A Lattice Boltzmann Scheme for Semiconductor Dynamics

On a superconvergent lattice Boltzmann boundary scheme

In a seminal paper [9] Ginzburg and Adler analyzed the bounce-back boundary conditions for the lattice Boltzmann scheme and showed that it could be made exact to second order for the Poiseuille flow if some expressions depending upon the parameters of the method were satisfied, thus defining so-called “magic parameters”. Using the Taylor expansion method that one of us developed, we analyze a s...

Simulation of the Dynamics of Polymers in Solution via a Hybrid Molecular Dynamics-Lattice Boltzmann Scheme

A lattice-Boltzmann relaxation scheme for coupled convection-radiation systems

The convection-radiation effects in thermal fluid flows are studied based on the Lattice Boltzmann method. Nine-velocity flow and temperature distributions are used to obtain the mass, momentum and energy equations in thermal incompressible flows by studying equivalent moment systems. The radiative heat flux in the energy equation is obtained using the discrete-ordinates solution of the radiati...

Quartic parameters for acoustic applications of lattice Boltzmann scheme

Using the Taylor expansion method, we show that it is possible to improve the lattice Boltzmann method for acoustic applications. We derive a formal expansion of the eigenvalues of the discrete approximation and fit the parameters of the scheme to enforce fourth order accuracy. The corresponding discrete equations are solved with the help of symbolic manipulation. The solutions are obtained in ...

Advection-diffusion lattice Boltzmann scheme for hierarchical grids

In this paper we describe an extension of a recently developed lattice Boltzmann method for solving the advection–diffusion equation. Our proposed approach allows to couple grids of different grid resolutions and includes a staggered timestepping scheme, interpolations in space and time and finally a scaling step ensuring the continuity of the desired macroscopic quantities across the grid inte...