分科会「非平衡現象の流体力学」（第20回）

平成27年度第7回講演会（日本航空宇宙学会関西支部分科会）

日時： 平成27年11月13日（金）　13:30-14:30
場所： 京都大学 桂キャンパスCクラスタ総合研究棟III（C3棟）　3階　b3n03室（航空宇宙工学専攻会議室）
講演： Diffuse interface modeling of subcritical and supercritical flames
Prof. Vincent Giovangigli
(Centre de Mathematiques Appliquees, Ecole Polytechnique, France)
要旨： During the ignition of rocket engines, or in Diesel engines, a transition may occur from subcritical to supercritical pressure conditions and such dynamics cannot be described by current fluid models. There is thus a need for models that transition smoothly from subcritical to supercritical pressure conditions.
With this aim in mind we present a liquid/gas diffuse interface model of Van der Waals/Korteweg type valid at all pressures. In the subcritical regime, the model describes
the continuous interface between a liquid and a gas mixture whereas in the supercritical domain the model thickens high density gradient zones. The interface model is further
embedded into a nonideal multicomponent reactive fluid framework. The resulting equations are used to investigate the interface between cold dense and hot light oxygen as well as the structure of diffusion flames between cold dense oxygen and gaseous like hydrogen at all pressures, either subcritical or supercritical.

分科会「非平衡現象の流体力学」（第19回）

平成27年度第6回講演会（日本航空宇宙学会関西支部分科会）

日時： 平成27年11月9日（月）　13:30-14:30
場所： 京都大学 桂キャンパスCクラスタ総合研究棟III（C3棟）　3階　b3n03室（航空宇宙工学専攻会議室）
講演： Boundary layers for the discrete Boltzmann equation: mixtures, polyatomic molecules, chemical reactions and quantum extensions
Prof. Niclas Bernhoff
(Dept. of Mathematics, Karlstad University, Karlstad, Sweden)
要旨： In the talk we will address two different questions.
1) An important aspect of constructing discrete velocity models (DVMs) for the Boltzmann equation is to obtain the right number of collision invariants. It is a well-known fact that DVMs can also have extra collision invariants, so called spurious collision invariants, in plus to the physical ones. A DVM with only physical collision invariants, and so without spurious ones, is called normal. The construction of such normal DVMs has been studied a lot in the literature for single species, but there are also several works where normal DVMs for binary mixtures are constructed. In this talk we will address ways of constructing DVMs for multi-component mixtures and for polyatomic molecules (here in the meaning that the molecules have one of a finite number of different internal energies, which can be changed, or not, during a collision). We present some general algorithms for constructing such models, but we also give some concrete examples of such constructions.
The two different approaches above can be combined to obtain multi-component mixtures with a finite number of different internal energies, and then they can be applied for DVMs for chemical reactions.
2) We also consider some problems related to the nonlinear half-space problem of condensation and evaporation for the discrete Boltzmann equation (DBE; the general discrete velocity model) for mixtures, polyatomic molecules, and chemical reactions, and for the discrete quantum Boltzmann equation. We assume that the flow tends to a stationary point (Maxwellian for the DBE) at infinity and that the outgoing flow is known at the wall (complete absorption at the wall). The number of conditions on the assigned data at the wall needed for existence of a unique solution is found. The number of parameters to be specified in the boundary conditions depends on if we have subsonic or supersonic condensation or evaporation. We obtain similar results for more general boundary conditions at the wall.All our results are valid for any finite number of velocities.

分科会「非平衡現象の流体力学」（第18回）

平成27年度第5回講演会（日本航空宇宙学会関西支部分科会）

日時： 平成27年7月29日（水）　16:30-17:30
場所： 京都大学 桂キャンパスCクラスタ総合研究棟III（C3棟）　3階　b3n03室（航空宇宙工学専攻会議室）
講演： Nonlinear stability of the Boltzmann Equation in a periodic box
Dr. Kung-Chien Wu
(Department of Mathematics, National Kaohsiung Normal University, Taiwan)
要旨： We study the nonlinear stability of the Boltzmann equation in the 3-dimensional periodic box. The initial perturbation is not necessary smooth. The convergence rate is algebraic for small time region and exponential for large time region. Moreover, the exponential decay rate depends on the size of the domain.

