Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-22T22:05:03.219Z Has data issue: false hasContentIssue false

The Modified Ghost Fluid Method Applied to Fluid-Elastic Structure Interaction

Published online by Cambridge University Press:  03 June 2015

Tiegang Liu*
Affiliation:
LMIB and School of Mathematics and Systems Science, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
A. W. Chowdhury
Affiliation:
Department of Mechanical Engineering, National University of Singapore, Singapore 119260, Singapore
Boo Cheong Khoo*
Affiliation:
Department of Mechanical Engineering, National University of Singapore, Singapore 119260, Singapore Singapore-MIT Alliance, 4 Engineering Drive 3, National University of Singapore, Singapore 117576, Singapore
*
Corresponding author. Email: [email protected]
URL:http://serve.me.nus.edu.sg/khoobc/Email: [email protected]
Get access

Abstract

In this work, the modified ghost fluid method is developed to deal with 2D compressible fluid interacting with elastic solid in an Euler-Lagrange coupled system. In applying the modified Ghost Fluid Method to treat the fluid-elastic solid coupling, the Navier equations for elastic solid are cast into a system similar to the Euler equations but in Lagrangian coordinates. Furthermore, to take into account the influence of material deformation and nonlinear wave interaction at the interface, an Euler-Lagrange Riemann problem is constructed and solved approximately along the normal direction of the interface to predict the interfacial status and then define the ghost fluid and ghost solid states. Numerical tests are presented to verify the resultant method.

Type
Research Article
Copyright
Copyright © Global-Science Press 2011

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] Adalsteinsson, D. and Sethian, J. A., The fast construction of extension velocities in level set methods, J. Comput. Phys., 148 (1999), pp. 222.Google Scholar
[2] Aivazis, M., Goddard, W. A., Meiron, D., Ortiz, M., Pool, J. and Shepherd, J., A virtual, test facility for simulating the dynamic response of materials, Comput. Sci. Eng., 2 (2000), pp. 4253.Google Scholar
[3] Arienti, M., Hung, P., Morano, E. and Shepherd, J., A level set approach to Euler-Lagrange coupling, J. Comput. Phys., 185 (2003), pp. 213251.CrossRefGoogle Scholar
[4] Chung, T. J., Applied Continuum Mechanics, Cambridge University Press, 1996.Google Scholar
[5] 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. 457492.CrossRefGoogle Scholar
[6] Fedkiw, R. P., Coupling an Eulerian fluid calculation to a Lagrangian solid calculation with the ghost fluid method, J. Comput. Phys., 175 (2002), pp. 200224.Google Scholar
[7] Figueroa, A., Vignon-Clementel, I., Jansen, K., Hughes, T. J. R. and Taylor, C. A., Simulation of blood flow and vessel deformation in three dimensional, patient-specific models of the cardiovascular system using a novel method for fluid-structure interaction, WIT Transactions on The Built Environment, WIT Press, 84 (2005), pp. 143152.Google Scholar
[8] Heys, J. J., Manteuffel, T. A., Mccormick, S. F. and Ruge, J. W., First-order system least squares (FOSLS) for coupled fluid-elastic problems, J. Comput. Phys., 195 (2004), pp. 560575.Google Scholar
[9] 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. 651681.Google Scholar
[10] Liu, T. G., Khoo, B. C. and Xie, W. F., Isentropic one-fluid modelling of unsteady cavitating flow, J. Comput. Phys., 201 (2004), pp. 80108.Google Scholar
[11] 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. 193221.Google Scholar
[12] 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. 898919.Google Scholar
[13] Liu, L. 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., 33 (2008), pp. 11051130.CrossRefGoogle Scholar
[14] 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 Navier equations, J. Sci. Comput., 36 (2008), pp. 4568.Google Scholar
[15] Miller, G. H. and Puckett, E. G., A high-order Godunov method for multiple condensed phases, J. Comput. Phys., 128 (1996), pp. 134164.Google Scholar
[16] Osher, S. and Sethian, J. A., Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79 (1988), pp. 1249.Google Scholar
[17] Palo, P., Survey of naval computational needs in fluid-structure interaction, IUTAM Symposium on Integrated Modeling of Fully Coupled Fluid Structure Interactions Using Analysis, Computations and Experiments, 126, Kluwer Academic Publishers, 2003.Google Scholar
[18] Schaäfer, M. and Teschauer, I., Numerical simulation of coupled fluid-solid problems, Comput. Methods. Appl. Mech. Eng., 190 (2001), pp. 36453667.CrossRefGoogle Scholar
[19] Schäfer, M., Coupled fluid-solid problems: surveys on numerical approaches and applications, PVP-Vol. 460, Emerging Technology in Fluids, Structures and Fluid-Structure Interactions>, ASME (2003).,+ASME+(2003).>Google Scholar
[20] Souli, M., Mahmadi, K. and Aquelet, N., ALE and fluid structure interface, Mat. Sci. Forum., 465466 (2004), pp. 143149.Google Scholar
[21] Tang, H. S. and Sotiropoulos, F., A second-order Godunov method for wave problems in coupled solid-water-gas systems, J. Comput. Phys., 151 (1999), pp. 790815.Google Scholar
[22] Toro, E. F., Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, New York, Springer, 1997.Google Scholar
[23] Udaykumar, H. S., Tran, L., Belk, D. M. and Vanden, K. J., An Eulerian method for computation of multimaterial impact with ENO shock-capturing and sharp interfaces, J. Com-put. Phys., 186 (2003), pp. 136177.CrossRefGoogle Scholar
[24] Wang, C. W., Liu, T. G. and Khoo, B. C., A real-ghost fluid method for the simulation of multi-medium compressible flow, SIAM Sci. Comput., 28 (2006), pp. 278302.CrossRefGoogle Scholar
[25] Xiao, L., Numerical Computation of Stress Waves in Solid, Akademie Verlag, 1997.Google Scholar
[26] Xie, W. F., Young, Y. L. and Liu, T. G., Multiphase modeling of dynamic fluid-structure interaction during close-in explosion, Int. J. Numer. Methods Eng., 70 (2008), pp. 10191043.Google Scholar