Implementation of an accelerator algorithm to solve the vorticity diffusion equation using a deterministic numerical method

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. In order to make the core spreading method implementation feasible, the computational cost of the numerical simulations is reduced by the use of fast multipole method; this method divides the computational domain using boxes to reduce the number of mathematical operations necessary to compute the velocity field, which is the most expensive step of the vortex method. (AU)