Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-23T15:41:07.042Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Part of: Basic methods in fluid mechanics Generalities, axiomatics, foundations of continuum mechanics of solids

Published online by Cambridge University Press:  03 May 2017

Haram Yeo  and
Hyungson Ki
Haram Yeo*
Affiliation:
Department of Mechanical Engineering, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulsan 44919, South Korea
Hyungson Ki*
Affiliation:
Department of Mechanical Engineering, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulsan 44919, South Korea
*
*Corresponding author. Email addresses:[email protected] (H. Yeo), [email protected] (H. Ki)
*Corresponding author. Email addresses:[email protected] (H. Yeo), [email protected] (H. Ki)
Get access

Abstract

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®.

Keywords

Flow induced stressunified momentum equationmonolithic approachsmeared interfacestationary boundary

MSC classification

Secondary: 74A10: Stress 76M12: Finite volume methods
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 1 , July 2017 , pp. 39 - 63
Copyright
Copyright © Global-Science Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Communicated by Lianjie Huang

References

[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) 3–16.Google Scholar
[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) 1005–1053.CrossRefGoogle ScholarPubMed
[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) 461–481.CrossRefGoogle Scholar
[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) 1346–1357.CrossRefGoogle Scholar
[5] Hou, G., Wang, J., Layton, A., Numerical methods for fluid-structure interaction - A review, Communications in Computational Physics, 12 (2012) 337–377.Google Scholar
[6] Felippa, C.A., Park, K.C., Farhat, C., Partitioned analysis of coupled mechanical systems, Computer Methods in Applied Mechanics and Engineering, 190 (2001) 3247–3270.Google Scholar
[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) 1973–2001.Google Scholar
[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) 4506–4527.Google Scholar
[9] Matthies, H.G., Niekamp, R., Steindorf, J., Algorithms for strong coupling procedures, Computer Methods in Applied Mechanics and Engineering, 195 (2006) 2028–2049.CrossRefGoogle Scholar
[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) 2087–2104.Google Scholar
[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) 1–23.CrossRefGoogle Scholar
[12] Ryzhakov, P.B., Rossi, R., Idelsohn, S.R., Oñate, E., Amonolithic Lagrangian approach for fluid-structure interaction problems, Computational Mechanics, 46 (2010) 883–899.Google Scholar
[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) 520–547.Google Scholar
[14] Peskin, C.S., Numerical analysis of blood flow in heart, Journal of Computational Physics, 25 (1977) 220–252.Google Scholar
[15] Peskin, C.S., The immersed boundary method, Acta Numerica, 11 (2002) 479–517.Google Scholar
[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) 317–327.Google Scholar
[17] Yang, J., Stern, F., A simple and efficient direct forcing immersed boundary framework for fluid-structure interactions, Journal of Computational Physics, 231 (2012) 5029–5061.Google Scholar
[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) 209–240.Google Scholar
[19] Schneiders, L., Hartmann, D., Meinke, M., Schröder, W., An accurate moving boundary formulation in cut-cell methods, Journal of Computational Physics, 235 (2013) 786–809.CrossRefGoogle Scholar
[20] Tseng, Y.-H., Ferziger, J.H., A ghost-cell immersed boundary method for flow in complex geometry, Journal of Computational Physics, 192 (2003) 593–623.Google Scholar
[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) 295–314.CrossRefGoogle Scholar
[22] Zhang, L., Gerstenberger, A., Wang, X., Liu, W.K., Immersed finite element method, Computer Methods in Applied Mechanics and Engineering, 193 (2004) 2051–2067.Google Scholar
[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) 178–205.CrossRefGoogle Scholar
[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) 283–303.CrossRefGoogle Scholar
[25] Baaijens, F.P.T., A fictitious domain/mortar element method for fluid-structure interaction, International Journal for Numerical Methods in Fluids, 35 (2001) 743–761.3.0.CO;2-A>CrossRefGoogle Scholar
[26] Yu, Z., A DLM/FD method for fluid/flexible-body interactions, Journal of Computational Physics, 207 (2005) 1–27.Google Scholar
[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) 5041–5052.Google Scholar
[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) 285–309.Google Scholar
[29] Ladd, A.J.C., Verberg, R., Lattice-Boltzmann simulations of particle-fluid suspensions, Journal of Statistical Physics, 104 (2001) 1191–1251.CrossRefGoogle Scholar
[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) 146–159.Google Scholar
[31] Patankar, S.V., Numerical Heat Transfer and Fluid Flow, (1980) Hemisphere Publishing Corporation.Google Scholar
[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) 387–411.Google Scholar
[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) 76–91.Google Scholar