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 (vr,vθ,vzandp) 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 fluxqr=r·vron a staggered grid simplifies the treatment of the region atr= 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 atr= 0, is also considered. Finally to emphasize the accurate treatment near the axis, the motion of a Lamb dipole crossing the origin is simulated.

Verzicco, R., Orlandi, P. (1996). A finite difference scheme for 3D incompressible flows in cylindrical coordinates. JOURNAL OF COMPUTATIONAL PHYSICS, 123, 402-414 [doi:10.1006/jcph.1996.0033].

### A finite difference scheme for 3D incompressible flows in cylindrical coordinates

#### 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 (vr,vθ,vzandp) 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 fluxqr=r·vron a staggered grid simplifies the treatment of the region atr= 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 atr= 0, is also considered. Finally to emphasize the accurate treatment near the axis, the motion of a Lamb dipole crossing the origin is simulated.
##### Scheda breve Scheda completa Scheda completa (DC)
1996
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore ING-IND/06 - FLUIDODINAMICA
English
Con Impact Factor ISI
Numerical method, Navier-Stokes equations, Cylindrical Coordinates, Second-Order Accuracy
http://www.sciencedirect.com/science/article/pii/S0021999196900339
Verzicco, R., Orlandi, P. (1996). A finite difference scheme for 3D incompressible flows in cylindrical coordinates. JOURNAL OF COMPUTATIONAL PHYSICS, 123, 402-414 [doi:10.1006/jcph.1996.0033].
Verzicco, R; Orlandi, P
Articolo su rivista
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2108/53061`
• ND
• 530
• 495