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A numerical method for two‐dimensional Navier–Stokes equation by multi‐point finite differences
Author(s) -
Saitoh Takeo
Publication year - 1977
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620110908
Subject(s) - mathematics , truncation error , crank–nicolson method , reduction (mathematics) , finite element method , navier–stokes equations , truncation (statistics) , numerical analysis , degree (music) , mathematical analysis , finite difference method , finite difference , geometry , mechanics , physics , acoustics , thermodynamics , statistics , compressibility
A numerical scheme with a high degree of accuracy has been developed for the full Navier–Stokes equations. The method utilizes the multi‐mesh points for space and time derivatives in order to improve the truncation error. Whereas the existing numerical method employing the finite difference scheme, e.g. the explicit, pure implicit, Crank–Nicolson, and DuFort–Frankel schemes, has the truncation errors of the order (Δ x ) 2 , Δ x being the spatial mesh length, the one for the present method is generally of the order (Δ x ) 3 . A numerical example is shown for a natural convection flow in a square box and the results are compared with those of Cormack et al . One order of magnitude reduction of the computing time for a constant degree of accuracy was attained for the two‐dimensional problems. Furthermore, a two order of magnitude reduction is to be expected when the method is applied for the three‐dimensional Navier–Stokes equations.