Algoritmo de solução para o método das abscissas prescritas para métodos de Lattice-Boltzmann em duas dimensões euclideanas

Abstract

ThelatticeBoltzmannmethods,mesoscopic,actbythenumericalsolutionoftheBoltzmann equation for a particle probabilistic distribution function, allowing the retrieval of the system macroscopic quantities. The particles are distributed and interact in lattices that discretize a velocity space and a spatial space. The set formed by the weights, discrete velocities and the scale of lattice is called stencil. The velocity space from the continuous equation discretization is a critical step in the Boltzmann stencils derivation. There are different ways to conduct it, such that one, prescribed abscissas method, works with a set of predefined dimensionless discrete velocities. The problem, a quadrature for the weights and the lattice scale determination, is equivalent to an internal product tensor between two Hermite tensor polynomials in the discrete space. There is no detailed in the bibliography about how to solve the quadratures, so this work will investigate algorithms to solve them, which lead to the creation of new lattice-Boltzmann methods.