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The calculation of high order singularities in the finite Taylor problem. (English) Zbl 0574.76110

Numerical methods for bifurcation problems, Proc. Conf., Dortmund/Ger. 1983, ISNM 70, 129-144 (1984).
[For the entire collection see Zbl 0535.00021.]
This paper is concerned with the numerical calculation of solutions of the Navier-Stokes equations for steady axisymmetric flow in the Taylor problem with small aspect ratio. The plan of the paper is as follows. Section 2 contains a description of the Taylor problem with small aspect ratio and the details of the finite-element method used for its numerical solution. The main theoretical results are contained in section 3, where a general nonlinear two parameter problem with symmetry is considered. Numerical methods for the computation of certain high order singular points are derived and analyzed. Section 4 describes how the algorithms are implemented in the Taylor problem and numerical results are given in section 5.

MSC:

76U05 General theory of rotating fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
76M99 Basic methods in fluid mechanics

Citations:

Zbl 0535.00021

Software:

MA32