Boundary Conditions for thermal Lattice Boltzmann simulations

My name is Friedemann Klaß and I am a PhD student in the Applied Mathematics and Numerical Analysis (AMNA) working group of the University of Wuppertal, where I also graduated from with a master‘s degree in mathematics and a minor in computer science. In my master‘s thesis, I studied boundary conditions for thermal lattice Boltzmann models.

Why I became a PhD student

Writing my master‘s thesis, I realized that I was only scratching the surface of the variety of aspects the field of Lattice Boltzmann has to offer. After a PhD position was offered to me, I took the opportunity to continue my work.

What I will do during my PhD

Lattice Boltzmann models form a relatively new class of methods in the field of computational fluid dynamics. The method operates on a mesoscopic scale, where virtual particles on a discrete grid move in a finite amount of directions and collide with each other. This turns out to be enough to recover the macroscopic Navier-Stokes equations if certain conditions are met.

Over the last few years, the method has been made capable to also simulate thermal flows.
One way to do this is increasing the amount of allowed directions in each grid node. This leads to added complexity in the treatment of boundary conditions, as the amount of directions along which unknown populations enter the computational domain increases and multiple boundary layers appear per boundary.

There exists little literature that explores boundary conditions for thermal lattice Boltzmann, which is precisely where the focus of my research lies.