Entropic Lattice Boltzmann Models for Fluid Dynamics

The main result of this thesis is the development of a new class of entropic
MRT models which combine the salient advantages from MRT and ELBM
while trying to circumvent their respective disadvantages. J.W. Gibbs’
seminal prescription for constructing optimal states by maximizing the entropy
under pertinent constraints is used to derive a novel lattice kinetic theory
and the the notion of modifying the viscosity to stabilize sub-grid simulations
is challenged in this kinetic framework. By exploiting the degrees of freedom
of MRT and by compliance to the discrete-time H-theorem, the advantages of
both MRT and ELBMcan be retained and the problems of parameter tuning
and fluctuating viscosity can be solved. The resulting models are accurate,
adaptive, parameter-free, efficient and, more importantly, very stable.