A fast algorithm for simulation of periodic flows using discrete vortex particles

Autor(es)

Ricciardi, Tulio R. ^[1] ; Wolf, William R. ^[1] ; Bimbato, Alex M. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, BR-13083860 Campinas, SP - Brazil

^[2] Sao Paulo State Univ, BR-12516410 Guaratingueta, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of the Brazilian Society of Mechanical Sciences and Engineering; v. 39, n. 11, p. 4555-4570, NOV 2017.
• Citações Web of Science: 0

Resumo

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(). 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. (AU)

• Processo FAPESP: 13/03413-4 - Investigação da geração e propagação de ruído em configurações aerodinâmicas utilizando aeroacústica computacional
• Beneficiário: William Roberto Wolf
• Modalidade de apoio: Auxílio à Pesquisa - Jovens Pesquisadores
• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: Francisco Louzada Neto
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs