A lattice Boltzmann approach for solving scalar transport equations.

A lattice Boltzmann (LB) approach is presented for solving scalar transport equations. In addition to the standard LB for fluid flow, a second set of distribution functions is introduced for transport scalars. This LB approach fully recovers the macroscopic scalar transport equation satisfying an exact conservation law.

Moment isotropy and discrete rotational symmetry of two-dimensional lattice vectors.

We present a direct proof of a theorem linking the order of moment isotropy and degree of discrete rotational symmetry for a two-dimensional set of lattice vectors. This theorem has been proved previously based on properties of sinusoidal functions. The new proof is based instead on purely linear algebraic arguments.

Thermal lattice Boltzmann model for gases with internal degrees of freedom.

We rigorously derive a dramatically simplified kinetic model for fluids with internal degrees of freedom. With proper discretization in velocity space, the model leads to a lattice Boltzmann model for polyatomic gases. The macroscopic recovery of correct hydrodynamics is theoretically shown and numerically validated.

Efficient kinetic method for fluid simulation beyond the Navier-Stokes equation.

We present a further theoretical extension to the kinetic-theory-based formulation of the lattice Boltzmann method of Shan [J. Fluid Mech. 550, 413 (2006)].

Extended volumetric scheme for lattice Boltzmann models.

An extended volumetric scheme is proposed for lattice Boltzmann (LB) models. This scheme is particularly desirable for multispeed LB models due to its removal of nonlocal advection. It recovers the same macroscopic hydrodynamics as the standard lattice Boltzmann method without any further treatments.

Lattice Boltzmann method for simulations of liquid-vapor thermal flows.

We present a lattice Boltzmann method that has the capability of simulating thermodynamic multiphase flows. This approach is fully thermodynamically consistent at the macroscopic level. Using this method, the liquid-vapor boiling process, including liquid-vapor formation and coalescence together with a full coupling of temperature, is simulated.

Extended Boltzmann kinetic equation for turbulent flows.

Complex fluid physics can be modeled using an extended kinetic (Boltzmann) equation in a more efficient way than using the continuum Navier-Stokes equations. Here, we explain this method for modeling fluid turbulence and show its effectiveness with the use of a computationally efficient implementation in terms of a discrete or "lattice" Boltzmann equation.

Red blood cells augment leukocyte rolling in a virtual blood vessel.

Leukocyte rolling and arrest on the vascular endothelium is a central event in normal and pathological immune responses. However, rigorous estimation of the fluid and surface forces involved in leukocyte-endothelial interactions has been difficult due to the particulate, non-Newtonian nature of blood. Here we present a Lattice-Boltzmann approach to quantify forces exerted on rolling leukocytes by red blood cells in a "virtual blood vessel.