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2009 | Vol. 50, no 4 | 297-315
Tytuł artykułu

The stochastic perturbation - based finite volume method for the flow problems

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This article is devoted to the mathematical formulation and computational implementation of the Stochastic Finite Volume Method for heat and fluid flow problems. It is based on the stochastic generalized perturbation technique, which allows for determination of the probabilistic moments of the state variables or functions of the general stationary transport equations with random parameters. Both numerical case studies contain a comparison of the stochastic perturbation approach of different orders, their relations to the Monte-Carlo simulation results as well as the effect of the perturbation parameter and input coefficient of variation on the output state functions.
Wydawca

Rocznik
Strony
297-315
Opis fizyczny
Bibliogr. 23 poz., wykr.
Twórcy
  • Technical University of Łódź, Faculty of Civil Engineering, Architecture and Environmental Engineering, Al. Politechniki 6, 90-924 Łódź, Poland, Marcin.Kaminski@p.lodz.pl
Bibliografia
  • 1. R. G. GHANEM, P. D. SPANOS, Stochastic Finite Elements. A Spectral Approach, Dover Publ. Inc., New York 2002.
  • 2. D. Xiu, Efficient collocational approach for parametric uncertainty analysis, Comm. Comput. Phys., 2, 293-309, 2007.
  • 3. M. KAMIŃ SKI, R. L. OSSOWSKI, The Stochastic perturbation based finite volume method for 1 &2D fluid and heat flow problems, Int. J. Mech. & Mech. Engrg., 14, 151-173, 2010.
  • 4. M. KLEIBER, T. D. HIEN, The Stochastic Finite Element Method, Wiley, Chichester 1992.
  • 5. I. BIJELONJA, I. DEMIRDZIC, S. MUZAFERIJA, A finite volume method for incompressible linear elasticity, Comput. Meth. Appl. Mech. Engrg., 195, 6378-6390, 2006.
  • 6. H. S. CARLSAW, J. C. JAEGER, Conduction of Heat in Solids, Oxford Sci. Pub., Clarendon Press, Oxford 1986.
  • 7. L. CUETO-FELGUEROSO, I. COLOMINAS, X. NOGUEIRA, M. CASTELEIRO, Finite volume solvers and Moving Least-Squares approximations for the compressible Navier-Stokes equations on unstructured grids, Comput. Meth. Appl. Mech. Engrg., 196, 4712-4736, 2007.
  • 8. J. DURANY, J. PEREIRA, F. VARAS, A cell-vertex finite volume method for thermohydrodynamic problems in lubrication theory, Comput. Meth. Appl. Mech. Engrg., 195, 5949-5961, 2006.
  • 9. I. DEMIRDZIC, D. MARTINOVIC. Finite volume method for thermo-elasto-plastic stress analysis, Comput. Methods Appl. Mech. Engrg., 109, 331-349, 1993.
  • 10. I. DEMIRDZIC, S. MUZAFERIJA, Finite volume method for stress analysis in complex domains, Int. J. Numer. Methods Engrg., 37, 3751-3766, 1994.
  • 11. E. ONATE, M. CERVERA, O. C. ZIENKIEWICZ, A finite volume format for structural mechanics, Int. J. Numer. Methods Engrg., 37, 181-201, 1994.
  • 12. C. BAILEY, M. CROSS, A finite volume procedure to solve elastic solid mechanics problems in three dimensions on an unstructured mesh, Int. J. Numer. Methods Engrg., 38, 1757-1776, 1995.
  • 13. M. A. WHEEL, A geometrically versatile finite volume formulation for plane elastostatic stress analysis, J. Strain Anal., 31. 2, 1996.
  • 14. M. A. WHEEL, A finite volume method for analysing the bending deformation of thick and thin plates, Comput. Methods Appl. Mech. Engrg., 147, 199-208, 1997.
  • 15. A. IVANKOVIC, I. DEMIRDZIC, J.G. WILLIAMS, P. S. LEEVER, Application finite volume method to the analysis of dynamic fracture problems, Int. J. Fract., 66, 4357-4371, 1994.
  • 16. G. A. TAYLOR, C. BAILEY, M. CROSS, Solution of the elastic/visco-plastic constitutive equations: a finite volume approach, Appl. Math. Model., 19, 743-760, 1995.
  • 17. N. A. FALLAH, C, BAILEY, M. CROSS, G. A. TAYLOR, Comparison of finite element and finite volume methods application in geometrically nonlinear stress analysis, Appl. Math. Model., 24, 439-455, 2000.
  • 18. N. A. FALLAH, C. BAILEY, M. CROSS, Finite volume method for stress analysis, [in:] Proceedings of the ACME’99. The seventh Annual Conference of the Association for Computational Mechanics in Engineering, pp. 135-138, Durham, UK, 1999.
  • 19. K, MANEERATANA, A. IVANKOVIC, Finite volume method for structural applications involving material and geometrical nonlinearities, [in:] Proceedings of the ECCM’99 European Conference on Computational Mechanics, 1999, Munich, Germany.
  • 20. I. DEMIRDZIC, S. MUZAFERUA, Numerical method for coupled fluid flow, heat transfer and stress analysis using unstructured moving meshes with cells of arbitrary topology, Comput. Methods Appl. Mech. Engrg., 125, 235-255, 1995.
  • 21. P. WENKE, M. A. WHEEL, A Finite Volume Method for predicting finite strain deformations in incompressible materials, [in:] Proceedings of the ECCM’99 European Conference on Computational Mechanics, 1999, Munich, Germany.
  • 22. M. KAMIŃSKI, Potential problems with random parameters by the generalized perturbation-based stochastic finite element method, Comput. & Struct., 88, 437-445, 2010.
  • 23. M. SCHAFER, Computational Engineering - Introduction to Numerical Methods, Springer Verlag, Berlin 2006.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0064-0001
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