A finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates. (English) Zbl 0849.76055

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. 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.


76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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