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A gluing method for non-matching meshes. (English) Zbl 1390.65041

Summary: This paper presents a gluing method for composite meshes. Different meshes are generated independently and are glued together using some new elements to connect them, referred to as extension elements. The resulting global mesh is non-conforming and consists of connected overlapping meshes. The method is inherently implicit, parallel and versatile, in the sense that it is PDE independent. The most cited gluing method is probably the Chimera method, used for overset grids, where patch meshes are superimposed onto a background mesh. The method employed here was originally devised for such situations and is now applied to disjoint or overlapping meshes. One of the advantages of the method is that the meshes do not have to coincide and can present a gap between them. The method is illustrated through some simple examples to demonstrate the mesh convergence. Finally, we consider the solution of the airflow in the complete respiratory system, by joining independent meshes for the large and small airways, and the simulation of the flow passing through a bypass in a stenosed artery.

MSC:

65F50 Computational methods for sparse matrices
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Software:

CUBIT; Alya; METIS
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Full Text: DOI

References:

[1] Nielsen, E.; Diskin, B., Discrete adjoint-based design for unsteady turbulent flows on dynamic overset unstructured grids, AIAA J, 51, 6, 1355-1373, (2013)
[2] Kao, K. H.; Liou, M. S.; Chow, C. Y., Grid adaptation using Chimera composite overlapping meshes, AIAA J, 32, 5, 942-949, (1994) · Zbl 0800.76324
[3] Meakin; Robert, L., An efficient means of adaptive refinement within systems of overset grids, AIAA Paper, A95, 1722, (1995)
[4] Dettmer, W.; Perić, D., A computational framework for fluid structure interaction: finite element formulation and applications, Comput Meth Appl Mech Eng, 195, 5754-5779, (2006) · Zbl 1155.76354
[5] Steger, J.; Benek, F. D.J., A Chimera grid scheme, Adv Grid Gener, 5, 59-69, (1983)
[6] Benek J. Chimera. a grid-embedding technique. Technical report, DTIC Document; 1986.
[7] Steger, J.; Benek, J., On the use of composite grid schemes in computational aerodynamics, Comput Meth Appl Mech Eng, 64, 301-320, (1987) · Zbl 0607.76061
[8] Chattot, J.; Wang, Y., Improvement treatment of intersecting bodies with the Chimera method and validation with a simple fast flow solver, Comput Fluids, 27, 721-740, (1998) · Zbl 0976.76053
[9] Houzeaux, G.; Codina, R., An iteration-by-subdomain overlapping Dirichlet/Robin domain decomposition method for advection-diffusion problems, J Comput Appl Math, 158, 2, 243-276, (2003) · Zbl 1033.65111
[10] Blacker T, Bohnhoff W, Edwards T. Cubit mesh generation environment. vol. 1: Users manual, Technical Report, Albuquerque (NM, USA): Sandia National Labs.; 1994.
[11] Clark, B.; Hanks, B.; Ernst, C., Conformal assembly meshing with tolerant imprinting, (Proceedings of the 17th international meshing roundtable, (2008), Springer), 267-280
[12] Tautges, T., The generation of hexahedral meshes for assembly geometry: survey and progress, Int J Numer Methods Eng, 50, 12, 2617-2642, (2001) · Zbl 1049.74055
[13] Staten, M. L.; Shepherd, J. F.; Ledoux, F.; Shimada, K., Hexahedral mesh matching: converting non-conforming hexahedral-to-hexahedral interfaces into conforming interfaces, Int J Numer Methods Eng, 82, 12, 1475-1509, (2010) · Zbl 1188.74095
[14] Fournier Y, Benhamadouche S, Monfort D, Laurence D. Non conforming meshes and rans/les coupling: two challenging aims for a CFD code. In: HT-FED-2004, 2004 ASME heat transfer/fluids engineering summer conference, Charlotte (USA); 2004.
[15] Lo, S., Automatic merging of tetrahedral meshes, Int J Numer Methods Eng, (2012) · Zbl 1352.65614
[16] Houzeaux, G.; Eguzkitza, B.; Aubry, R.; Owen, H.; Vázquez, M., A Chimera method for the Navier-Stokes equations, Int J Numer Meth Fluids, 75, 3, 155-183, (2014)
[17] Belgacem, F.; Maday, Y., The mortar element method for three dimensional finite elements, R.A.I.R.O. Modél Math Anal Numér, 31, 2, 289-302, (1997) · Zbl 0868.65082
[18] Cai, X.; Dryja, M.; Sarkis, M., Overlapping nonmatching grid mortar element methods for elliptic problems, SIAM J. Numer. Anal., 36, 2, 581-606, (1999) · Zbl 0927.65131
[19] Farhat, C.; Roux, F., A method of finite element tearing and interconnecting and its parallel solution algorithm, Int J Numer Methods Eng, 32, 6, 1205-1227, (1991) · Zbl 0758.65075
