Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T15:52:50.429Z Has data issue: false hasContentIssue false
  • English
  • Français

Modified Ghost Fluid Method as Applied to Fluid-Plate Interaction

Published online by Cambridge University Press:  03 June 2015

Liang Xu  and
Tiegang Liu
Liang Xu*
Affiliation:
China Academy of Aerospace Aerodynamics, Beijing 100074, China LMIB and School of Mathematics and Systems Science, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Tiegang Liu*
Affiliation:
LMIB and School of Mathematics and Systems Science, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
*
Email: xuliang@smss.buaa.edu.cn
Corresponding author. Email: liutg@buaa.edu.cn
Get access

Abstract

The modified ghost fluid method (MGFM) provides a robust and efficient interface treatment for various multi-medium flow simulations and some particular fluid-structure interaction (FSI) simulations. However, this methodology for one specific class of FSI problems, where the structure is plate, remains to be developed. This work is devoted to extending the MGFM to treat compressible fluid coupled with a thin elastic plate. In order to take into account the influence of simultaneous interaction at the interface, a fluid-plate coupling system is constructed at each time step and solved approximately to predict the interfacial states. Then, ghost fluid states and plate load can be defined by utilizing the obtained interfacial states. A type of acceleration strategy in the coupling process is presented to pursue higher efficiency. Several one-dimensional examples are used to highlight the utility of thismethod over looselycoupled method and validate the acceleration techniques. Especially, this method is applied to compute the underwater explosions (UNDEX) near thin elastic plates. Evolution of strong shock impacting on the thin elastic plate and dynamic response of the plate are investigated. Numerical results disclose that this methodology for treatment of the fluid-plate coupling indeed works conveniently and accurately for different structural flexibilities and is capable of efficiently simulating the processes of UNDEX with the employment of the acceleration strategy.

Keywords

65M0665N8574F10Fluid-structure interactionmodified ghost fluid methodcompressible flowthin elastic plateunderwater explosions
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 1 , February 2014 , pp. 24 - 48
Copyright
Copyright © Global-Science Press 2014

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.)

