Title : Lattice Boltzmann kinetic modeling of Hall MHD
Contact : Nathanael Machicoane
Abstract : The Lattice Boltzmann (LB) method has emerged as a conceptually different approach to Computational Fluid Dynamics (CFD). While conventional CFD methods rely on a macroscopic description, the LB method addresses fluid motions at an underlying mesoscopic level. Capturing the statistical behavior of fluid particles is here preferred to solving non-linear PDEs. This sounds unrealistic, however, it is possible because most details at the mesoscopic level play actually no role in the macroscopic world. Therefore, much simpler kinetic equations than the original Boltzmann equation may be designed. This is the idea behind the LB method.
In this seminar, we will show how the LB framework can be extended to address plasma dynamics by encompassing both the fluid dynamics driven by the Lorentz force and the magnetic induction equation, including the Hall effect. A significant advantage of dealing with a kinetic representation, is that the electric current density is directly embedded in the statistical solution, thus allowing for an intrinsically accurate description of the small-scale dynamics. Comparisons of numerical simulations with solar wind measurements demonstrate the strength of the numerical approach.