A second order splitting algorithm for thermally-driven flow problems

International Journal of Numerical Methods for Heat and Fluid Flow

Volumn 6, Issue 2, 1996, Pages 51-60

  Minev, P D ^a   Van De Vosse, F N ^a   Timmermans, L J P ^a   Van Steenhoven, A A ^a  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Differentially heated cavity; Operator splitting; Spectral element method; Thermally driven flows

Indexed keywords

APPROXIMATION THEORY; CAVITATION; FINITE ELEMENT METHOD; HEAT TREATMENT; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; ALGORITHMS; INTEGRATION; MATHEMATICAL OPERATORS; NUMERICAL METHODS; SPECTRUM ANALYSIS;

DIFFERENTIALY-HEATED CAVITY; SPLITTING TECHNIQUES; THERMALLY-DRIVEN FLOWS; BOUSSINESQ APPROXIMATION; DIFFERENTIALLY HEATED CAVITY; OPERATOR SPLITTING; RAYLEIGH NUMBERS; SPECTRAL ELEMENT METHOD; THERMALLY DRIVEN FLOWS;

FLOW OF FLUIDS; HEAT CONVECTION;

ALGORITHM; FLOW ANALYSIS; NAVIER-STOKES EQUATIONS; THERMAL EFFECTS;

EID: 0030094214     PISSN: 09615539     EISSN: None     Source Type: Journal    
DOI: 10.1108/09615539610113091     Document Type: Article

References (19)

1. Patera, A. T. A spectral element method for fluid dynamics: laminar flow in a channel expansion, J. Comp. Phys., 54, 468-488 (1984)
2. Timmermans, L. J. P. and van de Vosse, F. N. Spectral methods for advection-diffusion problems, Notes on numerical fluid mechanics: numerical methods for advection-diffusion problems (eds. C. Vreugdenhil and B. Koren), Vieweg, Braunschweig, 171-194 (1993)
3. Camuto, C., Hussaini, M. Y., Quarteroni, A. and Zang, T. A. Spectral methods in fluid dynamics, Springer-Verlag, New York, Berlin (1988)
4. Maday, Y. and Patera, A. T. Spectral element methods for the incompressible Navier-Stokes equations, State-of-the-art surveys on computational mechanics (ed. A. Noor), ASME, 71-143 (1989)
5. Karniadakis, G. E., Israeli, M. and Orszag, S. A. High-order methods for the incompressible Navier-Stokes equations, J. Comp. Phys., 97, 414-443 (1991)
6. Gresho, P. M. On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part 1: Theory', Int. J. Num. Meth. Fluids, 11, 587-620 (1990)
7. Timmermans, L. J. P., Minev, P. D. and van de Vosse, F. N. An approximate projection scheme for incompressible flow using spectral elements, in print Int. J. Num. Meth. Fluids
8. Orszag, S. A., Israeli, M. and Deville, M. O. Boundary conditions for incompressible flows, J. Sci. Comp., 1, 75-111 (1986)
9. de Vahl Davis, G. and Jones, I. P. Natural convection in a square cavity - a comparison exercise. Int. J. Num. Meth. Fluids, 3, 227-248 (1983)
10. de Vahl Davis, G. Natural convection of air in a square cavity: a benchmark numerical solution, Int. J. Num. Meth. Fluids. 3, 249-264 (1983)
11. Paolucci, S. and Chenowith, D. R. Transition to chaos in a differentially heated vertical cavity, J. Fluid Mech., 201, 379-410 (1989)
12. Timmermans, L. J. P., van de Vosse, F. N. and Minev, P. D. Taylor-Galerkin based spectral element methods for convection-diffusion problems, Int. J. Num. Meth. Fluids, 18, 853-870 (1994)
13. Maday, Y., Patera, A. T. and Ronquist, E. M. An operator-integration-factor splitting method for time-dependent problems: Application to incompressible fluid flow, J. Sci. Comp., 5, 263-291 (1990)
14. Timmermans, L. J. P. Analysis of spectral element methods with application to incompressible flow, PhD Thesis, Eindhoven University of Technology (1994)
15. Hawken, D. M., Tammadon-Jahromi, H. R., Townsend, P. and Webster, M. F. A Raylor-Galerkin based algorithm for viscous incompressible flow, Int. J. Num. Meth. Fluids, 10, 327-351 (1990)
16. Markatos, N. C. and Pericleous, K. A. Laminar and turbulent natural convection in an enclosed cavity, Int. J. Heat Mass Transfer, 27, 755-775 (1984)
17. Lankhorst, A. M. Laminar and turbulent natural convection in cavities, PhD thesis, Delft Univeristy of Technology (1991)
18. Gresho, P. M., Gartling, D. K., Torczynski, J. R., Cliffe, K. A., Winters, K. H., Garratt, T. J. Spence, A. and Goodrich, J. W. Is the steady viscous 2-d flow over a backward-facing step at Re = 800 stable?, Int. J. Num. Meth. Fluids, 17, 501-541 (1993)
19. Timmermans, L. J. P. and van de Vosse, F. N. Finite element preconditioned spectral element methods for convection-diffusion problems, Topics in applied mechanics: integration of theory and application in applied mechanics (eds. J. F. Dijksman and F. T. M. Nieuwstadt), Kluwer Academic Publishers, Dordrecht, Boston, London, 363-370 (1993)