A Finite-Difference Scheme for Three-Dimensional Incompressible Flows in Cylindrical Coordinates

ISSN： 0021-9991

Source： Journal of Computational Physics, Vol.123, Iss.2, 1996-02, pp. : 402-414

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Abstract

A finite-difference scheme for the direct simulation of the incompressible time-dependent three-dimensional Navier-Stokes equations in cylindrical coordinates is presented. The equations in primitive variables ( v r , v theta , v z and p ) are solved by a fractional-step method together with an approximate-factorization technique. Cylindrical coordinates are singular at the axis; the introduction of the radial flux q r = r · v r on a staggered grid simplifies the treatment of the region at r = 0. The method is tested by comparing the evolution of a free vortex ring and its collision with a wall with the theory, experiments, and other numerical results. The formation of a tripolar vortex, where the highest vorticity is at r = 0, is also considered. Finally to emphasize the accurate treatment near the axis, the motion of a Lamb dipole crossing the origin is simulated.