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Solution of Strongly Coupled Multiphysics Problems Using Space-Time Separated Representations—Application to Thermoviscoelasticity

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Abstract

The space-time separated representation method (Ladevèze, C. R. Acad. Sci. Paris 309(II):1095–1099, 1989; Ammar et al., J. Non-Newton. Fluid Mech. 144:98–121, 2007) is here extended to solve strongly coupled multiphysics problems. The feasibility of the method for dealing with strongly coupled multiphysics problems with different characteristic times is here discussed and a new strategy to solve the nonlinear system for the basis enrichment is proposed. The method is validated in the case of a strongly coupled thermoviscoelastic model.

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References

  1. Ladevèze P (1989) The large time increment method for the analysis of structures with non-linear behaviour described by internal variables. C R Acad Sci Paris 309(II):1095–1099 (in French)

    MATH  Google Scholar 

  2. Ammar A, Mokdad B, Chinesta F, Keunings R (2007) A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids. Part II: Transient simulation using space-time separated representations. J Non-Newton Fluid Mech 144:98–121

    Article  MATH  Google Scholar 

  3. Rambert G, Grandidier JC (2005) An approach to the coupled behaviour of polymers subjected to a thermo-mechanical loading in a gaseous environment. Eur J Mech A Solids 24:151–168

    Article  MATH  Google Scholar 

  4. Felippa CA, Park KC, Farhat C (2001) Partitioned analysis of coupled mechanical systems. Comput Methods Appl Mech Eng 190:3247–3270

    Article  MATH  Google Scholar 

  5. Dureisseix D, Bavestrello H (2006) Information transfer between incompatible finite element meshes: Application to coupled thermo-viscoelasticity. Comput Methods Appl Mech Eng 195:6523–6541

    Article  MATH  Google Scholar 

  6. Combescure A, Gravouil A (2002) A numerical scheme to couple subdomains with different time-steps for predominantly linear transient analysis. Comput Methods Appl Mech Eng 191:1129–1157

    Article  MATH  Google Scholar 

  7. Idesman A, Niekamp R, Stein E (2000) Continuous and discontinuous Galerkin methods with finite elements in space and time for parallel computing of viscoelastic deformation. Comput Methods Appl Mech Eng 190:1049–1063

    Article  MATH  Google Scholar 

  8. Ladevèze P (1985) On algorithm family in structural mechanics. C R Acad Sci Paris 300(II):41–44 (in French)

    MATH  Google Scholar 

  9. Ladevèze P (1999) Nonlinear computational structural mechanics—new approaches and non-incremental methods of calculation. Springer, New York

    MATH  Google Scholar 

  10. Néron D, Dureisseix D (2008) A computational strategy for poroelastic problems with a interface between coupled physics. Int J Numer Methods Eng 73(6):783–804

    Article  MATH  Google Scholar 

  11. Néron D, Dureisseix D (2008) A computational strategy for thermo-poroelastic structures with a time-space interface coupling. Int J Numer Methods Eng 75:1053–1084

    Article  MATH  Google Scholar 

  12. Ladevèze P, Passieux JC, Néron D (2009) The LATIN multiscale computational method and the proper generalized decomposition. Comput Methods Appl Mech Eng. doi:10.1016/j.cma.2009.06.023

    Google Scholar 

  13. Chatterjee A (2000) An introduction to the proper orthogonal decomposition. Curr Sci 78(7):808–817

    Google Scholar 

  14. Nouy A, Ladevèze P (2003) On a multiscale computational strategy with time and space homogenization for structural mechanics. Comput Methods Appl Mech Eng 192:3061–3087

    Article  MATH  Google Scholar 

  15. Nouy A (2007) A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations. Comput Methods Appl Mech Eng 196:4521–4537

    Article  MATH  MathSciNet  Google Scholar 

  16. Ammar A, Mokdad B, Chinesta F, Keunings R (2006) A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. J Non-Newton Fluid Mech 139:153–176

    Article  MATH  Google Scholar 

  17. Cognard JY, Ladeveze P, Talbot P (1999) A large time increment approach for thermo-mechanical problems. Adv Eng Softw 30:583–593

    Article  Google Scholar 

  18. Prulière E, Férec J, Chinesta F, Ammar A (2010) Int J Mater Form (to appear)

  19. Cochelin B, Damil N, Potier-Ferry M (1994) Eur J Finite Elem 3:281–297

    MATH  MathSciNet  Google Scholar 

  20. Gonzales D, Ammar A, Chinesta F, Cueto E (2009) Recent advances on the use of separated representations. Int J Numer Methods Eng. doi:10.1002/nme.2710

    Google Scholar 

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Authors and Affiliations

  1. Laboratoire de Mécanique et Physique des Matériaux, ENSMA, CNRS (UMR 6617), Téléport 2, 1 avenue Clément Ader, BP 40109, 86961, Futuroscope Cedex, France

    M. Beringhier, M. Gueguen & J. C. Grandidier

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  1. M. Beringhier
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  2. M. Gueguen
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  3. J. C. Grandidier
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Correspondence to M. Beringhier.

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Beringhier, M., Gueguen, M. & Grandidier, J.C. Solution of Strongly Coupled Multiphysics Problems Using Space-Time Separated Representations—Application to Thermoviscoelasticity. Arch Computat Methods Eng 17, 393–401 (2010). https://doi.org/10.1007/s11831-010-9050-5

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  • DOI: https://doi.org/10.1007/s11831-010-9050-5

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