Computations of an unsteady viscous flow in a three dimensional system of ducts. Part I: Formulation of the mathematical problem and numerical method

• Autorzy: Szumbarski J. , Olszewski P. , Styczek A. , Rokicki J.
• Języki publikacji: EN

Abstrakty

EN

Numerical modeling of an unsteady flow of a viscous incompressible fluid inside a branched pipe system is considered. The mathematical formulation is given with special emphasis on inlet/outlet conditions. The equivalent weak form of the initial-boundary value problem is presented. The numerical method based on solutions to particular Stokes problems is proposed and described in some details. Finally, some general remarks about the implementation issues within the framework of the spectral element discretization are made.

PL

W pracy rozważono problem numerycznego wyznaczania nieustalonego przepływu cieczy lepkiej w układzie trójwymiarowych przewodów. Podano sformułowanie wariacyjne zagadnienia uwzględniające uogólnione warunki brzegowe na wlotach/wylotach do obszaru ruchu. Opisano metodę obliczeniową, opartą na zastosowaniu wskaźników Lagrange'a i superpozycji szczególnych problemów Stokesa w każdym kroku czasowym.

Słowa kluczowe

EN

Navier-Stokes equations; defective boundary conditions; spectral element method

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2004
• Tom: Vol. 42 nr 1
• Strony: 21--39
• Opis fizyczny: Bibliogr 10 poz.

Twórcy

autor

Szumbarski J.

• Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology

autor

Olszewski P.

• Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology

autor

Styczek A.

• Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology

autor

Rokicki J.

• Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology

Bibliografia

• 1. Canuto C., Hussaini M.Y., Quarteroni A., Zang T.A., 1988, Spectral Methods in Fluid Dynamics, Springer Verlag, Berlin/New York
• 2. Couzy W., 1995, Spectral element discretization of the unsteady Navier-Stokes equations and its iterative solution on parallel computers, Ph.D. Thesis, Ecole Polytechnique Federale De Lausanne, No 1380
• 3. Couzy W., Deville M.O., 1994, Spectral-element preconditioners for the Uzawa pressure operator applied to incompressible flows. Journal of Scientific Computing, 9, 2, 107-122
• 4. Formaggia L., Gerbeau J.F., Nobile F., Quarteroni A., 2000, Numerical treatment of defective boundary conditions for the Navier-Stokes equations, EPFL, Departement de Mathematiques, Preprint 20.2000
• 5. Heywood J.G., Ranacher R., Turek S., 1996, Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations, International Journal for Numerical Methods in Fluids, 22, 325-352
• 6. Karniadakis G., Israeli M., Orszag S.A., 1991, High-order splitting methods for the incompressible Navier-Stokes equations, J. Comp. Phys., 97, 414- 443
• 7. Karniadakis G., Sherwin S.J., 1999, Spectral/hp Element Methods for CFD, Oxford University Press
• 8. Maday Y., Meiron D., Patera A., Ronquist E.M., 1993, Analysis of iterative methods for the steady and unsteady Stokes problem: application to spectral element discretizations, SIAM J. Sci. Comput., 14, 2, 310-337
• 9. Maday Y., Patera A.T., Ronquist E.M., 1990, An operator-integrationfactor splitting method for time-dependent problems: application to incompressible fluid flow, J. Sci. Comput., 5, 263-292 Computations of an unsteady viscous flow... 39
• 10. Quarteroni A., Saleri F., Veneziani A., 1999, Analysis of the Yosida method for the incompressible Navier-Stokes equations, Journal de Mathematiques Pures et Appliques, 78, 473-503