×
Beale, J. Thomas; Majda, Andrew

Rates of convergence for viscous splitting of the Navier-Stokes equations. (English) Zbl 0518.76027

Math. Comput. 37, 243-259 (1981).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0518.76027

Cited in 54 Documents

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
76M99 Basic methods in fluid mechanics

Keywords:

viscous splitting algorithms; high Reynolds number; error estimates uniform in viscosity; two- or three-dimensional; long-time estimate
PDFBibTeX XMLCite
\textit{J. T. Beale} and \textit{A. Majda}, Math. Comput. 37, 243--259 (1981; Zbl 0518.76027)
Full Text: DOI

References:

[1] G. K. Batchelor and H. K. Moffatt , 25th anniversary issue: editorial reflections on the development of fluid mechanics, Cambridge University Press, Cambridge-New York, 1981. J. Fluid Mech. 106 (1981).
[2] Alexandre Joel Chorin, Numerical study of slightly viscous flow, J. Fluid Mech. 57 (1973), no. 4, 785 – 796. · doi:10.1017/S0022112073002016
[3] Alexandre J. Chorin, Marjorie F. McCracken, Thomas J. R. Hughes, and Jerrold E. Marsden, Product formulas and numerical algorithms, Comm. Pure Appl. Math. 31 (1978), no. 2, 205 – 256. · Zbl 0358.65082 · doi:10.1002/cpa.3160310205
[4] David G. Ebin and Jerrold Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid., Ann. of Math. (2) 92 (1970), 102 – 163. · Zbl 0211.57401 · doi:10.2307/1970699
[5] Ole Hald and Vincenza Mauceri del Prete, Convergence of vortex methods for Euler’s equations, Math. Comp. 32 (1978), no. 143, 791 – 809. , https://doi.org/10.1090/S0025-5718-1978-0492039-1 Ole H. Hald, Convergence of vortex methods for Euler’s equations. II, SIAM J. Numer. Anal. 16 (1979), no. 5, 726 – 755. · Zbl 0427.76024 · doi:10.1137/0716055
[6] Tosio Kato, Nonstationary flows of viscous and ideal fluids in \?³, J. Functional Analysis 9 (1972), 296 – 305. · Zbl 0229.76018
[7] Tosio Kato, On classical solutions of the two-dimensional nonstationary Euler equation, Arch. Rational Mech. Anal. 25 (1967), 188 – 200. · Zbl 0166.45302 · doi:10.1007/BF00251588
[8] F. J. McGrath, Nonstationary plane flow of viscous and ideal fluids, Arch. Rational Mech. Anal. 27 (1967), 329 – 348. · Zbl 0187.49508 · doi:10.1007/BF00251436
[9] F. Milinazzo and P. G. Saffman, The calculation of large Reynolds number two-dimensional flow using discrete vortices with random walk, J. Computational Phys. 23 (1977), no. 4, 380 – 392. · Zbl 0347.76015
[10] Gilbert Strang, On the construction and comparison of difference schemes, SIAM J. Numer. Anal. 5 (1968), 506 – 517. · Zbl 0184.38503 · doi:10.1137/0705041
[11] Gilbert Strang, Accurate partial difference methods. II. Non-linear problems, Numer. Math. 6 (1964), 37 – 46. · Zbl 0143.38204 · doi:10.1007/BF01386051
[12] R. Temam, The Navier-Stokes Equations, North-Holland, Amsterdam, 1977.
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.