Abstract
This paper presents a set of parallel procedures for anisotropic mesh adaptation accounting for mixed element types used in boundary layer meshes, i.e., the current procedures operate in parallel on distributed boundary layer meshes. The procedures accept anisotropic mesh metric field as an input for the desired mesh size field and apply local mesh modifications to adapt the mesh to match/satisfy the specified mesh size field. The procedures fully account for the parametric geometry of curved domains and maintain the semi-structured nature of the boundary layer elements. The effectiveness of the procedures is demonstrated on three viscous flow examples that include the ONERA M6 wing, a heat transfer manifold, and a scramjet engine.
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References
Gropp W, Lusk E, Skjellum A (2014) Using MPI: portable parallel programming with the message-passing interface. MIT Press, Cambridge. https://mitpress.mit.edu/using-MPI-3ed
Ainsworth M, Oden JT (2000) A posteriori error estimation in finite element analysis. Wiley, New York
Alauzet F, Li X, Seol ES, Shephard MS (2006) Parallel anisotropic 3D mesh adaptation by mesh modification. Eng Comput 21(3):247–258. doi:10.1007/s00366-005-0009-3
Au P, Dompierre J, Labbe P, Guibault F, Camarero R (1998) Proposal of benchmarks for 3D unstructured tetrahedral mesh optimization. In: Proceedings of the 7th International Meshing Roundtable, pp 459–478
Bänsch E (1991) Local mesh refinement in 2 and 3 dimensions. IMPACT Comput Sci Eng 3(3):181–191
Becker R, Rannacher R (2001) An optimal control approach to a posteriori error estimation in finite element methods. Acta Numer 10(1):1–102
Botasso CL (2004) Anisotropic mesh adaption by metric-driven optimization. Int J Numer Methods Eng 60(3):597–639. doi:10.1002/nme.977
Bottasso CL, Detomi D (2002) A procedure for tetrahedral boundary layer mesh generation. Eng Comput 18(1):66–79. doi:10.1007/s003660200006
Bourgault Y, Picasso M, Alauzet F, Loseille A (2009) On the use of anisotropic a posteriori error estimators for the adaptative solution of 3D inviscid compressible flows. Int J Numer Methods Fluids 59(1):47–74. doi:10.1002/fld.1797
Buscaglia GC, Dari EA (1997) Anisotropic mesh optimization and its application in adaptivity. Int J Numer Methods Eng 40:4119–4136
Castro-Diáz MJ, Hecht F, Mohammadi B, Pironneau O (1997) Anisotropic unstructured mesh adaption for flow simulations. Int J Numer Methods Fluids 25:475–491
Chand KK, Diachin LF, Li X, Ollivier-Gooch C, Seol ES, Shephard MS, Tautges T, Trease H (2008) Toward interoperable mesh, geometry and field components for pde simulation development. Eng Comput 24(2):165–182. doi:10.1007/s00366-007-0080-z
Chandra S, Li X, Saif T, Parashar M (2007) Enabling scalable parallel implementations of structured adaptive mesh refinement applications. J Supercomput 39(2):177–203. doi:10.1007/s11227-007-0110-z
Chitale K, Sahni O, Tendulkar S, Nastasia R, Shephard M, Jansen K (2013) Boundary layer adaptivity for transonic turbulent flows. AIAA Paper 13-2445. doi:10.2514/6.2013-2445
Connell SD, Braaten ME (1995) Semistructured mesh generation for three-dimensional Navier–Stokes calculations. AIAA J 33(6):1017–1024
de Cougny HL, Shephard MS (1999) Parallel refinement and coarsening of tetrahedral meshes. Comput Methods Appl Mech Eng 46:1101–1125
de Cougny HL, Shephard MS, Georges MK (1990) Explicit node point mesh smoothing within the octree mesh generator. Tech. Rep. 1990-10, Rensselaer Polytechnic Institute, Troy
Cray: Cray XE6. [Online]. http://www.cray.com/Products/XE/CrayXE6System.aspx. Accessed 19 Sep 2012
Foster TM, Mohamed MS, Trevelyan J, Coates G (2012) Rapid re-meshing and re-solution of three-dimensional boundary element problems for interactive stress analysis. Eng Anal Bound Elem 36(9):1331–1343. doi:10.1016/j.enganabound.2012.02.020
Freitag LA, Ollivier-Gooch C (1997) Tetrahedral mesh improvement using swapping and smoothing. Int J Numer Methods Eng 40(21):3979–4002
Frey PJ, Alauzet F (2005) Anisotropic mesh adaptation for CFD computations. Comput Methods Appl Mech Eng 194(48–49):5068–5082. doi:10.1016/j.cma.2004.11.025
