Eventos Anais de eventos
EPTT 2024
14th Spring School on Transition and Turbulence
EVALUATION OF THE USE OF A FAST MULTIPOLE METHOD IN LAGRANGIAN SIMULATIONS
Submission Author:
Marília Vidille , SP
Co-Authors:
Marília Vidille, Luiz Antonio Alcântara Pereira, Alex Bimbato
Presenter: Marília Vidille
doi://10.26678/ABCM.EPTT2024.EPT24-0036
Abstract
This work shows the association of a fast multipole method with a Lagrangian method to simulate the flow around a circular cylinder. The discrete vortex method is the lagrangian computational technique used and it is characterized by the use of Lamb discrete vortex to represent the vorticity field. To simulate the advection in the discrete vortex method, it is necessary to know the velocity field in the position occupied by each discrete vortex used to discretize the vorticity field. This velocity field suffers three influences: the solid boundary, incident flow and vorticity field. The vorticity field contribution is taken into account by the vortex-vortex interaction, which is especially onerous when the Biot-Savart law is used: the computational costs is proportional to Z2, where Z is the amount of discrete vortices in the computational domain. So, the use of the Biot-Savart law makes the simulation prohibitive due to the CPU time. Therefore, the aim of this research is to use an accelerator algorithm, the fast multipole method, to reduce the vortex-vortex interaction. The main idea of the method is to divide the computational domain into square boxes, starting from a box of zero refinement level, which contains all discrete vortices presented in the computational domain. Then this initial box is divided into four equal boxes for the first refinement level. These boxes are then divided again into sixteen boxes for the second refinement level and so on. The main idea of the method is that the interaction occurs primarily between the boxes rather than between the particles, thereby reducing the use of the Biot-Savart law and, as a consequence, the final CPU time of the simulations.
Keywords
Accelerator Algorithm, fast multipole method, panel method, Lagrangian description
