Fluid-structure interaction using the Particle Finite Element Method

Published in Comput. Meth. Appl. Mech. Engng., Vol. 195 (17-18), pp. 2100-2123
doi: 10.1016/j.cma.2005.02.026

Abstract

In the present work a new approach to solve fluid-structure interaction problems is described. Both, the equations of motion for fluids and for solids have been approximated using a material (lagrangian) formulation. To approximate the partial differential equations representing the fluid motion, the shape functions introduced by the Meshless Finite Element Method (MFEM) have been used. Thus, the continuum is discretized into particles that move under body forces (gravity) and surface forces (due to the interaction with neighboring particles). All the physical properties such as density, viscosity, conductivity, etc., as well as the variables that define the temporal state such as velocity and position and also other variables like temperature are assigned to the particles and are transported with the particle motion. The so called Particle Finite Element Method (PFEM) provides a very advantageous and efficient way for solving contact and free-surface problems, highly simplifying the treatment of fluid-structure interactions.

Keywords: Fluid-Structure interaction, Particle methods, Lagrange formulations, Incompressible Fluid Flows, Meshless Methods, Finite Element Method.

References

[aub04] Aubry R., Idelsohn S.R. and Oñate. “The Particle Finite Element Method in

fluid mechanics including thermal convection-difusion”. Submitted to Computer & Structures. (2004).

[bel94] T. Belytschko, L. Gu and Y. Y. Lu, “Fracture and crack growth by element free Galergin methods”, Modelling Simul. Mater Sci. Eng., vol. 2, pp. 519-534, 1994.

[cod01] R.Codina, “Pressure Stability in fractional step finite element methods for incompressible flows”, Journal of Comput. Phisycs, 170,(2001) 112-140.

[cod96] Codina R, Cervera M. “Block-iterative algorithms for nonlinear coupled problems”. In: Papadrakakis M, Bugeda G, editors, Advanced Computational Methods in Structural mechanics. Barcelona: CIMNE, 1996.

[dua95] C. Duarte and J. D. Oden, “Hp clouds-a meshless method to solve boundary value problems”, Tech. Rep. 95-05, Texas institute for Computational and Applied Mechanics, Univerfsity of Texas, 1995.

[ede94] H. Edelsbrunner and E.P. Mucke, “Three-dimensional alpha-shape”. ACM Transactions on Graphics, 3, (1994), 43–72.

[ide03a] S.R. Idelsohn, E. Oñate, N. Calvo and F. Del Pin, “The meshless finite element method”, Int. J. for Numerical Methods in Engineering, Vol 58, Issue 4, (2003).

[ide04] S.R. Idelsohn, E. Oñate and F. Del Pin, “The particle finite element method: a powerful tool to solve incompressible flows with free-surfaces and breaking waves”. Int. J. for Numerical Methods in Engineering, Vol 61, Issue 7, (2004), Pages: 964-989.

[ide03b] S.R. Idelsohn, N. Calvo and E. Oñate, “Polyhedrization of an arbitrary 3D point set”. Computer Method in Applied Mechanics and Engineering, 192, pp 2649-2667 (2003).

[kos96] S. Koshizuka and Y. Oka “Moving particle semi-implicit method for fragmentation of incompressible fluid”, Nuclear Engineering Science, 123, (1996), 421–434.

[loh03] R. Löhner, J.D. Baum, E.L. Mestreau, D. Sharov, Ch. Charman and D. Pelessone “Adaptive Embedded Unstructured Grid Methods”; AIAA-03-1116 (2003).

[mok01] Mok DP, Wall WA. “Partitioned analysis schemes for the transient interaction of incompressible flows and nonlinear flexible structures”. In: Wall WA, Bletzinger K-U, Schweizerhof K, editors. Trends in Computational Structural Mechanics. Barcelona: CIMNE, 2001.

[mon81] R.A. Gingold and J.J. Monaghan, “Kernel estimates as a basis for general particle methods in hydrodynamics”, Journal of Computational Physics, vol. 46, pp. 429-453, 1981.

[mon97] R.A. Gingold and J.J. Monaghan, “Smoothed particle hydrodynamics, theory and application to non-spherical stars”, Mon. Nat. Roy. Astr. Soc., 181, (1997), 375–389.

[nay92] B. Nayroles, G. Touzot and P. Villon. “Generalizing the finite element method: diffuse approximation and diffuse elements”, Computational Mechanics, vol. 10, pp. 307-318, 1992.

[ona98] E. Oñate. “Derivation of stabilized equations for advective-diffusive transport and fluid flow problems”. Comput. Methods Appl. Mech. Engrg.,1998, 151:1-2, 233--267

[ona00] E. Oñate. “A stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation”. Comp. Meth. Appl. Mech. Engng. ,2000, 182:1-2, 355-370.

[ona02] E. Oñate, “Possibilities of finite calculus in computational mechanics”. (2002) Submitted to Int. J. Num. Meth. Engng.

[ona04] E. Oñate, S.R. Idelsohn, F. Del Pin and R. Aubry. “ The Particle Finite Element Method: an overview”. In press in International Journal of Computational Methods. (2004)

[pip95] Piperno S, Farhat C, Larrouturou B. ”Partitioned procedures for the transient solution of coupled aeroelastic problems”. Comp Meth Appl Mech Eng 1995;124:79-112.

[rad98] R. Radovitzky, M. Ortiz “Lagrangian finite element analysis of a Newtonian flows”. Int. J. Numer. Engng. 43, 607-619 (1998).

[ram87] B. Ramaswamy and M. Kawahara, “Lagrangian finite element analysis of Newtonian fluid flows”, Int. J. Num. Meth. Fluids, vol. 7, pp. 953-984, 1987.

[rug00] Rugonyi S, Bathe KJ. “On the analysis of fully-coupled fluid flows with structural interactions - a Coupling and Condensation Procedure”. Int. J of Comp Civil and Struct Engineering 2000; 1:29-41.

[rug01] Rugonyi S, Bathe KJ. “On finite element analysis of fluid flows fully coupled with structural interactions”. Computer Modeling and Simulation in Engineering (CMES) 2001; 2:195-212.

[Sou00] M. Souli, A. Ouahsine and L. Lewin, “Arbitrary Lagrangian Eulerian formulation for Fluid-Structure Interaction Problems”. Comp. Meth. In Applied Mech. and Eng. Vol. 190, pp 659-675 (2000).

[suk98] N. Sukumar, B. Moran and T. Belytschko, “The natural element method in solid mechanics”, International Journal for Numerical Methods in Engineering, vol. 43, pp. 839-887, 1998.

[zha01] Zhang H, Bathe KJ. “Direct and iterative computing of fluid flows fully coupled with structures”, in Computational Fluid and Solid Mechanics (K.J. Bathe, ed.), Elsevier, 2001.