zbMATH — the first resource for mathematics

Analysis and convergence of the MAC scheme. II: Navier-Stokes equations. (English) Zbl 0852.76066
Summary: 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 (in particular, part I of the present work [the first author, SIAM J. Numer. Anal. 29, No. 6, 1579-1591 (1992; Zbl 0764.76051)]) 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.

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D05 Navier-Stokes equations for incompressible viscous fluids
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
Full Text: DOI
[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 , 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. · Zbl 0585.65077
[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. · Zbl 0764.76051 · doi:10.1137/0729091 · doi.org
[5] R. A. Nicolaides, Direct discretization of planar div-curl problems, SIAM J. Numer. Anal. 29 (1992), no. 1, 32 – 56. · Zbl 0745.65063 · doi:10.1137/0729003 · doi.org
[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. · Zbl 0352.65057 · doi:10.1007/BF01389214 · doi.org
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.