A finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates
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.
scientific article; zbMATH DE number 881863