Transport in Transition Regimes

by Ben-Abdallah, Naoufel; Degond, Pierrenaoufel; Glassey, Robert T.; Arnold, Anton; Gamba, Irene M.; Levermore C. David; Ringhofer, Christian

• ISBN13: 9780387404950
• ISBN10: 0387404953
• Edition: 1st
• Format: Hardcover
• Copyright: 2003-10-01
• Publisher: Springer Verlag

Summary

IMA Volumes 135: Transport in Transition Regimes and 136: Dispersive Transport Equations and Multiscale Models focus on the modeling of processes for which transport is one of the most complicated components. This includes processes that involve a wide range of length scales over different spatio-temporal regions of the problem, ranging from the order of mean-free paths to many times this scale. Consequently, effective modeling techniques require different transport models in each region. The first issue is that of finding efficient simulations techniques, since a fully resolved kinetic simulation is often impractical. One therefore develops homogenization, stochastic, or moment based subgrid models. Another issue is to quantify the discrepancy between macroscopic models and the underlying kinetic description, especially when dispersive effects become macroscopic, for example due to quantum effects in semiconductors and superfluids. These two volumes address these questions in relation to a wide variety of application areas, such as semiconductors, plasmas, fluids, chemically reactive gases, etc.

Table of Contents

Foreword	v
Preface	vii
BGK-Burnett equations: A new set of second-order hydrodynamic equations for flows in continuum-transition regime	1	(36)
Ramesh K. Agarwal
Steady states for Streater's energy-transport models of self-gravitating particles	37	(20)
Piotr Biler
Jean Dolbeault
Maria J. Esteban
Peter A. Markowich
Tadeusz Nadzieja
Towards a hybrid Monte Carlo method for rarefied gas dynamics	57	(18)
Russel E. Caflisch
Lorenzo Pareschi
Comparison of Monte Carlo and deterministic simulations of a silicon diode	75	(10)
Jose A. Carrillo
Irene M. Gamba
Orazio Muscato
Chi-Wang Shu
Discrete-velocity models for numerical simulations in transitional regime for rarefied flows and radiative transfer	85	(18)
Pierre Charrier
Bruno Dubroca
Luc Mieussens
Rodolphe Turpault
Some recent results on the kinetic theory of phase transitions	103	(18)
Jean-Francois Collet
Thierry Goudon
Sara Hariz
Frederic Poupaud
Alexis Vasseur
Fluids with multivalued internal energy: the anisotropic case	121	(16)
P. Degond
M. Lemou
J.L. Lopez
A note on the energy-transport limit of the semiconductor Boltzmann equation	137	(18)
Pierre Degond
C. David Levermore
Christian Schmeiser
Generalized hydrodynamics and irreversible thermodynamics	155	(22)
Byung Chan Eu
A steady-state capturing method for hyperbolic systems with geometrical source terms	177	(12)
Shi Jin
Maximum entropy moment problems and extended Euler equations	189	(10)
Michael Junk
Numerical methods for radiative heat transfer in diffusive regimes and applications to glass manufacturing	199	(18)
Axel Klar
Guido Thommes
Hydrodynamic limits of the Boltzmann equation	217	(14)
Nader Masmoudi
Sobolev norm and carrier transport in semiconductors	231	(10)
Orazio Muscato
The evolution of a gas in a radiation field from a kinetic point of view	241	(8)
A. Nouri
Hybrid particle-based approach for the simulation of semiconductor devices: The full-band cellular automaton/Monte Carlo method	249	(16)
Marco Saraniti
Shela J. Wigger
Stephen M. Goodnick
Some remarks on the equations of Burnett and Grad	265	(14)
Henning Struchtrup
Boundary conditions and boundary layers for a class of linear relaxation systems in a quarter plane	279	(14)
Zhouping Xin
Wen-Qing Xu
Combined list of workshops participants for IMA volumes 135: transport in transition regimes and 136: dispersive transport equations and multiscale models	293