Dynamic adaptive finite element analysis of acoustic wave propagation due to underwater explosion for fluid-structure interaction problems

Abstract

In this paper, an investigation into the propagation of far field explosion waves in water and their effects on nearby structures are carried out. For the far field structure, the motion of the fluid surrounding the structure may be assumed small, allowing linearization of the governing fluid equations. A complete analysis of the problem must involve simultaneous solution of the dynamic response of the structure and the propagation of explosion wave in the surrounding fluid. In this study, a dynamic adaptive finite element procedure is proposed. Its application to the solution of a 2D fluid-structure interaction is investigated in the time domain. The research includes: a) calculation of the far-field scatter wave due to underwater explosion including solution of the time-depended acoustic wave equation, b) fluid-structure interaction analysis using coupled Euler-Lagrangian approach, and c) adaptive finite element procedures employing error estimates, and re-meshing. The temporal mesh adaptation is achieved by local regeneration of the grid using a time-dependent error indicator based on curvature of pressure function. As a result, the overall response is better predicted by a moving mesh than an equivalent uniform mesh. In addition, the cost of computation for large problems is reduced while the accuracy is improved.

Keywords

adaptive mesh / fluid-structure interaction / acoustic wave / finite element analysis / underwater explosion

References

[1] Bausys R, Wiberg NE. Adaptive finite element strategy for acoustic problems. Journal of Sound and Vibration, 1999, 226(5): 905-922

[2] Bell J, Berger M, Saltzman J, Welcome M. Three dimensional adaptive mesh refinement for hyperbolic conservation laws. SIAM Journal on Scientific Computing, 1994, 15(1): 127-138

[3] Berrone S, Marro M. Space-time adaptive simulations for unsteady Navier-Stokes problems. Computers & Fluids, 2009, 38(6): 1132-1144

[4] Bouillard P, Allard JF, Warzee G. Superconvergent patch recovery technique for the finite element method in acoustics. Communications in Numerical Methods in Engineering, 1996, 12(9): 581-594

[5] Cole RH (1948). Underwater explosions. Princeton University Press, Princeton, USA.

[6] Dapogny C, Dobrzynshi C, Frey P. Three-dimensional adaptive domain remeshing, implicit domain meshing, and applications to free and moving boundary problems. Journal of Computational Physics, 2014, 262(4): 358-378

[7] Emamzadeh S. Sh (2008). An adaptive finite element analysis of acoustic waves propagation due to underwater explosion for fluid-structure interaction problems. PhD thesis, Tarbiat Modares University, Tehran, 62-66. (in Persian)

[8] Ghanaat Y, Clough W, Redpath BB (1992). Experimental study of dam-water-foundation interaction. Proceedings of the Tenth World Conference on Earthquake Engineering, Madrid, Spain, 19-24.

[9] Gilardo FX (1995). A space marching adaptive re-meshing technique applied to the 3D Euler equations for supersonic flow. PhD thesis, University of Virginia, Charlottesville, 59-80.

[10] Harari I, Grosh K, Hughes TJR, Malhotra M, Pinnsky PM, Stewart JR, Thompson LL. Recent development in finite element methods for structural acoustics. Archives of Computational Methods in Engineering, 1996, 3(2-3): 131-311

[11] Hua F, Wang P, Chen X, Feng H. An adaptive mesh method for 1D hyperbolic conservation laws. Applied Numerical Mathematic, 2015, 91: 11-25

[12] Kadioglu SY, Sussman M. Adaptive solution techniques for simulating underwater explosions and implosions. Journal of Computational Physics, 2008, 227(3): 2083-2104

[13] Kim JH, Shin HC. Application of the ALE technique for underwater explosion analysis of a submarine liquefied oxygen tank. Ocean Engineering, 2008, 35(8-9): 812-822

[14] Howell LH, Bell J. An adaptive-mesh projection method for viscous incompressible flow. SIAM Journal on Scientific Computing, 1997, 18(4): 996-1013

[15] Mair HU. Review: Hydrocodes for structural response to underwater explosions. Shock and Vibration, 1999, 6(2): 81-96

[16] Pember RB, Howell LH, Bell J, Colella P, Crutchfield WY, Fiveland WA, Jessee JP. An adaptive projection method for unsteady low-Mach number combustion. Combustion Science and Technology, 1998, 140(1-6): 123-168

[17] Peraire J, Vahdati M, Morgan K, Zienkiewicz OC. Adaptive re-meshing for compressible flow computations. Journal of Computational Physics, 1987, 72(2): 449-466

[18] Ross MR, Felippa CA, Park KC, Sprague MA. Treatment of acoustic fluid-structure interaction by localized Lagrange multipliers: Formulation. Computer Methods in Applied Mechanics and Engineering, 2008, 197(33-40): 3057-3079

[19] Ross MR, Sprague MA, Felippa CA, Park KC. Treatment of acoustic fluid–structure interaction by localized Lagrange multipliers and comparison to alternative interface-coupling methods. Computer Methods in Applied Mechanics and Engineering, 2009, 198(9-12): 986-1005

[20] Shin YS. Ship shock modeling and simulation for far-field underwater explosion. Computers & Fluids, 2004, 82(23-26): 2211-2219

[21] Skamarock WC, Klemp JB. Adaptive grid refinement for two-dimensional and three-dimensional non hydrostatic atmospheric flow. Monthly Weather Review, 1993, 121(3): 788-804

[22] Sommerfeld A (1949). Partial differential equations in physics. Academic Press, New York, 188-190.

[23] Sprague MA, Geers TL. A spectral-element/finite-element analysis of a ship-like structure subjected to an underwater explosion. Computer Methods in Applied Mechanics and Engineering, 2006, 195(17-18): 2149-2167

[24] Sprague MA, Geers TL. Legendre spectral finite elements for structural dynamics analysis. Communications in Numerical Methods in Engineering, 2008, 24(12): 1953-1965

[25] Steinthorsson E, Modiano D, Crutchfield WY, Bell JB, Colella P (1995). An adaptive semi-implicit scheme for simulations of unsteady viscous compressible flow. Proceedings of the 12th AIAA Computational Fluid Dynamics Conference, Orlando, USA, AIAA Paper 95-1727-CP.

[26] Stevens DE, Bretherton CS. A forward-in-time advection scheme and adaptive multilevel flow solver for nearly incompressible atmospheric flow. Journal of Computational Physics, 1996, 129(2): 284-295

[27] Tetambe RP, Rajakumar C. Estimation of error in finite element acoustic analysis. Computers and Structures, 1996, 61(1): 13-19

[28] Wardlaw A (1998). Underwater explosion test cases. Office of Naval Research, Virginia, United States, Technical Report IHTR 2069, ADB238684.

[29] Yu Tiantang (2009). Dynamical response simulation of concrete dam subjected to under water contact explosion load. 2009 World Congress on Computer Science and Information Engineering, Los Angeles, USA, 767-774. DOI: 10.1109/CSIE.2009.106

[30] Zienkiewicz OC, Taylor RL, Nithiarasu P (2005). The finite element method for fluid dynamics. Sixth edition, Butterworth- Heinemann, Oxford, United Kingdom, 465-478.