×

zbMATH — the first resource for mathematics

An Eulerian approach for partitioned fluid-structure simulations on Cartesian grids. (English) Zbl 1228.74024
Summary: This paper describes an Eulerian approach for partitioned fluid-structure simulations based on a fluid solver using regularly and adaptively refined Cartesian grids. The particular focus is on efficient implementation and embedding of the fluid solver in the context of coupled simulations. Special subjects are the efficient layout of data structures and data access based on space-filling curves and on the realisation of geometry and topology changes. In addition, a coupling environment is presented that allows for an easy and flexible coupling of flow and structure codes. Simulation results are provided for large particle movements within the drift ratchet scenario.

MSC:
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S05 Finite element methods applied to problems in solid mechanics
76M12 Finite volume methods applied to problems in fluid mechanics
Software:
GENSMAC; MpCCI
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] MpCCI 3.0 (2007) Multidisciplinary simulations through code coupling. Fraunhofer SCAI, Sankt Augustin. http://www.mpcci.de/mpcci_manuals.html , manual
[2] Bader M, Bungartz HJ, Frank A, Mundani RP (2002) Space tree structures for PDE software. In: Sloot PMA, Tan CJK, Dongarra JJ, Hoekstra AG(eds) Proceedings of the international conference on computer science. LNCS, vol 2331. Springer, Heidelberg, pp 662–671 · Zbl 1056.65107
[3] Bijl H, van Zuijlen AH, Bosscher S (2006) Two level algorithms for partitioned fluid–structure interaction computations. In: Wesseling P, Oñate E, Périaux J (eds) ECCOMAS CFD 2006, european conference on computational fluid dynamics, TU delft · Zbl 1173.76369
[4] Blanke C (2004) Kontinuitätserhaltende Finite-Element-Diskretisierung der Navier–Stokes-Gleichungen. Diploma thesis, Fakultät für Mathematik, TU München
[5] Brenk M, Bungartz HJ, Mehl M, Mundani RP, Düster A, Scholz D (2005) Efficient interface treatment for fluid–structure interaction on cartesian grids. In: ECCOMAS COUPLED PROBLEMS 2005, Proceedings of the thematic conference on computational methods for coupled problems in science and engineering. International Center for Numerical Methods in Engineering (CIMNE)
[6] Brenk M, Bungartz HJ, Mehl M, Neckel T (2006) Fluid-structure interaction on cartesian grids: flow simulation and coupling environment. In: Bungartz HJ, Schäfer M(eds) Fluid–structure interaction. LNCSE, vol 53. Springer, Heidelberg, pp 233–269 · Zbl 1323.76047
[7] Brenk M, Bungartz HJ, Mehl M, Muntean IL, Neckel T, Weinzierl T (2007) Numerical simulation of particle transport in a drift ratchet. SIAM J Sci Comput (in review) · Zbl 1185.35159
[8] Chorin AJ (1968) Numerical solution of the Navier–Stokes equations. Math Comput 22: 745–762 · Zbl 0198.50103 · doi:10.1090/S0025-5718-1968-0242392-2
[9] Düster A, Bröker H, Heidkamp H, Heißerer U, Kollmannsberger S, Krause R, AMuthler, Niggl A, Nübel V, Rücker M, Scholz D (2004) AdhoC4–User’s guide. Lehrstuhl für Bauinformatik, TU München
[10] Emans M, Zenger C (2005) An efficient method for the prediction of the motion of individual bubbles. Int J Comput Fluid Dyn 19: 347–356 · Zbl 1103.76380 · doi:10.1080/10618560500067224
[11] Felippa CA, Park KC, Farhat C (2001) Partitioned analysis of coupled mechanical systems. Comput Methods Appl Mech Eng 190: 3247–3270 · Zbl 0985.76075 · doi:10.1016/S0045-7825(00)00391-1
[12] Geller S, Tölke J, Krafczyk M (2006) Lattice-Boltzmann method on quadtree type grids for fluid–structure interaction. In: Bungartz HJ, Schäfer M(eds) Fluid-structure interaction. LNCSE, vol 53. Springer, Heidelberg, pp 270–293 · Zbl 1323.76079
[13] Gresho PM, Sani RL (1998) Incompressible flow and the finite element method. Wiley,
[14] Griebel M, Zumbusch GW (1998) Hash-storage techniques for adaptive multilevel solvers and their domain decomposition parallelization. In: Mandel J, Farhat C, Cai XC (eds) Proceedings of domain decomposition methods 10, DD10, vol 218. AMS, Providence, pp 279–286. http://citeseer.ist.psu.edu/46737.html · Zbl 0910.65084
