Cliffe, K. A.; Spence, A. 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. Cited in 6 Documents MSC: 76U05 General theory of rotating fluids 76D05 Navier-Stokes equations for incompressible viscous fluids 76M99 Basic methods in fluid mechanics Keywords:steady axisymmetric flow; Taylor problem with small aspect ratio; finite- element method; nonlinear two parameter problem; high order singular points Citations:Zbl 0535.00021 Software:MA32 PDFBibTeX XML