A Lagrangian Finite Element Treatment of Transient Gravitational Waves in Compressible Viscous Fluids

• Autorzy: Staroszczyk R.
• Języki publikacji: EN

Abstrakty

EN

In this paper the problem of transient gravitational wave propagation in a viscous compressible fluid is investigated. The problem is formulated in the Lagrangian description and is solved numerically by a finite element method. In computations either fixed in space or moving meshes that follow the material fluid particles are used with the purpose to compare their numerical performance. As illustrations, results of numerical simulations carried out for plane flows in a domain of simple geometry are presented. First, the finite element results are compared with available experimental data for the case of small-amplitude waves in order to validate the numerical model. Then, the problem of large-amplitude transient water wave propagation over a horizontal bottom, involving the wave reflection at a rigid wall, is considered. For the flow parameters typical of a laboratory flume, the evolution of the free-surface elevation and the time variations of the surface displacements at chosen locations are shown for a range of different moving wall amplitudes and excitation times.

Słowa kluczowe

EN

Newtonian viscous fluid; gravitational wave; transient problem; Lagrangian formulation; finite element method

• Wydawca: Institute of Hydro-Engineering of Polish Academy of Sciences
• Czasopismo: Archives of Hydro-Engineering and Environmental Mechanics
• Rocznik: 2007
• Tom: Vol. 54, nr 4
• Strony: 261--284
• Opis fizyczny: Bibliogr. 24 poz., il.

Twórcy

autor

Staroszczyk R.

• Institute of Hydro-Engineering of the Polish Academy of Sciences, ul. Kościerska 7, 80-328 Gdańsk, Poland,

Bibliografia

• 1. Aubry R., Idelsohn S. R. and O˜nate E. (2005) Particle finite element method in fluid-mechanics including thermal convection-diffusion, Comput. Struct. 83 (17–18), 1459–1475. Bathe K. J. (1982) Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, New Jersey.
• 2. Braess H. and Wriggers P. (2000) Arbitrary Lagrangian Eulerian finite element analysis of free surface flows, Comput. Meth. Appl. Mech. Eng. 190 (1–2), 95–109.
• 3. Chadwick P. (1999) Continuum Mechanics: Concise Theory and Problems. Dover, Mineola, New York, 2nd edn.
• 4. Del Pin F., Idelsohn S., O˜nate E. and Aubry R. (2007) The ALE/Lagrangian Particle Finite Element Method: A new approach to computation of free-surface flows and fluid–object interactions, Comp. Fluids 36 (1), 27–38.
• 5. Feng Y. T. and Peric D. (2000) A time-adaptive space-time finite element method for incompressible Lagrangian flows with free surfaces: computational issues, Comput. Meth. Appl. Mech. Eng. 190 (5–7), 499–518.
• 6. Idelsohn S. R., Oñate E. and Del Pin F. (2003) A Lagrangian meshless finite element method applied to fluid–structure interaction problems, Comput. Struct. 81 (8–11), 655–671.
• 7. Idelsohn S. R., Oñate E. and Del Pin F. (2004) The particle finite element method: a powerful tool to solve incompressible flows with free-surfaces and breaking waves, Int. J. Numer. Meth. Eng. 61 (7), 964–989.
• 8. Idelsohn S. R., Oñate E., Del Pin F. and Calvo N. (2006) Fluid–structure interaction using the particle finite element method, Comput. Meth. Appl. Mech. Eng. 195 (17–18), 2100–2123.
• 9. Idelsohn S.R., Oñate E. and Sacco C. (1999) Finite element solution of free-surface ship–wave problems, Int. J. Numer. Meth. Eng. 45 (5), 503–528.
• 10. Liu I.S. (2002) Continuum Mechanics, Springer, Berlin.
• 11. Löhner R., Sacco C., O˜nate E. and Idelsohn S. (2002) A finite point method for compressible flow, Int. J. Numer. Meth. Eng. 53 (8), 1765–1779.
• 12. Oñate E., Idelsohn S.R., Zienkiewicz O.C. and Taylor R.L. (1996a) A finite point method in computational mechanics. Applications to convective transport and fluid flow, Int. J. Numer. Meth. Eng. 39 (22), 3839–3866.
• 13. Oñate E., Idelsohn S.R., Zienkiewicz O.C., Taylor R.L. and Sacco C. (1996b) A stabilized finite point method for analysis of fluid mechanics problems, Comput. Meth. Appl. Mech. Eng. 139 (1–4), 315–346.
• 14. Ortega E., Oñate E. and Idelsohn S. (2007) An improved finite point method for tridimensional potential flows, Comput. Mech. 40 (6), 949–963.
• 15. Parrinello F. and Borino G. (2007) Lagrangian finite element modelling of dam–fluid interaction: Accurate absorbing boundary conditions, Comput. Struct. 85 (11–14), 932–943.
• 16. Rabier S. and Medale M. (2003) Computation of free surface flows with a projection FEM in a moving mesh framework, Comput. Meth. Appl. Mech. Eng. 192 (41–42), 4703–4721.
• 17. Radovitzky R. and Ortiz M. (1998) Lagrangian finite element analysis of Newtonian viscous flow,
• 18. Int. J. Numer. Meth. Eng. 43 (4), 607–619.
• 19. Ramaswamy B. and Kawahara M. (1987) Lagrangian finite element analysis applied to viscous free surface flow, Int. J. Numer. Meth. Fluids 7 (9), 953–984.
• 20. Souli M. and Zolesio J. P. (2001) Arbitrary Lagrangian-Eulerian and free surface methods in fluid mechanics, Comput. Meth. Appl. Mech. Eng. 191 (3–5), 451–466.
• 21. Szmidt K. and Hedzielski B. (2007) On the transformation of long gravitational waves in a region of variable water depth: a comparison of theory and experiment, Arch. Hydro-Eng. Environ. Mech. 54 (2), 137–158.
• 22. Van Brummelen E.H., Raven H.C. and Koren B. (2001) Efficient numerical solution of steady free-surface Navier-Stokes flow, J. Comput. Phys. 174 (1), 120–137.
• 23. Zienkiewicz O. C. and Taylor R. L. (1989) The Finite Element Method, vol. 1, McGraw-Hill, London, 4th edn.
• 24. Zienkiewicz O. C. and Taylor R. L. (1991) The Finite Element Method, vol. 2, McGraw-Hill, London, 4th edn.