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Projection method III: Spatial discretization on the staggered grid
Author(s):
Weinan
E;
Jian-Guo
Liu.
Journal:
Math. Comp.
71
(2002),
27-47.
MSC (2000):
Primary 65M06, 76M20
Posted:
May 14, 2001
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Abstract:
In E & Liu (SIAM J Numer. Anal., 1995), we studied convergence and the structure of the error for several projection methods when the spatial variable was kept continuous (we call this the semi-discrete case). In this paper, we address similar questions for the fully discrete case when the spatial variables are discretized using a staggered grid. We prove that the numerical solution in velocity has full accuracy up to the boundary, despite the fact that there are numerical boundary layers present in the semi-discrete solutions.
References:
-
- 1.
- J.B. Bell, P. Colella, and H.M. Glaz, A second-order projection method for the incompressible Navier Stokes equations, J. Comput. Phys. 85 (1989), 257-283. MR 90i:76002
- 2.
- A.J. Chorin, Numerical solution of the Navier-Stokes equations, Math. Comp. 22 (1968), 745-762. MR 39:3723
- 3.
- Weinan E and J.-G. Liu, Projection method I: convergence and numerical boundary layers, SIAM J. Numer. Anal. 32 (1995), 1017-1057; Projection method II: Godunov-Ryabenki analysis, SIAM J. Numer. Anal. 33 (1996), 1597-1621. MR 96e:65061; MR 97i:76078
- 4.
- Weinan E and J.-G. Liu, Projection method for viscous incompressible flows, in ``Numerical Methods in Applied Sciences'', edited by W. Cai and C.-W. Shu, Science Press New York, Ltd, New York, (1996), 78-96
- 5.
- Weinan E and J.-G. Liu, Gauge method for viscous incompressible flows, preprint, (1996)
- 6.
- M. Fortin, R. Peyret, and R. Temam, Résolution numérique des équations de Navier-Stokes pour un fluide incompressible, J. Mecanique, 10 (1971) 357-390. MR 54:9343
- 7.
- F.H. Harlow and J.E. Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids, 8 (1965) 2182-2189.
- 8.
- J. Heywood and R. Rannacher, Finite element approximation of the nonstationary Navier-Stokes problem, part III. Smoothing property and higher order error estimates for spatial discretization, SIAM J. Numer. Anal., 25, (1988) 490-512. MR 89k:65114
- 9.
- J. Kim and P. Moin, Application of a fractional-step method to incompressible Navier-Stokes equations, J. Comp. Phys. 59 (1985), 308-323. MR 87a:76046
- 10.
- J. Shen, On error estimates of projection methods for Navier-Stokes equations: first order schemes, SIAM J. Numer. Anal. 29 (1992), 57-77. MR 92m:35213
- 11.
- J. Shen, On error estimates of some higher order projection and penalty-projection methods for Navier-Stokes equations, Numer. Math. 62 (1992), 49-73. MR 93a:35122
- 12.
- R. Temam, Sur l'approximation de la solution des equations de Navier-Stokes par la méthode des fractionnarires II, Arch. Rational Mech. Anal. 33 (1969), 377-385. MR 39:5968
- 13.
- J. van Kan, A second-order accurate pressure-correction scheme for viscous incompressible flow, SIAM J. Sci. Stat. Comp. 7 (1986), 870-891. MR 87h:76008
- 14.
- C. Wang and J.-G. Liu, Convergence of gauge method for incompressible flow, Math. Comp., 69 (2000), 1385-1407. MR 20001a:65103
- 15.
- B.R. Wetton, Ph.D Dissertation, New York University, 1991.
- 16.
- B.R. Wetton, Error analysis for Chorin's original fully discrete projection method and regularizations in space and time, SIAM J. Numer. Anal. 34 (1997), 1683-1697. MR 99c:65161
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Additional Information:
Weinan
E
Affiliation:
Courant Institute of Mathematical Sciences, New York, New York 10012
Email:
weinan@cims.nyu.edu
Jian-Guo
Liu
Affiliation:
Institute for Physical Science and Technology and Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email:
jliu@math.umd.edu
DOI:
10.1090/S0025-5718-01-01313-8
PII:
S 0025-5718(01)01313-8
Keywords:
Viscous incompressible flows,
projection method,
numerical boundary layer,
finite difference,
convergence
Received by editor(s):
May 19, 1997
Received by editor(s) in revised form:
March 1, 2000
Posted:
May 14, 2001
Copyright of article:
Copyright
2001,
American Mathematical Society
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