LFDM Method on the Navier-Stokes Equations in Three-dimensional Flow in Cylindrical Coordinates on the von Karman Problem

A numerical technique is presented for the approximate solution of the velocity-vorticity Navier-Stokes equation of motion of a viscous incompressible fluid in three dimensions in cylindrical coordinates. Each component of the vorticity equation with the temporary introduction of two unknown functions of the coordinates is separated into three parts that are reduced to ordinary differential equations associated with a finite-difference scheme. The use of suitable manipulations and the elimination of the unknown functions, leads finally to a linear system of algebraic equations that is solved using an iterative procedure. The numerical technique is tested on the von Karman problem.