Use of a deterministic method to solve the vorticity diffusion equation in the discrete vortex method

• Grant number: 18/00855-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2018
• End date: February 28, 2019
• Field of knowledge: Engineering - Mechanical Engineering - Transport Phenomena
• Principal Investigator: Alex Mendonça Bimbato
• Grantee: Leonardo Thomaz Villas Boas
• Host Institution: Faculdade de Engenharia (FEG). Universidade Estadual Paulista (UNESP). Campus de Guaratinguetá. Guaratinguetá , SP, Brazil

Abstract

The discrete vortex method discretizes the vorticity field using Lamb discrete vortex which are followed during every time step of the numerical simulation. In order to represent the flow vorticity dynamic each vortex suffers the advection and diffusion processes. The simulation of the vortex cloud advection process with high order schemes are sufficiently precision to this first step of the simulation. In the concerns of the diffusion process the literature presents many numerical methods developed to solve the vorticity diffusion equation properly. One of the most famous method used to simulate the vorticity diffusion is the random walk method which is a stochastic method, easy for implementation and with a low computational cost. However the most precise method to simulate the vorticity diffusion equation is the core spreading method which is a deterministic method that is more expensive than the random walk method. In this research project one proposes to implement the core spreading method in order to study the development of aircraft wakes. That is an important engineering problem since it is necessary to study wakes dissipation near the ground of airports in order to obtain even smaller time steps between take off and landing processes. This justify the use of the core spreading method associated with the vortex method (AU)