Optimal relaxation collisions for lattice Boltzmann methods

Single relaxation time model for entropic lattice Boltzmann methods.

For lattice Boltzmann methods based on entropy functions, we derive a collision integral which enables simple identification of transport coefficients, and which circumvents construction of the equilibrium. Implementation of the two-dimensional hydrodynamics demonstrates considerable increase of stability with respect to conventional lattice Boltzmann schemes.

Entropic Lattice Boltzmann Methods

We present a general methodology for constructing lattice Boltzmann models of hydrodynamics with certain desired features of statistical physics and kinetic theory. We show how a methodology of linear programming theory, known as Fourier-Motzkin elimination, provides an important tool for visualizing the state space of lattice Boltzmann algorithms that conserve a given set of moments of the dis...

Parallel Lattice Boltzmann Methods for CFD Applications

The lattice Boltzmann method (LBM) has evolved to a promising alternative to the well-established methods based on finite elements/volumes for computational fluid dynamics simulations. Ease of implementation, extensibility, and computational efficiency are the major reasons for LBM’s growing field of application and increasing popularity. In this paper we give a brief introduction to the involv...

Optimal Stability of Advection-Diffusion Lattice Boltzmann Models with Two Relaxation Times for Positive/Negative Equilibrium

Despite the growing popularity of Lattice Boltzmann schemes for describing multi-dimensional flow and transport governed by non-linear (anisotropic) advectiondiffusion equations, there are very few analytical results on their stability, even for the isotropic linear equation. In this paper, the optimal two-relaxation-time (OTRT) model is defined, along with necessary and sufficient (easy to use...

Entropic and multiple relaxation time lattice Boltzmann methods compared for time harmonic flows