Agradecimentos: The authors acknowledge the financial support received from Fundação de Amparo à Pesquisa do Estado de São Paulo, FAPESP, under Grants No. 2013/03413-4 and 2013/07375-0 and from Conselho Nacional de Desenvolvimento Científico e Tecnológico CNPq, under Grants No. 470695/2013-7 and...

Agradecimentos: The authors acknowledge the financial support received from Fundação de Amparo à Pesquisa do Estado de São Paulo, FAPESP, under Grants No. 2013/03413-4 and 2013/07375-0 and from Conselho Nacional de Desenvolvimento Científico e Tecnológico CNPq, under Grants No. 470695/2013-7 and 305277/2015-4. The authors also acknowledge CAPES for providing a M.Sc. scholarship to the first author. The computational resources provided by CENAPAD-SP under Project No. 551 are also acknowledged

We present a novel fast algorithm for flow simulations using the discrete vortex method, DVM, for problems with periodic boundary conditions. In the DVM, the solution of the velocity field induced by interactions among N discrete vortex particles is governed by the Biot–Savart law and, therefore,...

We present a novel fast algorithm for flow simulations using the discrete vortex method, DVM, for problems with periodic boundary conditions. In the DVM, the solution of the velocity field induced by interactions among N discrete vortex particles is governed by the Biot–Savart law and, therefore, leads to a computational cost proportional to O(N2). The proposed algorithm combines exponential and power series expansions implemented using a divide and conquer strategy to accelerate the calculation of the cotangent kernel that models periodic boundary conditions. The fast multipole method, FMM, is applied for the solution of singular terms appearing in the power series expansion and also for the exponential series expansion. Error and computational cost analyses are performed for the individual steps of the algorithm for double and quadruple machine precision. The current method presents more accurate solutions when compared to those obtained by periodic domain replication using the free-field FMM kernel. The novel algorithm provides computational savings of nearly 240 times for double-precision simulations with one million particles when compared to the direct calculation of the Biot–Savart law

CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQ

470695/2013-7; 305277/2015-4

FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP

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