[20] Stefanica D, Klawonn A. The FETI method for mortar finite elements. In: Proceedings of 11th international conference on domain decomposition methods, Citeseer; 1999. p. 121-9.
[21] Aminpour, M.; Ransom, J.; McCleary, S., A coupled analysis method for structures with independently modelled finite element subdomains, Int J Numer Methods Eng, 38, 21, 3695-3718, (1995) · Zbl 0836.73063
[22] Rixen, D.; Farhat, C.; Géradin, M., A two-step, two-field hybrid method for the static and dynamic analysis of substructure problems with conforming and non-conforming interfaces, Comput Methods Appl Mech Eng, 154, 3, 229-264, (1998) · Zbl 0958.74071
[23] Park, K.; Felippa, C.; Rebel, G., Interfacing nonmatching FEM meshes: the zero moment rule, Trends Comput Struct Mech, 355-367, (2001)
[24] Hansbo, A.; Hansbo, P.; Larson, M., A finite element method on composite grids based on nitsche’s method, ESAIM: Math Modell Numer Anal, 37, 03, 495-514, (2003) · Zbl 1031.65128
[25] Hansbo, P., Nitsche’s method for interface problems in computational mechanics, GAMM-Mitt, 28, 2, 183-206, (2005) · Zbl 1179.65147
[26] Tian, R.; Yagawa, G., Non-matching mesh gluing by meshless interpolation an alternative to Lagrange multipliers, Int J Numer Methods Eng, 71, 4, 473-503, (2007) · Zbl 1194.74478
[27] Cho, Y. S.; Jun, S.; Im, S.; Kim, H. G., An improved interface element with variable nodes for non-matching finite element meshes, Comput Methods Appl Mech Eng, 194, 27, 3022-3046, (2005) · Zbl 1092.74048
[28] Quarteroni, A.; Valli, A., Domain decomposition methods for partial differential equations, (1999), Oxford University Press USA · Zbl 0931.65118
[29] Boer, A. D.; Zuijlen, A. V.; Bijl, H., Review of coupling methods for non-matching meshes, Comput Methods Appl Mech Eng, 196, 8, 1515-1525, (2007) · Zbl 1173.74485
[30] Eguzkitza, B.; Houzeaux, G.; Aubry, R.; Vázquez, M., A parallel coupling strategy for the Chimera and domain decomposition methods in computational mechanics, Comput Fluids, 80, 128-141, (2013) · Zbl 1284.65166
[31] Dompierre J, Labbé P, Guibault F, Camarero R. Proposal of benchmarks for 3D unstructured Tetrahedral Mesh Optimization. Technical Report, Centre de Recherche en Calcul Appliqué; 1998.
[32] Roache, J., Verification of codes and calculations, AIAA J, 36, 5, 696-702, (1998)
[33] Owen, H.; Houzeaux, G.; Samaniego, C.; Lesage, A.; Vázquez, M., Recent ship hydrodynamics developments in the parallel two-fluid flow solver alya, Comput Fluids, 80, 168-177, (2013) · Zbl 1284.76073
[34] Hughes, T. J., Multiscale phenomena: green’s functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods, Comput Meth Appl Mech Eng, 127, 387-401, (1995) · Zbl 0866.76044
[35] Houzeaux, G.; Principe, J., A variational subgrid scale model for transient incompressible flows, Int J Comp Fluid Dyn, 22, 3, 135-152, (2008) · Zbl 1184.76802
[36] Houzeaux, G.; Aubry, R.; Vázquez, M., Extension of fractional step techniques for incompressible flows: the preconditioned orthomin(1) for the pressure Schur complement, Comput Fluids, 44, 297-313, (2011) · Zbl 1271.76208
[37] Aubry, R.; Mut, F.; Löhner, R.; Cebral, J., Deflated preconditioned conjugate gradient solvers for the pressure-Poisson equation, J Comput Phys, 227, 24, 10196-10208, (2008) · Zbl 1153.76035
[38] Soto, O.; Löhner, R.; Camelli, F., A linelet preconditioner for incompressible flow solvers, Int J Num Meth Heat Fluid Flow, 13, 1, 133-147, (2003) · Zbl 1059.76037
[39] Houzeaux, G.; Vázquez, M.; Aubry, R.; Cela, J., A massively parallel fractional step solver for incompressible flows, J Comput Phys, 228, 17, 6316-6332, (2009) · Zbl 1261.76030
[40] Houzeaux, G.; de la Cruz, R.; Owen, H.; Vázquez, M., Parallel uniform mesh multiplication applied to a Navier-Stokes solver, Comput Fluids, 80, 142-151, (2013) · Zbl 1284.76250
[41] Metis, family of multilevel partitioning algorithms. <http://glaros.dtc.umn.edu/gkhome/views/metis>.
[42] Löhner, R.; Mut, F.; Cebral, J.; Aubry, R.; Houzeaux, G., Deflated preconditioned conjugate gradient solvers for the pressure-Poisson equation: extensions and improvements, Int J Numer Meth Eng, 87, 2-14, (2011) · Zbl 1242.76128
[43] Doorly, D.; Taylor, D.; Gambaruto, A.; Schroter, R.; Tolley, N., Nasal architecture: form and flow, Philos Trans Roy Soc A: Math Phys Eng Sci, 366, 1879, 3225-3246, (2008)
[44] Soni, B.; Aliabadi, S., Large-scale CFD simulations of airflow and particle deposition in lung airway, Comput Fluids, 88, 804-812, (2013) · Zbl 1391.76899
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