Physically, since the Boltzmann equation describes the balancing of particle transfer, by solving for all the moments at a spatial node first, this relaxation somewhat enforces a local balancing of particle transfer at each spatial node.
This simplified form of the Boltzmann equation is obtained by assuming the approximate energy separatibility of and taking a truncated Legendre series expansion of [[sigma].
n] discretizations of the Boltzmann equation lead to non-symmetric linear systems that are difficult to solve efficiently, and standard Galerkin [P.
To derive the continuity equation of a phase, the Boltzmann equation is multiplied by the characteristic mass of the phase and is integrated over the velocity space.
By weighting the Boltzmann equation of each phase by property parameters and integrating over the velocity space, the continuity and momentum equations are derived.
First, the importance function is unknown; the Schrodinger equation doesn't let you calculate the interaction potential as easily as the Boltzmann equation
Here, we make use of an interpolation formula based on the numerical solution of Boltzmann equation
for the ratio of the evaporation rate in the slip and transition regime ([10.
The begin by describing plasma and its classification, then examine the phenomenological description of the charged vehicle transport, macroscopic plasma characteristics, elementary processes in the gas phase and on surfaces, the Boltzmann equation
and transport equations of charged particles, general properties of charges particle transport in gases, modeling of nonequilibrium (low-temperature) plasmas, the numerical procedure of modeling, capacity coupled plasma, inductively coupled plasma, magnetically enhanced plasma and plasma processing and related topics.
Other sections present work on direct numerical solution of the Boltzmann equation
, microflows, granular gases, molecular beams, and gas phase molecular collision dynamics.