Vortex breakdown simulation: A circumspect study of the steady, laminar, axisymmetric model

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Abstract

The incompressible, axisymmetric, steady Navier-Stokes equations are written using the streamfunction-vorticity formulation. The resulting equations are discretized using a second-order, central difference scheme. The discretized equations are linearized and then solved using an exact LU decomposition, Gaussian elimination and Newton iteration. Solutions are presented for Reynolds numbers based on vortex core radius ranging from 100 to 1800 and swirl parameter ranging from 0.9 to 1.1. The effects of inflow boundary conditions, location of farfield and outflow boundaries and mesh refinement are examined. Finally, the stability of the steady solutions is investigated by solving the time-dependent equations.

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