MODIFICATION OF THE EULER EQUATIONS FOR VORTICITY CONFINEMENT - APPLICATION TO THE COMPUTATION OF INTERACTING VORTEX RINGS

A new ''vorticity confinement '' method is described which involves ad ding a term to the momentum conservation equations of fluid dynamics. This term depends only on local variables and is zero outside vortical regions. The partial differential equations with this extra term admi t solutions that consist of Lagrangian-like confined vortical regions, or covons, in the shape of two-dimensional (2-D) vortex ''blobs'' and three-dimensional (3-D) vortex filaments, which convect in a constant external velocity field with a fixed internal structure, without spre ading, even if the equations contain diffusive terms. Solutions of the discretized equations on a fixed Eulerian grid show the same behavior , in spite of numerical diffusion. Effectively, the new term, together with diffusive terms, constitute a new type of regularization of the inviscid equations which appears to be very useful in the numerical so lution of flow problems involving thin vortical regions. The discretiz ed Euler equations with the extra term can be solved on fairly coarse, Eulerian computational grids with simple low-order (first- or second- ) accurate numerical methods, but will still yield concentrated vortic es which convect without spreading due to numerical diffusion. Since o nly a fixed grid is used with local variables, the vorticity confineme nt method is quite general and can automatically accommodate changes i n vortex topology, such as merging. Applications are presented for inc ompressible flow in 3D, where pairs of thin vortex rings interact and, in some cases, merge.