PART III: Lattice Boltzmann schemes in LBM_Saclay

This section focuses on the description of Lattice Boltzmann schemes in LBM_Saclay. It is seprated into four main subsections: 1) Streaming and collision operators, 2) Equilibrium distribution functions, 3) LBM for Navier-Stokes/Korteweg model and 4) Forces and other schemes.

Streaming and collision operators

Streaming and collision operators

We start with the Lattices and streaming and we give precisions on the streaming stage. Next section Collisions operators in LBM_Saclay focuses on four most popular collision operators \(\Omega_i^{\iota}(f_{i},f_{i}^{eq})\) with \(\iota=BGK, TRT, MRT, CM\).

Equilibrium distribution functions

Equilibrium distribution functions

In this sections, the equilibrium distribution functions \(f_i^{eq}\) will be described for incompressible Navier-Stokes equations and for transport equations.

LBM for Navier-Stokes/Korteweg model

LBM for Navier-Stokes/Korteweg model

The Navier-Stokes/Korteweg model (NSK) is a popular alternative model for simulating two-phase flows without introducing a phase-field \(\phi\). That model is a low Mach formulation of the Navier-Stokes equations, where \(\rho\) plays the role of phase index. The two-phase behavior is obtained by an appropriate choice of the Equation of State (EoS).

Forces and Other schemes

Forces and other schemes

Finally the last term \(\mathcal{F}_i\) is detailed with discretization of other differential operators (gradients and Laplacian).