Generalized Algebraic Kernels and Multipole Expansions for massively parallel Vortex Methods
Parallel vortex particle methods are an efficient technique for large-scale simulations of turbulent fluid flows. One of their big advantages is the intrinsic adaptivity of vortex particles, since computational elements exist only where the vorticity field is non-zero. To overcome O(N2)-complexity of the corresponding N-body problem, multipole-based fast summation methods can be used here as well, which reduce the computational costs to at least O(NlogN).
Since vortex particle methods are dominated by high order non-Coulombian interaction kernels, the parallel Barnes-Hut tree code PEPC and its underlying theory have been extended to handle generalized algebraic smoothing kernels of arbitrary order. However, a stable implementation using particles for discretizing the vorticity field must provide a scheme for treating the overlap condition, which is required for convergent regularized vortex particle methods. Therefore, the code also includes an implementation of the concept of remeshing to account for long-term accuracy.