A useful relationship between time-dependent and steady state solutions of the Boltzmann equation

1996 ◽  
Vol 101 (A6) ◽  
pp. 13523-13526 ◽  
Author(s):  
John W. Bieber
Keyword(s):  
Steady State ◽  
Boltzmann Equation ◽  
Time Dependent ◽  
The Boltzmann Equation ◽  
Steady State Solutions

scholarly journals Thermal ignition in a reactive slab with unsymmetric boundary temperatures

1983 ◽  
Vol 24 (3) ◽  
pp. 279-288 ◽  
Author(s):  
K. K. Tam ◽  
P. B. Chapman
Keyword(s):  
Steady State ◽  
Critical Role ◽  
Upper And Lower Solutions ◽  
Lower Solution ◽  
Time Dependent ◽  
Thermal Ignition ◽  
Time Dependent Problem ◽  
Steady State Solutions

AbstractThe problem of thermal ignition in a reactive slab with unsymmetric temperatures equal to 0 and T is considered. Steady state upper and lower solutions are constructed. It is found that T plays a critical role. Results similar to the case with symmetric boundary temperatures are expected when T is small. When T is sufficiently large, there is only one steady state upper or lower solution. The time dependent problem is then considered. Phenomena suggested by studying the upper and lower steady state solutions are confirmed.

Laser Beam-Hygroscopic Aerosol Interactions

1977 ◽  
Vol 99 (2) ◽  
pp. 281-286 ◽  
Author(s):  
G. E. Caledonia ◽  
J. D. Teare
Keyword(s):  
Steady State ◽  
Laser Beam ◽  
Water Droplet ◽  
Atmospheric Aerosol ◽  
Phase Shifts ◽  
Time Dependent ◽  
Small Water ◽  
Steady State Solutions

A model for the prediction of the temperature and vapor fields created about a small water droplet undergoing irradiation by a laser beam has been developed. Time-dependent and steady-state solutions of the model are discussed. Estimates of characteristic phase shifts to be expected in propagating through standard atmospheric aerosol distributions are also presented. While the model is quite general, the calculations are limited to DF laser wavelengths.

Variance Reduction in Particle Methods for Solving the Boltzmann Equation

2006 ◽  
Author(s):  
Lowell L. Baker ◽  
Nicolas G. Hadjiconstantinou
Keyword(s):  
Boltzmann Equation ◽  
Shear Flow ◽  
Variance Reduction ◽  
Simulation Method ◽  
Reduction Technique ◽  
Particle Simulation ◽  
Time Dependent ◽  
Particle Methods ◽  
The Boltzmann Equation ◽  
Particle Simulation Method

We present a new particle scheme for solving the Boltzmann equation; this scheme incorporates a recently developed variance reduction technique discussed in [L. L. Baker and N. G. Hadjiconstantinou, Physics of Fluids, vol. 17, art. no 051703, 2005] which exhibits a significant computational efficiency advantage for low speed flows, compared to traditional particle methods. This paper describes how this variance reduction approach, achieved by simulating only the deviation from equilibrium, can be implemented as a particle simulation method. The new scheme is validated using time dependent shear flow calculations.

Coupled electron and atomic kinetics through the solution of the Boltzmann equation for generating time-dependent X-ray spectra

2006 ◽  
Vol 99 (1-3) ◽  
pp. 584-594 ◽  
Author(s):  
M.E. Sherrill ◽  
J. Abdallah, Jr. ◽  
G. Csanak ◽  
D.P. Kilcrease ◽  
E.S. Dodd ◽  
...  
Keyword(s):  
Boltzmann Equation ◽  
Time Dependent ◽  
X Ray ◽  
The Boltzmann Equation ◽  
Atomic Kinetics

Time-Dependent Simulations of Shear-Thinning Elastic Flows Through Contractions

2001 ◽  
Author(s):  
Paulo J. Oliveira
Keyword(s):  
Steady State ◽  
Unsteady Flow ◽  
Experimental Work ◽  
Shear Thinning ◽  
Time Dependent ◽  
Numerical Work ◽  
Viscoelastic Models ◽  
Vortex Merging ◽  
Constant Viscosity ◽  
Steady State Solutions

Abstract Past numerical work with constant-viscosity viscoelastic fluids through planar contractions has enabled steady-state solutions to be obtained at relatively high Weissenberg numbers (We up to 10). Those solutions for the upper-convected Maxwell and Oldroyd-B models showed steady flow patterns for increasing We with the appearance of lip-vortices, vortex growth, and comer-lip vortex merging, in agreement with recent simulations and some experimental work. When similar simulations were performed with two shear-thinning viscoelastic models, namely the Phan-Thien – Tanner and the Giesekus models, steady state solutions could not be obtained beyond a certain value of We, but the solution was seen to follow a periodic unsteady flow pattern. The present paper reports preliminary numerical results which highlight the formation of the lip vortices through a sequence of time dependent events.

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