Optimal combination of vortexincell and fast multipole methods
Abstract
In vortex methods, an efficient alternative to fast multipole methods is to use gridbased Poisson solvers. Efficient solvers have an l O(M log M) computational cost (M being the number of grid points), and the constant in front is significantly smaller than that associated with the l O (N log N) multipole methods (N being the number of vortex particles). This approach then calls for a hybrid particlegrid method: the vortexincell (VIC) method. As the Poisson equation for the streamfunction is then solved on a grid, this requires that appropriate boundary conditions be specified on the grid surface. In usual VIC applied to open problems, the grid is taken ``sufficiently'' large that approximate analytical boundary conditions can be used. The better the required quality, the larger the required grid. We here propose an original approach where the exact boundary condition is obtained dynamically using the fast multipole method. This combination is quite optimal: a compact VIC grid (enclosing tightly and dynamically the nonzero vorticity field) can be used while the proper boundary condition is enforced efficiently. This ``VIC + multipole'' approach is between 15 and 20 times faster compared to the pure multipole method. Moreover, as the grid is compact, fairly large problems can also be handled on a PC. Examples will be presented: an unstable zero circulation vortex in 2D, and an unstable fourvortex aircraft wake system in 3D.
 Publication:

APS Division of Fluid Dynamics Meeting Abstracts
 Pub Date:
 November 2003
 Bibcode:
 2003APS..DFD.DH008C