O estudo de simulações da magnetohidrodinâmica via método de Lattice Boltzmann

Abstract

The studies of plasma dynamics present many challenges in theoretical physics due to their set of non-linear equations, making their behaviors complex for analytical descriptions, being barely possible for simplified cases. Therefore, it is necessary to use numerical methods for better understanding of their behaviors in situations close to reality. This dissertation presents revisions of the theory of fluid dynamics to build the model of magnetoidrodynamics in lattice Boltzmann (LB) and its applications being two-dimensional with nine discrete velocities (D2Q9) through computer codes in the Python language, using the libraries NumPy and Matplotlib. The simulated models form the vortices of an incompressible Newtonian fluid, the vortices in the conducting fluid through the Orszang-Tang model and the Hartmann flow. The LB method is a numerical approach that operates at the mesoscopic scale and is therefore used as a solution to the statistics of the particle distribution function instead of directly solving the non-linear coupling equations of the Navier-Stokes equations and the equations of the magnetohydrodynamics (MHD). The method applied to the MHD is highly parallel, capable of substituting the difficult solution of the nonlinear convective derivatives of the MHD by a simple linear advective in the lattice. New methods in LB, currently, are being created and improved, demonstrating more and more numerical stabilities, significant for computational applications, being also strong candidates for simulations close to real.