Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
IMPLEMENTATION OF AN ACCELERATOR ALGORITHM TO REDUCE THE COMPUTATIONAL COSTS 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.COBEM2021.COB2021-0239
Abstract
The purely lagrangian discrete vortex method is a computation technique in which meshes are avoided. The method is used to represent a flow property as the vorticity field. In order to represent such property, the vorticity transport equation is obtained from the Navier-Stokes and continuity equations and the viscous splitting algorithm is used; according to it, one can solve the advection and diffusion equations separately but in the same time increment, just to make the vortex method implementation easier. The diffusion equation is solved by the classical random walk method; according to it, each discrete vortex used to represent the vorticity field is dislocated in a radial and circumferential direction to simulate vorticity scattering. The advection equation is solved using the material derivative in a classical lagrangian approach. One of the most problems when using lagrangian simulations concerns to the solution of advection equation, since it is necessary to compute the velocity field in the position occupied by each one of N discrete vortex present in the computational domain. In a typical problem the velocity field is composed by three contributions: (i) the incident flow; (ii) the boundary surfaces; (iii) the vortex-vortex interaction. The vortex-vortex interaction is especially expensive since its computational cost is proportional to N2 when the Biot-Savart law is used. The aim of the present work is to implement a fast multipole method to reduce the computational costs associated to the Biot-Savart computations. The fast multipole method divides the computational domain using boxes which contains the discrete vortices; the goal of the algorithm is to promote more interactions between boxes than interactions between particles. One hopes that the computational costs can be proportional to N log N or even to N. In order to simplify the numerical implementation of the fast multipole method the physical situation investigated is the tip vortices detached from airplane wings; there are no incident flow and solid boundaries in the problem. The pair of vortices is represented by Lamb discrete vortices and their trajectories, predicted by the numerical method, are compared to experimental data available in the literature. The velocity field is composed only by the vortex-vortex interaction which is computed using only the Biot-Savart law and using the fast multipole method to verify the CPU time reduction.
Keywords
Discrete Vortex Method, fast multipole method, CPU time reduction, Lagrangian description
