A vorticity preserving finite difference discretization for the incompressible Navier-Stokes equations

MOX 83

A vorticity preserving finite difference discretization for the incompressible Navier-Stokes equations

Friday 26th May 2006

Abba', A.; Bonaventura, L.

A finite difference discretization of the three-dimensional, incompressible Navier Stokes equations is introduced, based on ideas that have been applied successfully to geophysical flows over the last four decades. The proposed spatial discretization is mass conservative and vorticity preserving, in the sense that a discrete form of the vorticity equation is derived naturally from the discrete momentum equation by application of a discrete rotation operator. A vorticity preserving discretization of the viscous terms and an appropriate treatment for rigid wall boundary conditions are also proposed. The relationship of this approach to other similar techniques is discussed. The results are compared to those of a standard finite difference discretization approach in a number of relevant test cases, which demonstrate the advantages of the proposed method, especially when strong vorticity production takes place at the boundaries.

This report, or a modified version of it, has been also submitted to, or published on
A. Abbà and L. Bonaventura, A vorticity preserving finite difference discretization for the incompressible Navier-Stokes equations, International Journal of Numerical Methods in Fluids, Vol. 56, pp. 1101-1106, 2008