Skip to main content
    • Aa
    • Aa

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)
Hide All

Communicated by Lianjie Huang

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1] Y. Bazilevs , M.-C. Hsu , Y. Zhang , W. Wang , X. Liang , T. Kvamsdal , R. Brekken , J.G. Isaksen , A fully-coupled fluid-structure interaction simulation of cerebral aneurysms, Computational Mechanics, 46 (2009) 316.

[2] D. Kamensky , M.C. Hsu , D. Schillinger , J.A. Evans , A. Aggarwal , Y. Bazilevs , M.S. Sacks , T.J.R. Hughes , An immersogeometric variational framework for fluid-structure interaction: Application to bioprosthetic heart valves, Computer Methods in Applied Mechanics and Engineering, 284 (2015) 10051053.

[3] M.-C. Hsu , I. Akkerman , Y. Bazilevs , Finite element simulation of wind turbine aerodynamics: Validation study using NREL Phase VI experiment, Wind Energy, 17 (2014) 461481.

[5] G. Hou , J. Wang , A. Layton , Numerical methods for fluid-structure interaction - A review, Communications in Computational Physics, 12 (2012) 337377.

[6] C.A. Felippa , K.C. Park , C. Farhat , Partitioned analysis of coupled mechanical systems, Computer Methods in Applied Mechanics and Engineering, 190 (2001) 32473270.

[7] C. Farhat , K.G. van der Zee , P. Geuzaine , 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] P. Causin , J.F. Gerbeau , F. Nobile , Added-mass effect in the design of partitioned algorithms for fluid-structure problems, Computer Methods in Applied Mechanics and Engineering, 194 (2005) 45064527.

[9] H.G. Matthies , R. Niekamp , J. Steindorf , Algorithms for strong coupling procedures, Computer Methods in Applied Mechanics and Engineering, 195 (2006) 20282049.

[10] B. Hübner , E. Walhorn , D. Dinkler , A monolithic approach to fluid-structure interaction using space-time finite elements, Computer Methods in Applied Mechanics and Engineering, 193 (2004) 20872104.

[11] M. Heil , 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] P.B. Ryzhakov , R. Rossi , S.R. Idelsohn , E. Oñate , Amonolithic Lagrangian approach for fluid-structure interaction problems, Computational Mechanics, 46 (2010) 883899.

[14] C.S. Peskin , Numerical analysis of blood flow in heart, Journal of Computational Physics, 25 (1977) 220252.

[15] C.S. Peskin , The immersed boundary method, Acta Numerica, 11 (2002) 479517.

[17] J. Yang , F. Stern , A simple and efficient direct forcing immersed boundary framework for fluid-structure interactions, Journal of Computational Physics, 231 (2012) 50295061.

[18] T. Ye , R. Mittal , H.S. Udaykumar , W. Shyy , An accurate Cartesian gridmethod for viscous incompressible flows with complex immersed boundaries, Journal of Computational Physics, 156 (1999) 209240.

[19] L. Schneiders , D. Hartmann , M. Meinke , W. Schröder , An accurate moving boundary formulation in cut-cell methods, Journal of Computational Physics, 235 (2013) 786809.

[20] Y.-H. Tseng , J.H. Ferziger , A ghost-cell immersed boundary method for flow in complex geometry, Journal of Computational Physics, 192 (2003) 593623.

[22] L. Zhang , A. Gerstenberger , X. Wang , W.K. Liu , Immersed finite element method, Computer Methods in Applied Mechanics and Engineering, 193 (2004) 20512067.

[23] A.J. Gil , A. Arranz Carreño , J. Bonet , O. Hassan , An enhanced immersed structural potential method for fluid-structure interaction, Journal of Computational Physics, 250 (2013) 178205.

[25] F.P.T. Baaijens , A fictitious domain/mortar element method for fluid-structure interaction, International Journal for Numerical Methods in Fluids, 35 (2001) 743761.

[26] Z. Yu , A DLM/FD method for fluid/flexible-body interactions, Journal of Computational Physics, 207 (2005) 127.

[27] M.R. Swift , E. Orlandini , W.R. Osborn , J.M. Yeomans , Lattice Boltzmann simulations of liquid-gas and binary fluid systems, Physical Review E, 54 (1996) 50415052.

[28] A.J.C. Ladd , Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part I. Theoretical foundation, Journal of Fluid Mechanics, 271 (1994) 285309.

[30] M. Sussman , P. Smereka , S. Osher , A level set approach for computing solutions to incompressible two-phase flow, Journal of Computational Physics, 114 (1994) 146159.

[33] R. Glowinski , G. Guidoboni , T.W. Pan , Wall-driven incompressible viscous flow in a two-dimensional semi-circular cavity, Journal of Computational Physics, 216 (2006) 7691.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Communications in Computational Physics
  • ISSN: 1815-2406
  • EISSN: 1991-7120
  • URL: /core/journals/communications-in-computational-physics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 52 *
Loading metrics...

Abstract views

Total abstract views: 130 *
Loading metrics...

* Views captured on Cambridge Core between 3rd May 2017 - 22nd September 2017. This data will be updated every 24 hours.