Navier–Stokes problems with random coefficients by the Weighted Least Squares Technique Stochastic Finite Volume Method

• Autorzy: Kamiński M. , Ossowski R. L.

Identyfikatory

DOI

10.1016/j.acme.2013.12.004

• Języki publikacji: EN

Abstrakty

EN

The main aim of this article is numerical solution to the Navier–Stokes equations for incompressible, non-turbulent and subsonic fluid flows with Gaussian physical random parameters. It is done with the use of the specially adopted Finite Volume Method extended towards probabilistic analysis by the generalized stochastic perturbation technique. The key feature of this approach is the weighted version of the Least Squares Method implemented symbolically in the system MAPLE to recover nodal polynomial response functions of the velocities, pressures and temperatures versus chosen input random variable(s). Such an implementation of the Stochastic Finite Volume Method is applied to model 3D flow problem in the statistically homogeneous fluid with uncertainty in its viscosity and, separately, coefficient of the heat conduction. Probabilistic central moments of up to the fourth order and the additional characteristics are determined and visualized for the cavity lid driven flow owing to the specially adopted graphical environment FEPlot. Further numerical extension of this technique is seen in an application of the Taylor–Newton–Gauss approximation technique, where polynomial approximation may be replaced with the exponential or hyperbolic ones.

Słowa kluczowe

EN

Stochastic Finite Volume Method; generalized stochastic perturbation technique; weighted least squares method; Navier-Stokes equations; symbolic computing

PL

równania Naviera-Stokesa; przepływ ciepła; analiza naprężeń

• Wydawca: Springer ; Wrocław University of Science and Technology
• Czasopismo: Archives of Civil and Mechanical Engineering
• Rocznik: 2014
• Tom: Vol. 14, no. 4
• Strony: 745--756
• Opis fizyczny: Bibliogr. 10 poz., rys., wykr.

Twórcy

autor

Kamiński M.

• Department of Structural Mechanics, Technical University of Łódź, Al. Politechniki 6, 90-924 Łódź, Poland

autor

Ossowski R. L.

• Department of Structural Mechanics, Technical University of Łódź, Al. Politechniki 6, 90-924 Łódź, Poland

Bibliografia

• [1] H.S. Carlsaw, J.C. Jaeger, Conduction of Heat in Solids, Oxford Sci. Pub., Clarendon Press, Oxford, 1986.
• [2] L. Cueto-Felgueroso, I. Colominas, X. Nogueira, M. Casteleiro, Finite volume solvers and Moving Least-Squares approximations for the compressible Navier-Stokes equationson unstructured grids, Computer Methods in Applied Mechanics and Engineering 196 (2007) 4712–4736.
• [3] I. Demirdzic, S. Muzaferija, Numerical method for coupled fluid flow, heat transfer and stress analysis using unstructured moving meshes with cells of arbitrary topology, Computer Methods in Applied Mechanics and Engineering 125 (1995) 235–255.
• [4] J. Durany, J. Pereira, F. Varas, A cell-vertex finite volume method for thermo-hydrodynamic problems in lubrication theory, Computer Methods in Applied Mechanics and Engineering 195 (2006) 5949–5961.
• [5] M. Kamiński, The Stochastic Perturbation Method for Computational Mechanics, Wiley, Chichester, 2013.
• [6] M. Kamiński, R.L. Ossowski, On application of the Stochastic Finite Volume Method in some Navier–Stokes problems, Computer Modeling in Engineering and Sciences 80 (1) (2011) 113–140.
• [7] M. Kamiński, G.F. Carey, Stochastic perturbation-based finite element approach to fluid flow problems, International Journal of Numerical Methods for Heat & Fluid Flow 15 (2005) 671–697.
• [8] M. Schäfer, Computational Engineering – Introduction to Numerical Methods, Springer-Verlag, Berlin, 2006.
• [9] http://vbn.aau.dk/en/persons/erik-lun(eacec6ff-lb29-4366- a9ee-35a1b28a95b5).html.
• [10] http://openfvm.sourceforge.net.