×

A 3D common-refinement method for non-matching meshes in partitioned variational fluid-structure analysis. (English) Zbl 1416.74089

Summary: We present a three-dimensional (3D) common-refinement method for non-matching unstructured meshes between non-overlapping subdomains of incompressible turbulent fluid flow and nonlinear hyperelastic structure. The fluid flow is discretized using a stabilized Petrov-Galerkin method, and the large deformation structural formulation relies on a continuous Galerkin finite element method. An arbitrary Lagrangian-Eulerian formulation with a nonlinear iterative force correction (NIFC) coupling is achieved in a staggered partitioned manner by means of fully decoupled implicit procedures for the fluid and solid discretizations. To begin, we first investigate the accuracy of common-refinement method (CRM) to satisfy the traction equilibrium condition along the fluid-elastic interface with non-matching meshes. We systematically assess the accuracy of CRM against the matching grid solution by varying grid mismatch between the fluid and solid meshes over a tubular elastic body. We demonstrate the second-order accuracy of CRM through uniform refinements of fluid and solid meshes along the interface. We then extend the error analysis to transient data transfer across non-matching meshes between the fluid and solid solvers. We show that the common-refinement discretization across non-matching fluid-structure grids yields accurate transfer of the physical quantities across the fluid-solid interface. We next solve a 3D fluid-structure interaction (FSI) problem of a cantilevered hyperelastic plate behind a circular bluff body and verify the accuracy of coupled solutions with respect to the available solution in the literature. By varying the solid interface resolution, we generate various non-matching grid ratios and quantify the accuracy of CRM for the nonlinear structure interacting with a laminar flow. We illustrate that the CRM with the partitioned NIFC treatment is stable for low solid-to-fluid density ratio and non-matching meshes for the 3D FSI problem. Finally, we demonstrate the 3D parallel implementation of the common-refinement with the NIFC method for a realistic engineering problem of drilling riser undergoing complex vortex-induced vibration with strong added mass effects and turbulent wake flow.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76D05 Navier-Stokes equations for incompressible viscous fluids
74B20 Nonlinear elasticity
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Lee, S.-C.; Vouvakis, M. N.; Lee, J.-F., A non-overlapping domain decomposition method with non-matching grids for modeling large finite antenna arrays, J. Comput. Phys., 203, 1, 1-21 (2005) · Zbl 1059.78042
[2] Peng, Z.; Lee, J.-F., Non-conformal domain decomposition method with second-order transmission conditions for time-harmonic electromagnetics, J. Comput. Phys., 229, 16, 5615-5629 (2010) · Zbl 1193.78003
[3] Hüeber, S.; Wohlmuth, B. I., Thermo-mechanical contact problems on non-matching meshes, Comput. Methods Appl. Mech. Eng., 198, 15, 1338-1350 (2009) · Zbl 1227.74072
[4] El-Abbasi, N.; Bathe, K.-J., Stability and patch test performance of contact discretizations and a new solution algorithm, Comput. Struct., 79, 1473-1486 (2001)
[5] Flemisch, B.; Puso, M. A.; Wohlmuth, B. I., A new dual mortar method for curved interfaces: 2D elasticity, Int. J. Numer. Methods Eng., 63, 813-832 (2005) · Zbl 1084.74050
