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Analysis and convergence of the MAC scheme.
II. Navier-Stokes equations


Authors: R. A. Nicolaides and X. Wu
Journal: Math. Comp. 65 (1996), 29-44
MSC (1991): Primary 76M25, 76D05, 65N12
MathSciNet review: 1320897
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Abstract: The MAC discretization scheme for the incompressible Navier-Stokes equations is interpreted as a covolume approximation to the equations. Using some results from earlier papers dealing with covolume error estimates for div-curl equation systems, and under certain conditions on the data and the solutions of the Navier-Stokes equations, we obtain first-order error estimates for both the vorticity and the pressure.


References [Enhancements On Off] (What's this?)

  • 1 N. Baba and H. Miyata, Numerical study of the three dimensional separating flow about obstacles with sharp corners, 11th Internat. Conf. Numer. Methods Fluid Dynamics (D. L. Dwoyer et al., eds.), Lecture Notes in Phys., vol. 323 Springer-Verlag, Berlin and New York, 1989 pp. 126--131.
  • 2 Vivette Girault and Pierre-Arnaud Raviart, Finite element methods for Navier-Stokes equations, Springer Series in Computational Mathematics, vol. 5, Springer-Verlag, Berlin, 1986. Theory and algorithms. MR 851383
  • 3 R. A. Nicolaides, Flow discretization by complementary volume techniques, AIAA Paper 89-1978, Proc. 9th AIAA meeting, Buffalo, New York, June, 1989.
  • 4 R. A. Nicolaides, Analysis and convergence of the MAC scheme. I. The linear problem, SIAM J. Numer. Anal. 29 (1992), no. 6, 1579–1591. MR 1191137, 10.1137/0729091
  • 5 R. A. Nicolaides, Direct discretization of planar div-curl problems, SIAM J. Numer. Anal. 29 (1992), no. 1, 32–56. MR 1149083, 10.1137/0729003
  • 6 R. A. Nicolaides and X. Wu, Numerical solution of the Hamel problem by a covolume method, Advances in Computational Fluid Dynamics (W. G. Habashi and M. Hafez,eds.), Gordon and Breach, 1995.
  • 7 T. A. Porsching, Error estimates for MAC-like approximations to the linear Navier-Stokes equations, Numer. Math. 29 (1977/78), no. 3, 291–306. MR 0471622

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Additional Information

R. A. Nicolaides
Affiliation: Department of Mathematics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213

X. Wu
Affiliation: Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong
Address at time of publication: Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong
Email: xwu@hkbu.edu.hk

DOI: https://doi.org/10.1090/S0025-5718-96-00665-5
Keywords: Covolume, MAC, Navier-Stokes
Received by editor(s): October 25, 1991
Received by editor(s) in revised form: December 2, 1993
Additional Notes: This work was supported by the United States Air Force under grant AFOSR 90-0359
Article copyright: © Copyright 1996 American Mathematical Society