Boltzmann Transport Equation [1-2] has been modelled in close conjunction with Maxwell’s equation, investigations for 2D and 3D transport carriers have been proposed. Exact solution of Boltzmann Equation still remains the core field of research. We have worked towards evaluation of 2D and 3D solutions of BTE. Application of our work can be extended to study the electromagnetic wave transport in...

The Lattice Boltzmann method, a molecule kinetic-based approach, is presented to solve fluid dynamics. Based on the theory of turbulence and molecule kinetics, an extended Lattice Boltzmann equation is put forward to solve turbulent flow with high Reynolds number, in which sub-grid turbulence model is used to simulate vortex viscosity as well as turbulence relaxation time is introduced to modif...

Lees-Edwards boundary conditions (LEbc) for Molecular Dynamics simulations [1] are an extension of the well known periodic boundary conditions and allow the simulation of bulk systems in a simple shear flow. We show how the idea of LEbc can be implemented in lattice Boltzmann simulations and how LEbc can be used to overcome the problem of a maximum shear rate that is limited to less then 1/Ly (...

This work investigates the possibility of particle-based algorithms for the Navier-Stokes equations and higher order continuum approximations of the Boltzmann equation; such algorithms would generalize the well-known Pullin scheme for the Euler equations. One such method is proposed in the context of a discrete velocity model of the Boltzmann equation. Preliminary results on shock structure are...

In this paper we present lattice Boltzmann (LB) schemes for convection diffusion coupled to fluid flow on two-dimensional rectangular lattices. Via inverse Chapman-Enskog analysis of LB schemes including source terms, we show that for consistency with physics it is required that the moments of the equilibrium distributions equal those of the Maxwell-Boltzmann distribution. These constraints can...

In order to simulate the rarefied plasma flow within pulsed plasma thrusters (PPTs), a fully kinetic approach for the Boltzmann-Maxwell equations is under development by IAG (Institute of Aerodynamics and Gas Dynamics, Universität Stuttgart), IRS (Institute of Space Systems, Universität Stuttgart), ASE (Applied Supercomputing in Engineering, German Research School for Simulation Sciences) and I...

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...

We study discrete solvent effects on the interaction of two parallel charged surfaces in ionic aqueous solution. These effects are taken into account by adding a bilinear nonlocal term to the free energy of Poisson–Boltzmann theory. We study numerically the density profile of ions between the two plates, and the resulting interplate pressure. At large plate separations the two plates are decoup...

In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of equilibrium theory to nonequililbrium processes is usually made through the assumption of local thermodynamic equilibr...

The paper presents some approximation methods for the Boltz-mann equation. In the rst part fully implicit discretization techniques for the spatially homogeneous Boltzmann equation are investigated. The implicit equation is solved using an iteration process. It is shown that the iteration converges to the correct solution for the moments of the distribution function as long as the mass conserva...