Garimella RV, Shephard MS (2000) Boundary layer mesh generation for viscous flow simulations. Int J Numer Methods Eng 49:193–218
George P, Borouchaki H, Laug P (2002) An efficient algorithm for 3D adaptive meshing. Adv Eng Softw 33(7):377–387
Giles MB, Süli E (2002) Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality. Acta Numer 11(1):145–236
Hassan O, Morgan K, Probert EJ, Peraire J (1996) Unstructured tetrahedral mesh generation for three-dimensional viscous flows. Int J Numer Methods Eng 39:549–567
Hassan O, Morgan K, Weatherill N (2007) Unstructured mesh methods for the solution of the unsteady compressible flow equations with moving boundary components. Philos Trans R S A Math Phys Eng Sci 365(1859):2531–2552
Ito Y, Murayama M, Yamamoto K, Shih AM, Soni BK (2013) Efficient hybrid surface/volume mesh generation using suppressed marching-direction method. AIAA J 51(6):1450–1461
Ito Y, Nakahashi K (2002) Unstructured mesh generation for viscous flow computations. In: Proceedings of the 11th International Meshing Roundtable, pp 367–377
Joe B (1995) Construction of three-dimensional improved-quality triangulations using local transformations. SIAM J Sci Comput 16(6):1292–1307
Kallinderis Y, Kavouklis C (2005) A dynamic adaptation scheme for general 3-D hybrid meshes. Comput Methods Appl Mech Eng 194(48–49):5019–5050. doi:10.1016/j.cma.2004.11.023
Kallinderis Y, Vijayan P (1993) Adaptive refinement-coarsening scheme for three-dimensional unstructured meshes. AIAA J 31(8):1440–1447
Kavouklis C, Kallinderis Y (2010) Parallel adaptation of general three-dimensional hybrid meshes. J Comput Phys 229(9):3454–3473. doi:10.1016/j.jcp.2010.01.011
Khawaja A, Kallinderis Y (2000) Hybrid grid generation for turbomachinery and aerospace applications. Int J Numer Methods Eng 49(1–2):145–166
Khawaja A, Minyard T, Kallinderis Y (2000) Adaptive hybrid grid methods. Comput Methods Appl Mech Eng 189(4):1231–1245. doi:10.1016/S0045-7825(99)00375-8
Li X (2003) Mesh modification procedures for general 3D non-manifold domains. Ph.D. Dissertation, Department of Mechanical Engineering, Rensselaer Polytechnic Institute, Troy
Li X, Remacle JF, Chevaugeon N, Shephard MS (2004) Anisotropic mesh gradation control. In: Proceedings of the 13th International Meshing Roundtable, pp 401–412
Li X, Shephard M, Beall M (2005) 3D anisotropic mesh adaptation by mesh modifications. Comput Methods Appl Mech Eng 194(48–49):4915–4950. doi:10.1016/j.cma.2004.11.019
Li X, Shephard MS, Beall MW (2003) Accounting for curved domains in mesh adaptation. Int J Numer Methods Eng 58(2):247–276. doi:10.1002/nme.772
Liu A, Joe B (1994) On the shape of tetrahedra from bisection. Math Comput 63(207):141–154
Löhner R, Baum JD (1992) Adaptive h-refinement on 3D unstructured grids for transient problems. Int J Numer Methods Fluids 14(12):1407–1419
Lohner R, Cebral J (2000) Generation of non-isotropic unstructured grids via directional enrichment. Int J Numer Methods Eng 49(1–2):219–232
Loseille A, Löhner R (2013) Robust boundary layer mesh generation. In: Proceedings of the 21st International Meshing Roundtable, pp 493–511
Marcum DL (1995) Generation of unstructured grids for viscous flow applications. AIAA Paper 95-0212
Muller J, Sahni O, Li X, Jansen KE, Shephard MS, Taylor CA (2005) Anisotropic adaptive finite element method for modeling blood flow. Comput Methods Biomech Biomed Eng 8(5):295–305. doi:10.1080/10255840500264742
NASA: CIAM Axisymmetric Scramjet. [Online]. http://hapb-www.larc.nasa.gov/Public/Engines/Ciam/Ciam.html. Accessed 19 Sep 2012
NASA: FUN3D online manual. [Online]. http://fun3d.larc.nasa.gov/. Accessed 19 Sep 2012
Oliker L, Biswas R, Gabow HN (2000) Parallel tetrahedral mesh adaptation with dynamic load balancing. Parallel Comput 26(12):1583–1608
Ovcharenko A, Ibanez D, Delalondre F, Sahni O, Jansen KE, Carothers CD, Shephard MS (2012) Neighborhood communication paradigm to increase scalability in large-scale dynamic scientific applications. Parallel Comput 38(3):140–156. doi:10.1016/j.parco.2011.10.013
