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Multiple discrete solutions of the incompressible steady-state Navier- Stokes equations. (English) Zbl 0642.76032

This paper discusses the computation of multiple solutions of various discretizations of the steady state incompressible Navier-Stokes equations. Solution paths (\(\alpha\),R) satisfying the discrete system of equations \(H(\alpha,R)=0\), where \(\alpha\) represents the discrete flow field and R is the Reynolds number, are computed using a pseudo arc- length continuation procedure. For flows over the back end of an axially symmetric body with a cusped tail in a coaxial circular cylinder, the solution paths often exhibit “hairpin” turning points. Dependence of the paths on the mesh spacing and various selections for the discretizations of the convective and diffusive terms are presented.

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76M99 Basic methods in fluid mechanics

Software:

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References:

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