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The Newton‐Raphson approximation applied to the Navier‐Stokes equations with application to the base flow problem
Author(s) -
Parmet I. L.,
Saibel E.
Publication year - 1968
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19680480102
Subject(s) - navier–stokes equations , rotational symmetry , newton's method , stokes flow , flow (mathematics) , base (topology) , mathematics , hagen–poiseuille flow from the navier–stokes equations , mathematical analysis , mechanics , physics , nonlinear system , geometry , compressibility , quantum mechanics
When the Newton‐Raphson method is applied to the Navier–Stokes equations for axisymmetric flow, both Stokes and Oseen approximations may be obtained depending on the trial solutions selected. This suggests that the method may be continued to obtain higher order, and presumably better approximate solutions to the Navier‐Stokes equations. The method is illustrated on the axisymmetric base flow problem.