asymptotically optimal block quantization. IEEE Trans. Inf. Theory 1979, 25(4):373-380.
18. Grandy J. Conservative remapping and region overlays by intersecting arbitrary polyhedra. J. Comput. Phys. 1999, 148(2):133-166.
19. Gruber Peter M. Optimum quantization and its applications. Adv. Math. 2004, 186(2):456-497.
20. Harribey T., Breil J., Maire P.-H., Shashkov M. A swept-intersection-based remapping method in a ReALE framework. Int. J. Numer. Methods Fluids 2013, 72:697-708.
21. Thibault Harribey, Breil Jérôme, Maire Pierre-Henri, Shashkov Mikhail A swept-intersection-based remapping method in a ReALE framework. Int. J. Numer. Methods Fluids 2013, 72(6):697-708.
22. Frédéric Hecht, BAMG: bi-dimensional anisotropic mesh generator. Website: , 1998. http://www-rocq1.inria.fr/gamma/cdrom/www/bamg/eng.htm.
23. Hirt C., Amsden A., Cook J.J.L. An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J. Comput. Phys. 1974, 14(3):227-253.
24. Huang Weizhang, Russell Robert D. Adaptive Moving Mesh Methods 2010, Springer.
25. Igra O., Falcovitz J., Reichenbach H., Heilig W. Experimental and numerical study of the interaction between a planar shock wave and a square cavity. J. Fluid Mech. 1996, 313(1):105-130.
26. Ju Lili, Du Qiang, Gunzburger Max Probabilistic methods for centroidal Voronoi tessellations and their parallel implementations. Parallel Comput. 2002, 28(10):1477-1500.
27. Ju Lili, Gunzburger Max, Zhao Weidong Adaptive finite element methods for elliptic PDEs based on conforming centroidal Voronoi-Delaunay triangulations. SIAM J. Sci. Comput. 2006, 28(6):2023-2053.
28. Kamm James R., Timmes F.X. On efficient generation of numerically robust Sedov solutions. Astrophys. J. Suppl. Ser. 2007, submitted for publication.
29. Kucharik M., Shashkov M., Wendroff B. An efficient linearity-and-bound-preserving remapping methods. J. Comput. Phys. 2003, 188:462-471.
30. Lipnikov K., Shashkov M. The error-minimization-based strategy for moving mesh methods. Commun. Comput. Phys. 2006, 1(1):53-80.
31. Liu Yang, Wang Wenping, Lévy Bruno, Sun Feng, Yan Dong-Ming, Lu Lin, Yang Chenglei On centroidal Voronoi tessellation-energy smoothness and fast computation. ACM Trans. Graph. 2009, 28(4):101.
32. Löhner Rainald An adaptive finite element scheme for transient problems in CFD. Comput. Methods Appl. Mech. Eng. 1987, 61(3):323-338.
33. Löhner Rainald Applied CFD Techniques. An Introduction Based on Finite Element Methods 2001, Wiley.
34. Loubère R., Maire P.-H., Shashkov M. ReALE: a reconnection arbitrary-Lagrangian-Eulerian method in cylindrical geometry. Comput. Fluids 2011, 46(1):59-69.
35. Loubère R., Maire P.-H., Shashkov M., Breil J., Galera S. ReALE: a reconnection-based arbitrary-Lagrangian-Eulerian method. J. Comput. Phys. 2010, 229(12):4724-4761.
36. MacQueen James Some methods for classification and analysis of multivariate observations. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability 1967, vol. 1:281-297.
37. Maire P.-H. A high-order cell-centered Lagrangian scheme for two-dimensional compressible fluid flows on unstructured meshes. J. Comput. Phys. 2009, 228(7):2391-2425.
38. Maire Pierre-Henri, Abgrall Rémi, Breil Jérôme, Ovadia Jean A cell-centered Lagrangian scheme for two-dimensional compressible flow problems. SIAM J. Sci. Comput. 2007, 29(4):1781-1824.
39. Hoa Nguyen, Burkardt John, Gunzburger Max, Ju Lili, Saka Yuki Constrained CVT meshes and a comparison of triangular mesh generators. Comput. Geom. 2009, 42(1):1-19.
40. Hoa Nguyen, Gunzburger Max, Ju Lili, Burkardt John Adaptive anisotropic meshing for steady convection-dominated problems. Comput. Methods Appl. Mech. Eng. 2009, 198(37):2964-2981.
41. Okabe A., Boots B., Sugihara K., Nok Chiu S.N. Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. Wiley Series in Probability and Statistics 2000.
42. Del Pino Stéphane Metric-based mesh adaptation for 2D Lagrangian compressible flows. J. Comput. Phys. 2011, 230(5):1793-1821.
43. Quinn Jonathan, Sun Feng, Langbein Frank C., Lai Yu-Kun, Wang Wenping, Martin Ralph R. Improved initialisation for centroidal Voronoi tessellation and optimal Delaunay triangulation. Comput. Aided Des. 2012, 44(11):1062-1071.
44. Shashkov M.Yu., Solovjov A.V. A generalization of the notion of Dirichlet cell for non-convex domain 1990, Technical report, preprint No. 32 (in Russian), Keldysh Institute of Applied Mathematics, USSR Academy of Sciences, Moscow, Russia.
45. Shashkov M.Yu., Solovjov A.V. Numerical simulation of two-dimensional flows by the free-lagrangian flow simulations 1991, Technical report, Report TUM-M9105, Mathematisches Institut, Technische Universität, München, available at:. http://cnls.lanl.govshashkov.
46. Sod G.A. Numerical Methods in Fluid Dynamics. Initial and Initial Boundary-Value Problems 1985, Cambridge University Press.
47. Starinshak D.P., Owen J.M., Johnson J.N. A new parallel algorithm for constructing Voronoi tessellations from distributed input data. Comput. Phys. Commun. 2014, 185:3204-3214.
48. Tang H., Tang T. Adaptive mesh methods for one-and two-dimensional hyperbolic conservation laws. SIAM J. Numer. Anal. 2003, 41(2):487-515.
49. Tang Hua-Zhong A moving mesh method for the Euler flow calculations using a directional monitor function. Commun. Comput. Phys. 2006, 1:656-676.
50. Tournois Jane, Alliez Pierre, Devillers Olivier 2D centroidal Voronoi tessellations with constraints. Numer. Math., Theory Methods Appl. 2010, 3(2).
51. Vilar François A high-order discontinuous Galerkin discretization for solving two-dimensional Lagrangian hydrodynamics November 2012, Theses, Université Sciences et Technologies, Bordeaux I. https://tel.archives-ouvertes.fr/tel-00765575.