Pain CC, Umpleby AP, de Oliveira CRE, Goddard AJH (2001) Tetrahedral mesh optimization and adaptivity for steady-state and transient finite element calculations. Comput Methods Appl Mech Eng 190(29–30):3771–3796. doi:10.1016/S0045-7825(00)00294-2
Park YM, Kwon OJ (2005) A parallel unstructured dynamic mesh adaptation algorithm for 3-D unsteady flows. Int J Numer Methods Fluids 48(6):671–690
Peraire J, Peiro J, Morgan K (1992) Adaptive remeshing for three-dimensional compressible flow computation. J Comput Phys 103(2):269–285. doi:10.1016/0021-9991(92)90401-J
Pirzadeh S (1994) Unstructured viscous grid generation by the advancing-layers method. AIAA J 32(8):1735–1737
Sahni O, Jansen KE, Shephard MS, Taylor CA, Beall MW (2008) Adaptive boundary layer meshing for viscous flow simulations. Eng Comput 24(3):267–285. doi:10.1007/s00366-008-0095-0
Sahni O, Muller J, Jansen KE, Shephard MS, Taylor CA (2006) Efficient anisotropic adaptive discretization of the cardiovascular system. Comput Methods Appl Mech Eng 195(41–43):5634–5655. doi:10.1016/j.cma.2005.10.018
Sahni O, Zhou M, Shephard MS, Jansen KE (2009) Scalable implicit finite element solver for massively parallel processing with demonstration to 160K cores. In: Proceedigs of the 2009 ACM/IEEE Conference on High Performance Computing
Sandia National Laboratories: Zoltan unstructured communication utilities. [Online]. http://www.cs.sandia.gov/Zoltan/ug_html/ug_util_comm.html. Accessed 19 Sep 2012
Seol ES, Shephard MS (2006) Efficient distributed mesh data structure for parallel automated adaptive analysis. Eng Comput 22(3–4):197–213
Shephard MS, Beall MW, O’Bara RM, Webster BE (2004) Toward simulation-based design. Finite Elem Anal Design 40(12):1575–1598. doi:10.1016/j.finel.2003.11.004
Stogner RH, Carey GF, Murray BT (2008) Approximation of Cahn–Hilliard diffuse interface models using parallel adaptive mesh refinement and coarsening with C1 elements. Int J Numer Methods Eng 76(5):636–661. doi:10.1002/nme.2337
Toussaint GT, Verbrugge C, Wang C, Zhu B (1993) Tetrahedralization of simple and non-simple polyhedra. In: Proceedings of the 5th Canadian Conference on Computational Geometry, pp 24–29
Schmitt V, Charpin F (1979) Pressure distribution on the ONERA-M6-Wing at transonic mach numbers. In: Report of the Fluid Dynamics Panel Working Group 04, vol 138. AGARD
Verfürth R (1996) A review of posteriori error estimation and adaptive mesh-refinement techniques. Teubner-Wiley, Stuttgart
Whiting CH, Jansen KE (2001) A stabilized finite element method for the incompressible Navier–Stokes equations using a hierarchical basis. Int J Numer Methods Fluids 35(1):93–116
Xie T, Seol ES, Shephard MS (2012) Generic components for petascale automated adaptive simulations. Eng Comput (Accepted for publication)
Zhang L, Chang X, Duan X, Zhao Z, He X (2012) Applications of dynamic hybrid grid method for three-dimensional moving/deforming boundary problems. Comput Fluids 62:45–63. doi:10.1016/j.compfluid.2012.03.008
Zhou M, Sahni O, Kim HJ, Figueroa CA, Taylor CA, Shephard MS, Jansen KE (2010) Cardiovascular flow simulation at extreme scale. Comput Mechan 46(1):71–82. doi:10.1007/s00466-009-0450-z
Acknowledgments
This work is supported by the National Science Foundation under Grant No. 0749152, and by the U.S. Department of Energy under DOE Grant No. DE-FC02-06ER25769, and by the NASA STTR Part II Grant No. BEE103/NNX11CC69C. Computing support is provided by the National Energy Research Scientific Computing Center for granting access to the Hopper Cray XE6 supercomputer. Resources at the Center for Computational Innovations (CCI) at Rensselaer were also used for testing and development. The authors would like to acknowledge the help of Dr. L. Fovargue on the ONERA M6 case and F. Nihan Cayan and O. Breslouer for help with the scramjet case.
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Sahni, O., Ovcharenko, A., Chitale, K.C. et al. Parallel anisotropic mesh adaptation with boundary layers for automated viscous flow simulations. Engineering with Computers 33, 767–795 (2017). https://doi.org/10.1007/s00366-016-0437-2
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DOI: https://doi.org/10.1007/s00366-016-0437-2