A vorticity-velocity method for the numerical solution of 3D incompressible flows

A new method for the numerical solution of the 3D Navier-Stokes equations written in terms of vorticity-velocity is presented. The advantages of this formulation with respect to primitive variables and vorticity-vector-potential ones are discussed in view of physical as well as engineering applications. A suitable form of the continuum equations, the most appropriate discretization scheme, and variable location in order to guarantee the solenoidality of the velocity and vorticity fields are introduced and justified. A 3D lid driven cavity problem for 400 >= Re =< 3200 is chosen as a test case for comparison and validation purposes. A parallel implementation of the method as been performed on a shared memory architecture mainframe. Speedup results and efficiency considerations are given and discussed.

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