Parallel multipole implementation of the generalized Helmholtz decomposition for solving viscous flow problems

Abstract

SUMMARYThe evaluation of a domain integral is the dominant bottleneck in the numerical solution of viscous ow problems by vorticity methods, which otherwise demonstrate distinct advantages over primitive variable methods. By applying a Barnes-Hut multipole acceleration technique, the operation count for the integration is reduced from O(N 2 ) to O(N log N ), while the memory requirements are reduced from O(N 2 ) to O(N ). The algorithmic parameters that are necessary to achieve such scaling are described. The parallelization of the algorithm is crucial if the method is to be applied to realistic problems. A parallelization procedure which achieves almost perfect scaling is shown. Finally, numerical experiments on a driven cavity benchmark problem are performed. The actual increase in performance and reduction in storage requirements match theoretical predictions well, and the scalability of the procedure is very good.

The extended boundary node method for three-dimensional potential theory

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Cell‐based volume integration for boundary integral analysis

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A fast method for nonlinear three-dimensional free-surface waves

“…Applications in fluid mechanics seem to be rather sparse compared to other fields. However, there are several possibilities to use the FMA for incompressible flows: potential flow equations as first suggested by Rokhlin (1985), but also Stokes flow (Gómez & Powert 1997;Mammoli & Ingber 2000;Kropinski 2001), vortex methods (Pringle 1994;Scorpio & Beck 1996) and the possibility to come as a component of Navier-Stokes solvers via generalized Helmholtz decomposition (Brown et al 2003). Water-wave computations with multipole-accelerated codes also exist.…”