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

✍ Scribed by R. Verzicco; P. Orlandi

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 508 KB
• Volume: 123
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.0033

✦ Synopsis

A finite-difference scheme for the direct simulation of the incompressible time-dependent three-dimensional Navier-Stokes equa- [6] proposed an accurate method for three-dimensional tions in cylindrical coordinates is presented. The equations in primipipe flows with Jacobi polynomials for the radial direction. tive variables (v r , v , v z and p) are solved by a fractional-step method These polynomials were introduced to minimize the together with an approximate-factorization technique. Cylindrical coupling of the momentum equations, nevertheless the coordinates are singular at the axis; the introduction of the radial discretization produced large nondiagonal sparse matrices flux q r ϭ r и v r on a staggered grid simplifies the treatment of the region at r ϭ 0. The method is tested by comparing the evolution to be inverted. Buell et al. [7] developed a Galerkin of a free vortex ring and its collision with a wall with the theory, method to simulate the natural convection in a circular experiments, and other numerical results. The formation of a tripolar enclosure. In the radial direction Bessel functions were vortex, where the highest vorticity is at r ϭ 0, is also considered.

used and the condition of finiteness of the solution was

Finally to emphasize the accurate treatment near the axis, the motion of a Lamb dipole crossing the origin is simulated. ᮊ 1996 Aca-applied at r ϭ 0. However, the Galerkin method was demic Press, Inc.

used to reduce the linearized perturbation equations to an eigenvalue problem and no information was provided about the extension of the method to the full Navier-