References

[1]Cockburn, B., Lin, S. Y. and Shu, C. W., TVB Runge-Kutta local projection discontinuous Galerkinfinite element method for conservation laws III: one dimensional systems, J. Comput. Phys., 84 (1989), pp. 90–113.Google Scholar
[2]Cockburn, B., Hou, S. AND Shu, C. W., The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case, Math. Comput., 54 (1990), pp. 545–581.Google Scholar
[3]Harten, A. and Osher, S., Uniformly high-order accurate nonoscillatory schemes I, SIAM J. Numer. Anal., 24 (1987), pp. 279–309.Google Scholar
[4]Jiang, G. S. and Shu, C. W., Efficient implementation of weighted ENO schemes, J. Comput. Phys., 126 (1996), pp. 202–228.CrossRefGoogle Scholar
[5]Jaiman, R. K., Jiao, X., Geubelle, P. H. and Loth, E., Conservative load transfer along curved fluid-solid interface with non-matching meshes, J. Comput. Phys., 218 (2006), pp. 372–397.CrossRefGoogle Scholar
[6]Farhat, C., Der Zee, K. G. van and Geuzaine, P., Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity, Comput. Methods Appl. Mech. Eng., 195 (2006), pp. 1973–2001.Google Scholar
[7]Zuijlen, A. V., Boer, A. d. and Bijl, H., Higher-order time integration through smooth mesh deformation for 3D fluid-structure interaction simulations, J. Comput. Phys., 224 (2007), pp. 414430.Google Scholar
[8]Jaiman, R., Geubelle, P., Loth, E. and Jiao, X., Combined interface boundary condition method for unsteady fluid-structure interaction, Comput. Methods Appl. Mech. Eng., 200 (2011), pp. 27–39.Google Scholar
[9]Nakata, T. and Liu, H., A fluid-structure interaction model of insect flight with flexible wings, J. Comput. Phys., 231 (2012), pp. 1822–1847.Google Scholar
[10]Fedkiw, R. P., Aslam, T., Merriman, B. AND Osher, S., A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method), J. Comput. Phys., 152 (1999), pp. 457–492.Google Scholar
[11]Fedkiw, R. P., Coupling an Eulerian fluid calculation to a Lagrangian solid calculation with the ghost fluid method, J. Comput. Phys., 175 (2002), pp. 200–224.Google Scholar
[12]Liu, T. G., Khoo, B. C. and Yeo, K. S., Ghost fluid method for strong shock impacting on material interface, J. Comput. Phys., 190 (2003), pp. 651–681.Google Scholar
[13]Liu, T. G., Khoo, B. C. and Wang, C. W., The ghost fluid method for compressible gas-water simulation, J. Comput. Phys., 204 (2005), pp. 193–221.Google Scholar
[14]Wang, C. W., Liu, T. G. and Khoo, B. C., A real-ghost fluid method for the simulation of multimedium compressible flow, SIAM J. Sci. Comput., 28 (2006), pp. 278–302.Google Scholar
[15]Qiu, J. X., Liu, T. G. and Khoo, B. C., Simulations of compressible two-medium flow by Runge-Kutta discontinuous Galerkin methods with the ghost fluid method, Commun. Comput. Phys., 3 (2008), pp. 479–504.Google Scholar
[16]Wang, C. W., Tang, H. Z. and Liu, T. G., An adaptive ghost fluid finite volume method for compressible gas-water simulations, J. Comput. Phys., 227 (2008), pp. 6385–6409.Google Scholar
[17]Barton, P. T. AND Drikakis, D., An Eulerian method for multi-component problems in nonlinear elasticity with sliding interfaces, J. Comput. Phys., 229 (2010), pp. 5518–5540.Google Scholar
[18]Xu, L. and Liu, T. G., Optimal error estimation of the modified ghost fluid method, Commun. Comput. Phys., 8 (2010), pp. 403–426.Google Scholar
[19]Xu, L. and Liu, T. G., Accuracies and conservation errors of various ghost fluid methods for multimedium Riemann problem, J. Comput. Phys., 230 (2011), pp. 4975–4990.Google Scholar
[20]Liu, T. G., Khoo, B. C. and Xie, W. F., The modified ghost fluid method as applied to extreme fluid-structure interaction in the presence of cavitation, Commun. Comput. Phys., 1 (2006), pp. 898–919.Google Scholar
[21]Xie, W. F., Young, Y. L., Liu, T. G. and Khoo, B. C., Dynamic response of deformable structures subjected to shock load and cavitation reload, Comput. Mech., 40 (2007), pp. 667–681.Google Scholar
[22]Liu, T. G., Xie, W. F. and Khoo, B. C., The modified ghost fluid method for coupling of fluid and structure constituted with hydro-elasto-plastic equation of state, SIAM J. Sci. Comput., 30 (2008), pp. 1105–1130.Google Scholar
[23]Xie, W. F., Young, Y. L. and Liu, T. G., Multiphase modeling of dynamic fluid-structure interaction during close-in explosion, In T. J. Numer. Meth. Eng., 74 (2008), pp. 1019–1043.Google Scholar
[24]Tang, H. S. and Sotiropoulos, F., A second-order Godunov method for wave problems in coupled solid-watergas systems, J. Comput. Phys., 151 (1999), pp. 790–815.CrossRefGoogle Scholar
[25]Liu, T. G., Ho, J. Y., Khoo, B. C. and Chowdhury, A. W., Numerical simulation of fluid-structure interaction using modified ghost fluid method and Naviers equations, J. Sci. Comput., 36 (2008), pp. 45–68.Google Scholar
[26]Liu, T. G., Chowdhury, A. W. and Khoo, B. C., The modified ghost fluid method applied to fluid-elastic structure interaction, Adv. Appl. Math. Mech., 3 (2011), pp. 611–632.Google Scholar
[27]Xie, W. F., Liu, Z. K. and Young, Y. L., Application of a coupled Eulerian-Lagrangian method to simulate interactions between deformable composite structures and compressible multiphase flow, In T. J. Numer. Meth. Eng., 80 (2009), pp. 1497–1519.Google Scholar
[28]Young, Y. L., Liu, Z. K. and Xie, W. F., Fluid-structure and shock-bubble interaction effects during underwater explosions near composite structures, ASME J. Appl. Mech., 76 (2009), 051303.Google Scholar
[29]Liu, Z. K., Xie, W. F. and Young, Y. L., Numerical modeling of complex interactions between underwater shocks and composite structures, Comput. Mech., 43 (2009), pp. 239–251.Google Scholar
[30]Liu, Z. K., Xie, W. F. and Young, Y. L., Transient response of partially-bonded sandwich plates subject to underwater explosions, Shock Vib., 17 (2010), pp. 233–250.Google Scholar
[31]Leer, B. van, Towards the ultimate conservative difference scheme IV: a new approach to numerical convection, J. Comput. Phys., 23 (1977), pp. 276–299.Google Scholar
[32]Harten, A., Lax, P. D. and Van, B. Leer, On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Rev., 25 (1983), pp. 35–61.Google Scholar
[33]Liu, T. G., Khoo, B. C. and Yeo, K. S., The simulation of compressible multi-medium flow, Part I: a new methodology with test applications to 1D gas-gas and gas-water cases, Comput. Fluids, 30 (2001), pp. 291–314.Google Scholar
[34]Sussman, M., Smereka, P. and Osher, S., A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys., 114 (1994), pp. 146–159.Google Scholar
[35]Unverdi, S. O. and Tryggvason, G., A front-tracking method for viscous incompressible multifluid flows, J. Comput. Phys., 100 (1992), pp. 25–37.Google Scholar
[36]Timoshenko, S. AND Woinowsky-Krieger, S., Theory of Plates and Shells, Second ed., McGraw Hill, 1959.Google Scholar