In this mini-course we hell expound the main ideas behind the Lattice Boltzmann for fluids (and beyond). After revisiting the fundamentals of Boltzmann kinetic theory we shall describe the principles which govern the transcription of the Boltzmann to the lattice framework. These principles shall be illustrated first for the simple case of advection-diffusion-reaction equations in one space dimensions. Subsequently, we shall describe the LB formulation of Navier-Stokes hydrodynamics in two and three spatial dimensions, as well as the techniques to impose the most common boundary conditions. Finally, we shall illustrate the extension to non-ideal fluids with applications to multiphase flows with dynamic phase transitions.
All theoretical subjects are accompanied by hand-on lectures/exercises using simple warm-up codes. For historical reasons, such codes are written in fortran, but transcription to C, matlab or python is straightforward.
As a final exam, the students will be required to solve some simple exercises requiring the development of their own computer programs and present a final project on a subject of their choice, possibility related to their own original research.
Some notions of numerical computing and coding practice (in whatever language). Some fore-knowledge of statistical physics and most notably Boltzmann’s kinetic theory would be helpful.
Lecture 1: Reminder of Boltzmann Kinetic Theory Lecture 2: Lattice Boltzmann for Transport Problems (Advection-Diffusion-Reaction)
Lecture 3: Lattice Boltzmann for Navier-Stokes Fluids: basic theory Lecture 4: : applications
Lecture 5: Lattice Boltzmann for non-ideal fluids: basic theory Lecture 6: : applications