A mass conserving multi-domain spectral collocation method for the stokes problem

Computers and Fluids

Volumn 26, Issue 8, 1997, Pages 825-840

  Phillips, Timothy N ^a   Owens, Robert G ^b  

^a ABERYSTWYTH UNIVERSITY   (United Kingdom)

^b EDINBURGH NAPIER UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; MATHEMATICAL MODELS; VELOCITY;

MULTIDOMAIN SPECTRAL COLLOCATION METHOD; STOKES PROBLEM;

COMPUTATIONAL FLUID DYNAMICS;

INCOMPRESSIBLE FLUID; NAVIER-STOKES EQUATIONS; REYNOLDS NUMBER;

DIFFERENTIAL EQUATIONS; FLUID FLOW; INCOMPRESSIBLE; NAVIER STOKES EQUATIONS; PARTIAL;

EID: 0031277683     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7930(97)00027-3     Document Type: Article

References (19)

1. Korczak, K. Z. and Patera, A. T., Isoparametric spectral element method for solution of the Navier-Stokes equations in complex geometry. Journal of Computational Physics, 1986, 62, 361-382.
2. Phillips, T. N. and Roberts, G. W., The treatment of spurious pressure modes in spectral incompressible flow calculations. Journal of Computational Physics, 1993, 105, 105-164.
3. Owens, R. G. and Phillips, T. N., Compatible pseudospectral approximations for incompressible flow in an undulating tube. Journal of Rheology, 1993, 37, 1181-1199.
4. Chorin, A. J., Numerical solution of the Navier-Stokes equations. Mathematics of Computation, 1968, 22, 745-762.
5. Temam, R., Une methode d'approximation de la solution des equations de Navier-Stokes. Bulletin of the Society for Mathematics (France), 1968, 96, 115-152.
6. Temam, R., Navier-Stokes Equations. Elsevier, Amsterdam, 1984.
7. Van Kan, J., A second-order accurate pressure-correction scheme for viscous incompressible flow. SIAM Journal of Scientific and Statistical Computing, 1986, 7, 870-891.
8. Bell, J. B., Colella, P. and Glaz, H. M., A 2nd-order projection method for the incompressible Navier-Stokes equations. Journal of Computational Physics, 1989, 85, 257-283.
9. Tau, E. Y., A second-order projection method for the incompressible Navier-Stokes equations in arbitrary domains. Journal of Computational Physics, 1994, 115, 147-152.
10. Jacobs, S. J., An accurate split step scheme for viscous incompressible fluid flow. Journal of Computational Physics, 1995, 119, 26-33.
11. Zhu, Journal of, The second-order projection method for the backward-facing step flow. Journal of Computational Physics, 1995, 117, 318-331.
12. Minion, M. L., A projection method for locally refined grids. Journal of Computational Physics, 1996, 127, 158-178.
13. Timmermans, L. J. P., Minev, P. D. and Vandevosse, F. N., An approximate projection scheme for incompressible-flow using spectral elements. International Journal of Numerical Methods in Fluids, 1996, 22, 673-688.
14. Almgren, A. S., Bell, J. B. and Szymczak, W. G., A numerical method for the incompressible Navier-Stokes equations based on an approximate projection. SIAM Journal of Scientific Computing, 1996, 17, 358-369.
15. 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. International Journal of Numerical Methods in Fluids, 1990, 11, 587-620.
16. Pilitsis, S. and Beris, A. N., Calculations of steady-state viscoelastic flow in an undulating tube. Journal of Non-Newtonian Fluid Mechanics, 1989, 31, 231-287.
17. Maday, Y., Patera, A. T. and Rønquist, E. M., A well-posed optimal spectral element approximation for the Stokes problem. Technical Report no. 87-48, ICASE, Hampton, VA, 1987.
18. Canuto, C., Hussaini, M. Y., Quarteroni, A. and Zang, T. A., Spectral Methods in Fluid Dynamics. Springer, Berlin, 1987.
19. Ku, H. C., Taylor, T. D. and Hirsh, R. S., Pseudospectral methods for solution of the incompressible Navier-Stokes equations. Computers and Fluids, 1987, 15, 195-214.