[6] Lee, I.; Roh, J. H.; Oh, I. K., Aerothermoelastic phenomena of aerospace and composite structures, J. Therm. Stresses, 26, 526-546 (2003)
[7] Jaiman, R. K.; Jiao, X.; Geubelle, P. H.; Loth, E., Conservative load transfer along curved fluid-solid interface with nonmatching meshes, J. Comput. Phys., 218, 372-397 (2006) · Zbl 1158.76405
[8] Jaiman, R. K.; Shakib, F.; Oakley, O. H.; Constantinides, Y., Fully coupled fluid-structure interaction for offshore applications, (ASME Offshore Mechanics and Arctic Engineering OMAE09-79804 CP (2009))
[9] Law, Y. Z.; Jaiman, R. K., Wake stabilization mechanism of low-drag suppression devices for vortex-induced vibration, J. Fluids Struct., 70, 428-449 (2017)
[10] Blevins, R. D., Flow-Induced Vibration (1990), Van Nostrand Reinhold Co., Inc.: Van Nostrand Reinhold Co., Inc. New York
[11] Blom, F. J., A monolithical fluid-structure interaction algorithm applied to the piston problem, Comput. Methods Appl. Mech. Eng., 167, 369-391 (1998) · Zbl 0948.76046
[12] Hübner, B.; Walhorn, E.; Dinkler, D., A monolithic approach to fluid-structure interaction using space-time finite elements, Comput. Methods Appl. Mech. Eng., 193, 23, 2087-2104 (2004) · Zbl 1067.74575
[13] Hron, J.; Turek, S., A Monolithic FEM/Multigrid Solver for an ALE Formulation of Fluid-Structure Interaction with Applications in Biomechanics (2006), Springer · Zbl 1323.74086
[14] Liu, J.; Jaiman, R. K.; Gurugubelli, P. S., A stable second-order scheme for fluid-structure interaction with strong added-mass effects, J. Comput. Phys., 270, 687-710 (2014) · Zbl 1349.76236
[15] Gurugubelli, P. S.; Jaiman, R. K., Self-induced flapping dynamics of a flexible inverted foil in a uniform flow, J. Fluid Mech., 781, 657-694 (2015) · Zbl 1359.76168
[16] Felippa, C. A.; Park, K. C.; Farhat, C., Partitioned analysis of coupled mechanical systems, Comput. Methods Appl. Mech. Eng., 190, 3247-3270 (2001) · Zbl 0985.76075
[17] Cebral, J. R.; Lohner, R., Conservative load projection and tracking for fluid-structure problems, AIAA J., 35, 4, 687-692 (1997) · Zbl 0895.73077
[18] Farhat, C.; van der Zee, K. G.; Geuzaine, P., Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity, Comput. Methods Appl. Mech. Eng., 195, 1973-2001 (2006) · Zbl 1178.76259
[19] Piperno, S.; Farhat, C., Partitioned procedures for the transient solution of coupled aeroelastic problems Part 1: Model problem, theory, and two-dimensional application, Comput. Methods Appl. Mech. Eng., 124, 79-112 (1995) · Zbl 1067.74521
[20] Yenduri, A.; Ghoshal, R.; Jaiman, R. K., A new partitioned staggered scheme for flexible multibody interactions with strong inertial effects, Comput. Methods Appl. Mech. Eng., 315, 316-347 (2017) · Zbl 1439.70011
[21] Jaiman, R. K.; Sen, S.; Gurugubelli, P. S., A fully implicit combined field scheme for freely vibrating square cylinders with sharp and rounded corners, Comput. Fluids, 112, 1-18 (2015) · Zbl 1390.76324
[22] Jaiman, R. K.; Geubelle, P. H.; Loth, E.; Jiao, X., Combined interface condition method for unsteady fluid-structure interaction, Comput. Methods Appl. Mech. Eng., 200, 27-39 (2011) · Zbl 1225.74091
[23] Jaiman, R. K.; Pillalamarri, N. R.; Guan, M. Z., A stable second-order partitioned iterative scheme for freely vibrating low-mass bluff bodies in a uniform flow, Comput. Methods Appl. Mech. Eng., 301, 187-215 (2016) · Zbl 1425.74156
[24] Fernández, M. A.; Gerbeau, J.-F.; Grandmont, C., A projection algorithm for fluid-structure interaction problems with strong added-mass effect, C. R. Math., 342, 4, 279-284 (2006) · Zbl 1148.74020