[15] Günther F, Mehl M, Pögl M, Zenger C (2006) A cache-aware algorithm for PDEs on hierarchical data structures based on space-filling curves. SIAM J Sci Comput 28(5): 1634–1650 · Zbl 1162.68406 · doi:10.1137/040604078
[16] Harlow FH, Welch JE (1965) Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface. Phys Fluids 8(12): 2182–2189 · Zbl 1180.76043 · doi:10.1063/1.1761178
[17] Kettner C, Reimann P, Hänggi P, Müller F (2000) Drift ratchet. Phys Rev E 61: 312–323 · doi:10.1103/PhysRevE.61.312
[18] Krahnke A (2005) Adaptive Verfahren höherer Ordnung auf cache-optimalen Datenstrukturen für dreidimensionale Probleme, Dissertation. TU München
[19] Masud A, Hughes TJR (1997) A space–time galerkin/least-squares finite element formulation of the navier–stokes equations for moving domain problems. Comput Methods Appl Mech Eng 146: 91–126 · Zbl 0899.76259 · doi:10.1016/S0045-7825(96)01222-4
[20] Matthias S, Müller F (2003) Asymmetric pores in a silicon membrane acting as massively parallel brownian ratchets. lett Nat 424: 53–57 · doi:10.1038/nature01736
[21] Mehl M (2006) Cache-optimal data-structures for hierarchical methods on adaptively refined space-partitioning grids. In: International conference on high performance computing and communications 2006, HPCC06. LNCS, vol 4208. Springer, Heidelberg, pp 138–147
[22] Mehl M, Weinzierl T, Zenger C (2006) A cache-oblivious self-adaptive full multigrid method. Numer Linear Algebra 13(2–3): 275–291 · Zbl 1174.65550 · doi:10.1002/nla.481
[23] Michler C (2005) Efficient numerical methods for fluid–structure interaction, Ph D thesis. PrintPartners Ipskamp
[24] Mittal R, Iaccarino G (2005) Immersed boundary methods. Annu Rev Fluid Mech 37: 239–261 · Zbl 1117.76049 · doi:10.1146/annurev.fluid.37.061903.175743
[25] Pögl M (2004) Entwicklung eines cache-optimalen 3D Finite-Element-Verfahrens für große Probleme, Fortschritt-Berichte VDI, Informatik Kommunikation 10, vol 745. VDI Verlag, Düsseldorf
[26] Sagan H (1994) Space-filling curves. Springer, New York · Zbl 0806.01019
[27] Scholz D, Kollmannsberger S, Düster A, Rank E (2006) Thin solids for fluid–structure interaction. In: Bungartz HJ, Schäfer M(eds) Fluid–structure interaction. LNCSE, vol 53. Springer, Heidelberg, pp 294–335 · Zbl 1323.74094
[28] Tomé MF, McKee S (1994) GENSMAC: a computational marker and cell method for free surface flows in general domains. J Comput Phys 110: 171–186 · Zbl 0790.76058 · doi:10.1006/jcph.1994.1013
[29] Turek S, Schäfer M (1996) Benchmark computations of laminar flow around a cylinder. In: Hirschel EH (ed) Flow simulation with high-performance computers II, vol 52. NNFM, Vieweg
[30] Verstappen RWCP, Veldman AEP (2003) Symmetry-preserving discretization of turbulent channel flow. J Comput Phys 187: 343–368 · Zbl 1062.76542 · doi:10.1016/S0021-9991(03)00126-8
[31] Vierendeels J (2006) Implicit coupling of partitioned fluid–structure interaction solvers using reduced-order models. In: Bungartz HJ, Schäfer M(eds) Fluid–Structure interaction, modelling, simulation, optimisation. Springer, Heidelberg, pp 1–18 · Zbl 1323.74112
[32] Wagner T (2005) Randbehandlung höherer Ordnung für ein cache-optimales Finite-Element-Verfahren auf kartesischen Gittern. Diploma thesis, Institut für Informatik, TU München
[33] Wang W (2001) Special bilinear quadrilateral elements for locally refined finite element grids. SIAM J Sci Comput 22(6): 2029–2050 · Zbl 0990.65111 · doi:10.1137/S1064827599358911
[34] Yigit S, Heck M, Sternel DC, Schäfer M (2007) Efficiency of fluid–structure interaction simulations with adaptive underrelaxation and multigrid acceleration. Int J Multiphys 1: 85–99 · doi:10.1260/175095407780130535
[35] Zumbusch G (2001) Adaptive parallel multilevel methods for partial differential equations. Habilitationsschrift, Universität Bonn, Bonn
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.