Eventos Anais de eventos
ENCIT 2022
19th Brazilian Congress of Thermal Sciences and Engineering
USE OF A FAST MULTIPOLE METHOD TO REDUCE THE COMPUTATIONAL COSTS OF AIRCRAFT WAKES SIMULATIONS
Submission Author:
Marília Vidille , SP
Co-Authors:
Marília Vidille, Paulo Guimarães de Moraes, Luiz Antonio Alcântara Pereira, Alex Bimbato
Presenter: Marília Vidille
doi://10.26678/ABCM.ENCIT2022.CIT22-0027
Abstract
The discrete vortex method is a purely lagrangian computational technique, whose objective is to solve the vorticity transport equation, obtained from the Navier-Stokes and the continuity equations. The technique consists of represent the vorticity field using Lamb discrete vortex. To make the solution feasible, the viscous splitting algorithm is used and, according to it, is possible to simulate the advection and diffusion processes separately but in the same time increment. To simulate the diffusion, it is possible to use the traditional random walk method or the core spreading method, whereby the discrete vortices grow until a limit and split in four new particles. To simulate the advection, it is necessary to know the velocity field in the position occupied by each particle and it suffers three influences: incident flow, solid boundary and the discrete vortex cloud. The vortex-vortex interaction is especially onerous, because its computational cost is proportional to Z 2 , where Z is the amount of particles in the computational domain, when the Biot-Savart law is used. The solid boundary is represented by a source panel method and, in order to satisfy the no-slip boundary condition, at each time of the numerical simulation, a discrete vortex is positioned in the neighborhood of each panel to simulate the boundary layer formation. The increase in the number of particles, because of the core spreading method or the vorticity generation, makes the simulation prohibitive due to the CPU time. Therefore, the aim of the present research is to explore the implementation of an accelerator algorithm, the fast multipole method, who divides the computational domain in square boxes and enables more interactions among boxes than interactions among particles. The physical situation studied in this paper refers to the behavior of vortices detached from airplane wings near the ground. The phenomenon is especially important during the landing and take-off operations, since it may cause accidents in airports. The strategy used consists in analyse the CPU time and the errors in the velocity field computation generated by the fast multipole method when it is compared to the Biot-Savart law calculations. The results show that is possible to reduce the CPU time with acceptable errors which will be important in order to use the discrete vortex method to studied more complex engineering problems.
Keywords
Lagrangian description, Discrete Vortex Method, fast multipole method, CPU time reduction, panel method