[25] Fernández, M. A.; Gerbeau, J.-F.; Grandmont, C., A projection semi-implicit scheme for the coupling of an elastic structure with an incompressible fluid, Int. J. Numer. Methods Eng., 69, 4, 794-821 (2007) · Zbl 1194.74393
[26] Baek, H.; Karniadakis, G. E., A convergence study of a new partitioned fluid-structure interaction algorithm based on fictitious mass and damping, J. Comput. Phys., 231, 2, 629-652 (2012) · Zbl 1426.76496
[27] Badia, S.; Quaini, A.; Quarteroni, A., Splitting methods based on algebraic factorization for fluid-structure interaction, SIAM J. Sci. Comput., 30, 4, 1778-1805 (2008) · Zbl 1368.74021
[28] Badia, S.; Quaini, A.; Quarteroni, A., Modular vs. non-modular preconditioners for fluid-structure systems with large added-mass effect, Comput. Methods Appl. Mech. Eng., 197, 49, 4216-4232 (2008) · Zbl 1194.74058
[29] Guidoboni, G.; Glowinski, R.; Cavallini, N.; Canic, S., Stable loosely-coupled-type algorithm for fluid-structure interaction in blood flow, J. Comput. Phys., 228, 18, 6916-6937 (2009) · Zbl 1261.76056
[30] Matthies, H. G.; Niekamp, R.; Steindorf, J., Algorithms for strong coupling procedures, Comput. Methods Appl. Mech. Eng., 195, 2028-2049 (2006) · Zbl 1142.74050
[31] Ahn, H.; Kallinderis, Y., Strongly coupled flow/structure interactions with a geometrically conservative ALE scheme on general hybrid meshes, J. Comput. Phys., 219, 671-696 (2006) · Zbl 1189.74035
[32] Farhat, C.; Lesoinne, M.; Le Tallec, P., Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: Momentum and energy conservation, optimal discretization and application to aeroelasticity, Comput. Methods Appl. Mech. Eng., 157, 1-2, 95-114 (1998) · Zbl 0951.74015
[33] De Boer, A.; Van Zuijlen, A.; Bijl, H., Review of coupling methods for non-matching meshes, Comput. Methods Appl. Mech. Eng., 196, 8, 1515-1525 (2007) · Zbl 1173.74485
[34] Jaiman, R. K.; Jiao, X.; Geubelle, P. H.; Loth, E., Conservative load transfer along curved fluid-solid interface with non-matching meshes, J. Comput. Phys., 218, 1, 372-397 (2006) · Zbl 1158.76405
[35] Jaiman, R. K.; Jiao, X.; Geubelle, P. H.; Loth, E., Assessment of conservative load transfer for fluid-solid interface with non-matching meshes, Int. J. Numer. Methods Eng., 64, 15, 2014-2038 (2005) · Zbl 1122.74544
[36] Jiao, X.; Heath, M. T., Common-refinement-based data transfer between non-matching meshes in multiphysics simulations, Int. J. Numer. Methods Eng., 61, 14, 2402-2427 (2004) · Zbl 1075.74711
[37] Jiao, X.; Heath, M. T., Overlaying surface meshes, Part I: Algorithms, Int. J. Comput. Geom. Appl., 14, 06, 379-402 (2004) · Zbl 1080.65015
[38] Slattery, S. R., Mesh-free data transfer algorithms for partitioned multiphysics problems: Conservation, accuracy, and parallelism, J. Comput. Phys., 307, 164-188 (2016) · Zbl 1352.65038
[39] Jiao, X.; Heath, M. T., Overlaying surface meshes, Part II: Topology preservation and feature matching, Int. J. Comput. Geom. Appl., 14, 06, 403-419 (2004) · Zbl 1080.65016
[40] van Brummelen, E. H., Added mass effects of compressible and incompressible flows in fluid-structure interaction, J. Appl. Mech., 76, Article 02106 pp. (2009)
[41] Jaiman, R. K.; Parmar, M. K.; Gurugubelli, P. S., Added mass and aeroelastic stability of a flexible plate interacting with mean flow in a confined channel, J. Appl. Mech., 81, Article 041006 pp. (2014)
[42] Forster, C.; Wall, W. A.; Ramm, E., Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows, Comput. Methods Appl. Mech. Eng., 196, 1278-1293 (2007) · Zbl 1173.74418
