Numerical study of the Yosida method applied to viscous incompressible internal flows with open boundary conditions

• Autorzy: Szumbarski J.
• Języki publikacji: EN

Abstrakty

EN

The Yosida methods for incompressible viscous flows are investigated numerically in the aspect of local and global errors of volume conservation. Unsteady Stokes and Navier–Stokes flows past an obstacle inserted into 2D channel are used as the test cases. Open boundary conditions are imposed at the channel’s inlet and outlet. The results obtained by the Yosida-based Spectral Element Method (SEM) solvers are compared to the results obtained by the SEM solver using exact factorization of the Uzawa system. Analysis of parametric variation of the velocity divergence and the flow rate errors is presented. It is concluded that switching to higher-order Uzawa methods reduces substantially volume conservation errors and removes numerical artifacts observed at the channel’s inlet when the basic Yosida method is used.

Słowa kluczowe

EN

Navier-Stokes equations; Yosida method; spectral element method; open boundary conditions

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2016
• Tom: Vol. 68, nr 2
• Strony: 133--160
• Opis fizyczny: Bibliogr. 15 poz., rys.

Twórcy

autor

Szumbarski J.

• Institute of Aeronautics and Applied Mechanics Warsaw University of Technology 24 Nowowiejska St. 00-655 Warszawa, Poland

Bibliografia

• 1. J.-L. Guermond, P. Minev, J. Shen, An overview of projection methods for incompressible flows, Computer Methods in Applied Mechanics and Engineering, 195, 6011–6045, 2006.
• 2. J.-L. Guermond, Overview of fractional step techniques for the incompressible Navier–Stokes equations, CEMRACS’12 talk. CIRM, Marseille, July 16–20, 2012.
• 3. H. Johnston, J.-G. Liu, Accurate, stable and efficient Navier–Stokes solvers based on explicit treatment of the pressure term, Journal of Computational Physics, 199, 221–259, 2004.
• 4. J.-G. Liu, L. Liu, R.L. Pego, Stable and accurate pressure approximation for unsteady incompressible viscous flow, Journal of Computational Physics, 229, 3428–3453, 2010.
• 5. J.B. Perot, An analysis of the fractional step method, Journal of Computational Physics, 108, 51–58, 1993.
• 6. A. Quarteroni, F. Saleri, A. Veneziani, Analysis of the Yosida method for the incompressible Navier–Stokes equations, J. Math. Pures Appl., 78, 9, 473–503, 1999.
• 7. A. Quarteroni, F. Saleri, A. Veneziani, Factorization methods for the numerical approximation of Navier–Stokes equations, Computer Methods in Applied Mechanics and Engineering, 188, 505–526, 2000.
• 8. P. Gervasio, F. Saleri, A. Veneziani, Algebraic fractional-step schemes with spectral methods for the incompressible Navier–Stokes equations, Journal of Computational Physics, 214, 347–365, 2006.
• 9. A. Veneziani, U. Villa, ALADINS: An ALgebraic splitting time ADaptive solver for the Incompressible Navier–Stokes equations, Journal of Computational Physics, 238, 359–375, 2013.
• 10. Y. Maday, A.T. Patera, E.M. Ronquist, An operator-integration-factor splitting method for time-dependent problems: application to incompressible fluid flow, Journal of Scientific Computing, 5, 263–292, 1990.
• 11. M.O. Deville, P.F. Fisher, E.H. Mund, High-Order Methods for Incompressible Fluid Flow, Cambridge University Press, 2002.
• 12. G.E. Karniadakis, S. Sherwin, Spectral/hp Element Methods for CFD, 2nd ed., Oxford University Press, 2005.
• 13. W. Couzy, M.O. Deville, Spectral-element for the Uzawa pressure operator applied to incompressible flows, J. Scientific Computing, 9, 2, 107–122, 1994.
• 14. J. Szumbarski, P. Olszewski, K. Wawruch, Z. Małota, Computations of an unsteady viscous flow in a three dimensional system of ducts. Part 2: Implementation of spectral element method and sample results, Journal of Theoretical and Applied Mechanics, 42, 4, 869–903, 2004.
• 15. P.F. Fisher, Projection techniques for iterative solution of Ax = b with successive right hand sides, Computer Methods in Applied Mechanics and Engineering, 163, 193–204, 1998.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.