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This article is devoted to the mathematical formulation and computational implementation of the Stochastic Finite Volume Method for 1 and 2D fluid and heat flow problems. It is based on the stochastic generalized perturbation technique, which allows for a determination of the probabilistic moments of the state variables or functions for 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.
Czasopismo
Rocznik
Tom
Strony
151--173
Opis fizyczny
Bibliogr. 10 poz.
Twórcy
autor
autor
- Department of Steel Structures, Technical University of Łódź, Al Politechniki 6, 90-924 Łódź, Poland
Bibliografia
- [1] Bijelonja, I., Demirdzic, I. and Muzaferija, S.: A finite volume method for incompressible linear elasticity, Computer Methods in Applied Mechanics and Engineering, 195, 6378-6390, 2006.
- [2] Carlsaw, H.S. and Jaeger, J.C.: Conduction of Heat in Solids, Oxford Sci. Pub., Clarendon Press, Oxford, 1986.
- [3] Cueto-Felgueroso, L., Colominas, I., Nogueira, X. and Casteleiro, M.: Finite volume solvers and Moving Least-Squares approximations for the compressible Navier-Stokes equations on unstructured grids, Computer Methods in Applied Mechanics and Engineering, 196, 4712-4736, 2007.
- [4] Durany, J., Pereira, J. and Varas, F.: A cell-vertex finite volume method for thermohydrodynamic problems in lubrication theory, Computer Methods in Applied Mechanics and Engineering, 195, 5949-5961, 2006.
- [5] Ghanem, R.G. and Spanos, P.D.: Stochastic Finite Elements. A Spectral Approach, Dover Publ. Inc., New York, 2002.
- [6] Kamiński, M.: On generalized stochastic perturbation-based finite element method, Communications in Numerical Methods in Engineering, 22, 23-31, 2006.
- [7] Kamiński, M. and Ossowski, R.: An introduction to the perturbation-based stochastic finite volume method for plane heat conduction problems, Proceedings of the 12th WSEAS international conference on Computers, p. 1032-1038,23-25, Heraklion, Greece, 2008.
- [8] Kleiber, M. and Hien, T. D.: The Stochastic Finite Element Method, Wiley, Chichester , 1992.
- [9] Schafer, M.: Computational Engineering - Introduction to Numerical Methods, Springer Verlag, Berlin, 2006.
- [10] Xiu, D.: Efficient collocational approach for parametric uncertainty analysis, Comm. Comput. Phys., 2, 2, 293-309, 2007.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD9-0023-0009