[43] Causin, P.; Gerbeau, J. F.; Nobile, F., Added-mass effect in the design of partitioned algorithms for fluid-structure problems, Comput. Methods Appl. Mech. Eng., 194, 4506-4527 (2005) · Zbl 1101.74027
[44] Jaiman, R. K.; Guan, M. Z.; Miyanawala, T. P., Partitioned iterative and dynamic subgrid-scale methods for freely vibrating square-section structures at subcritical Reynolds number, Comput. Fluids, 133, 68-89 (2016) · Zbl 1390.76056
[45] Hughes, T. J.R.; Liu, W.; Zimmerman, T., Lagrangian-Eulerian finite element formulation for incompressible viscous flows, Comput. Methods Appl. Mech. Eng., 29, 329-349 (1981) · Zbl 0482.76039
[46] Donea, J.; Giuliani, S.; Halleux, J. P., Arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions, Comput. Methods Appl. Mech. Eng., 33, 689-723 (1982) · Zbl 0508.73063
[47] Kuhl, E.; Askes, H.; Steinmann, P., An ALE formulation based on spatial and material settings of continuum mechanics. Part 1: Generic hyperelastic formulation, Comput. Methods Appl. Mech. Eng., 193, 39, 4207-4222 (2004) · Zbl 1068.74078
[48] Bower, A. F., Applied Mechanics of Solids (2009), CRC Press
[49] Jansen, K. E.; Whitting, C. H.; Hulbert, G. M., A generalized-\(α\) method for integrating the filtered Navier-Stokes equations with a stabilized finite element method, Comput. Methods Appl. Mech. Eng., 190, 305-319 (2000) · Zbl 0973.76048
[50] Bazilevs, Y.; Takizawa, K.; Tezduar, T. E., Computational Fluid-Structure Interaction: Methods and Applications (2013), Wiley
[51] Antman, S. S., Nonlinear Problems of Elasticity (2005), Springer-Verlag: Springer-Verlag New York · Zbl 1098.74001
[52] Breziniski, C.; Zaglia, M. R., Generalizations of Aitken’s process for accelerating the convergence of sequence, J. Comput. Appl. Math., 26, 171-189 (2007) · Zbl 1182.65007
[53] Buoso, D.; Karapiperi, A.; Pozza, S., Generalizations of Aitken’s process for a certain class of sequences, Appl. Numer. Math., 90, 38-54 (2015) · Zbl 1326.65011
[54] Saad, Y.; Schultz, M. H., GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 7, 3, 856-869 (1986) · Zbl 0599.65018
[55] Woodsend, K.; Gondzio, J., Hybrid MPI/OpenMP parallel linear support vector machine training, J. Mach. Learn. Res., 10, Aug, 1937-1953 (2009) · Zbl 1235.68205
[56] G. Karypis, V. Kumar, A software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices, University of Minnesota, Department of Computer Science and Engineering, Army HPC Research Center, Minneapolis, MN.; G. Karypis, V. Kumar, A software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices, University of Minnesota, Department of Computer Science and Engineering, Army HPC Research Center, Minneapolis, MN.
[57] Smith, L.; Bull, M., Development of mixed mode MPI/OpenMP applications, Sci. Program., 9, 2-3, 83-98 (2001)
[58] Turek, S.; Hron, J., Proposal for numerical benchmarking of fluid-structure interaction between an elastic object and laminar incompressible flow, (Fluid-Structure Interaction (2006), Springer), 371-385 · Zbl 1323.76049
[59] Vortex induced vibration data repository, http://web.mit.edu.sg/towtank/www/vivdr/downloadpage.html; Vortex induced vibration data repository, http://web.mit.edu.sg/towtank/www/vivdr/downloadpage.html
[60] Joshi, V.; Jaiman, R. K., A variationally bounded scheme for delayed detached eddy simulation: Application to vortex-induced vibration of offshore riser, Comput. Fluids, 157, 84-111 (2017) · Zbl 1390.76326
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.