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A Unified Momentum Equation Approach for Computing Flow-Induced Stresses in Structures with Arbitrarily-Shaped Stationary Boundaries

  • Haram Yeo (a1) and Hyungson Ki (a1)

This article presents a novel monolithic numerical method for computing flow-induced stresses for problems involving arbitrarily-shaped stationary boundaries. A unified momentum equation for a continuum consisting of both fluids and solids is derived in terms of velocity by hybridizing the momentum equations of incompressible fluids and linear elastic solids. Discontinuities at the interface are smeared over a finite thickness around the interface using the signed distance function, and the resulting momentum equation implicitly takes care of the interfacial conditions without using a body-fitted grid. A finite volume approach is employed to discretize the obtained governing equations on a Cartesian grid. For validation purposes, this method has been applied to three examples, lid-driven cavity flow in a square cavity, lid-driven cavity flow in a circular cavity, and flow over a cylinder, where velocity and stress fields are simultaneously obtained for both fluids and structures. The simulation results agree well with the results found in the literature and the results obtained by COMSOL Multiphysics®.

Corresponding author
*Corresponding author. Email addresses: (H. Yeo), (H. Ki)
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Communicated by Lianjie Huang

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[1] Bazilevs, Y., Hsu, M.-C., Zhang, Y., Wang, W., Liang, X., Kvamsdal, T., Brekken, R., Isaksen, J.G., A fully-coupled fluid-structure interaction simulation of cerebral aneurysms, Computational Mechanics, 46 (2009) 316.
[2] Kamensky, D., Hsu, M.C., Schillinger, D., Evans, J.A., Aggarwal, A., Bazilevs, Y., Sacks, M.S., Hughes, T.J.R., An immersogeometric variational framework for fluid-structure interaction: Application to bioprosthetic heart valves, Computer Methods in Applied Mechanics and Engineering, 284 (2015) 10051053.
[3] Hsu, M.-C., Akkerman, I., Bazilevs, Y., Finite element simulation of wind turbine aerodynamics: Validation study using NREL Phase VI experiment, Wind Energy, 17 (2014) 461481.
[4] Paik, K.-J., Carrica, P.M., Lee, D., Maki, K., Strongly coupled fluid-structure interaction method for structural loads on surface ships, Ocean Engineering, 36 (2009) 13461357.
[5] Hou, G., Wang, J., Layton, A., Numerical methods for fluid-structure interaction - A review, Communications in Computational Physics, 12 (2012) 337377.
[6] Felippa, C.A., Park, K.C., Farhat, C., Partitioned analysis of coupled mechanical systems, Computer Methods in Applied Mechanics and Engineering, 190 (2001) 32473270.
[7] Farhat, C., van der Zee, K.G., Geuzaine, P., Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity, Computer Methods in Applied Mechanics and Engineering, 195 (2006) 19732001.
[8] Causin, P., Gerbeau, J.F., Nobile, F., Added-mass effect in the design of partitioned algorithms for fluid-structure problems, Computer Methods in Applied Mechanics and Engineering, 194 (2005) 45064527.
[9] Matthies, H.G., Niekamp, R., Steindorf, J., Algorithms for strong coupling procedures, Computer Methods in Applied Mechanics and Engineering, 195 (2006) 20282049.
[10] Hübner, B., Walhorn, E., Dinkler, D., A monolithic approach to fluid-structure interaction using space-time finite elements, Computer Methods in Applied Mechanics and Engineering, 193 (2004) 20872104.
[11] Heil, M., An efficient solver for the fully coupled solution of large-displacement fluid-structure interaction problems, Computer Methods in Applied Mechanics and Engineering, 193 (2004) 123.
[12] Ryzhakov, P.B., Rossi, R., Idelsohn, S.R., Oñate, E., Amonolithic Lagrangian approach for fluid-structure interaction problems, Computational Mechanics, 46 (2010) 883899.
[13] Franci, A., Oñate, E., Carbonell, J.M., Unified Lagrangian formulation for solid and fluid mechanics and FSI problems, Computer Methods in Applied Mechanics and Engineering, 298 (2016) 520547.
[14] Peskin, C.S., Numerical analysis of blood flow in heart, Journal of Computational Physics, 25 (1977) 220252.
[15] Peskin, C.S., The immersed boundary method, Acta Numerica, 11 (2002) 479517.
[16] Mohd-Yusof, J., Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries, in: Annual Research Briefs, Center for Turbulence Research, Stanford University, Stanford, (1997) 317327.
[17] Yang, J., Stern, F., A simple and efficient direct forcing immersed boundary framework for fluid-structure interactions, Journal of Computational Physics, 231 (2012) 50295061.
[18] Ye, T., Mittal, R., Udaykumar, H.S., Shyy, W., An accurate Cartesian gridmethod for viscous incompressible flows with complex immersed boundaries, Journal of Computational Physics, 156 (1999) 209240.
[19] Schneiders, L., Hartmann, D., Meinke, M., Schröder, W., An accurate moving boundary formulation in cut-cell methods, Journal of Computational Physics, 235 (2013) 786809.
[20] Tseng, Y.-H., Ferziger, J.H., A ghost-cell immersed boundary method for flow in complex geometry, Journal of Computational Physics, 192 (2003) 593623.
[21] Lee, J., You, D., An implicit ghost-cell immersed boundary method for simulations of moving body problems with control of spurious force oscillations, Journal of Computational Physics, 233 (2013) 295314.
[22] Zhang, L., Gerstenberger, A., Wang, X., Liu, W.K., Immersed finite element method, Computer Methods in Applied Mechanics and Engineering, 193 (2004) 20512067.
[23] Gil, A.J., Carreño, A. Arranz, Bonet, J., Hassan, O., An enhanced immersed structural potential method for fluid-structure interaction, Journal of Computational Physics, 250 (2013) 178205.
[24] Glowinski, R., Pan, T.W., Periaux, J., A fictitious domain method for Dirichlet problem and applications, Computer Methods in Applied Mechanics and Engineering, 111 (1994) 283303.
[25] Baaijens, F.P.T., A fictitious domain/mortar element method for fluid-structure interaction, International Journal for Numerical Methods in Fluids, 35 (2001) 743761.
[26] Yu, Z., A DLM/FD method for fluid/flexible-body interactions, Journal of Computational Physics, 207 (2005) 127.
[27] Swift, M.R., Orlandini, E., Osborn, W.R., Yeomans, J.M., Lattice Boltzmann simulations of liquid-gas and binary fluid systems, Physical Review E, 54 (1996) 50415052.
[28] Ladd, A.J.C., Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part I. Theoretical foundation, Journal of Fluid Mechanics, 271 (1994) 285309.
[29] Ladd, A.J.C., Verberg, R., Lattice-Boltzmann simulations of particle-fluid suspensions, Journal of Statistical Physics, 104 (2001) 11911251.
[30] Sussman, M., Smereka, P., Osher, S., A level set approach for computing solutions to incompressible two-phase flow, Journal of Computational Physics, 114 (1994) 146159.
[31] Patankar, S.V., Numerical Heat Transfer and Fluid Flow, (1980) Hemisphere Publishing Corporation.
[32] Ghia, U., Ghia, K.N., Shin, C.T., High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, Journal of Computational Physics, 48 (1982) 387411.
[33] Glowinski, R., Guidoboni, G., Pan, T.W., Wall-driven incompressible viscous flow in a two-dimensional semi-circular cavity, Journal of Computational Physics, 216 (2006) 7691.
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Communications in Computational Physics
  • ISSN: 1815-2406
  • EISSN: 1991-7120
  • URL: /core/journals/communications-in-computational-physics
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