Project Description

Full thesis available here.

The standard Lattice Boltzmann (LB) equation is a Computational Fluid Dynamics (CFD) method that approximates the
incompressible solution of the Navier-Stokes (NS) equations in the low Mach and Knudsen number limit. This Thesis focuses on the
development of new approaches for two numerical aspects of lattice Boltzmann methods: (i) Boundary Conditions, modifying
existing open boundary conditions for the treatment of the interaction between boundaries and pressure waves, and extending
macroscopic-gradient-related conditions in arbitrary geometries; and (ü) Preconditioning, developing equivalent lattice Boltzmann
methods of time-derivative preconditioned Navier-Stokes schemes, and analyzing its improved behavior. These developments are
expected to further increase the applicability of the lattice Boltzmann method as a standard CFD technique.