分科会「非平衡現象の流体力学」（第17回）

平成27年度第4回講演会（日本航空宇宙学会関西支部分科会）

日時： 平成27年7月1日（水）　13:30-14:30
場所： 京都大学 桂キャンパスCクラスタ総合研究棟III（C3棟）　3階　b3n03室（航空宇宙工学専攻会議室）
講演： Hydrodynamics models derived from kinetic theory for weakly ionized plasma flow out of thermal and chemical equilibrium with consistent thermodynamics
(joint work with B. Graille and T. Magin)
Prof. Marc Massot
(Laboratoire EM2C, Ecole Centrale Paris, France)
要旨： Based on kinetic theory, we give a complete description of the Kolesnikov effect in multicomponent partially ionized plasmas, or crossed contributions to the mass and energy transport fluxes coupling the electrons and heavy particles. The electromagnetic field influence, an ionization mechanism, and  a possible thermal nonequilibrium of the translational energy of the electrons and heavy particles, given their strong disparity of  mass, are accounted for. We conduct a dimensional analysis of the Boltzmann equation and use a multiscale  Chapman-Enskog method with a mixed hyperbolic/parabolic scaling to derive, for the continuum regime,  macroscopic conservation equations and expressions for the transport coefficients and chemical production rates. The model satisfies the law of mass action and the first and second laws of thermodynamics and has a well defined mathematical structure.

分科会「非平衡現象の流体力学」（第16回）

平成27年度第3回講演会（日本航空宇宙学会関西支部分科会）

日時： 平成27年5月1日（金）　16:30-17:30
場所： 京都大学 桂キャンパスCクラスタ総合研究棟III（C3棟）　3階　b3n03室（航空宇宙工学専攻会議室）
講演： A numerical study of hyperbolic models for chemotaxis
Prof. Magali Ribot
(Laboratoire J. A. Dieudonné, Université de Nice-Sophia Antipolis, France)
要旨： In this talk, I will consider hyperbolic – parabolic  systems for chemotaxis, which are very close to models for self-gravitating  systems.  I will concentrate here for the space dependency on a bounded interval in the  one-dimensional case. I will begin with a simple hyperbolic system, based on the Cattaneo system and I will present in that case a new kind of well-balanced schemes, which show a good accuracy around the stationary solutions.  However, we observe unexpected blow-up phenomena of the solutions of the system. Therefore, a second hyperbolic model based on Euler system is  analyzed : for this system I will give a complete description of the stationary solutions, I will present some numerical simulations around the stationary solutions and I will make some comparisons with the linked parabolic system.  At last, I will describe some applications to the wound healing modeling by casting the first  system on networks.

分科会「非平衡現象の流体力学」（第15回）

平成27年度第2回講演会（日本航空宇宙学会関西支部分科会）

日時： 平成27年4月24日（金）　16:30-17:30
場所： 京都大学 桂キャンパスCクラスタ総合研究棟III（C3棟）　3階　b3n03室（航空宇宙工学専攻会議室）
講演： From Vlasov-Poisson to Euler for trapped particles
Prof. Julien Barre
(Laboratoire J. A. Dieudonné, Université de Nice-Sophia Antipolis, France)
要旨： Motivated by experimental studies on clouds of cold atoms, we investigate the strong interaction limit (a.k.a. “quasi neutral” limit) for a Vlasov-Poisson-Fokker-Planck equation in an external potential. We show that under certain conditions, the dynamics reduces to an incompressible fluid equation: Euler or the lake equation, depending on the external potential. We will illustrate this convergence by some direct numerical simulations of the particles system.

分科会「非平衡現象の流体力学」（第14回）

平成27年度第1回講演会（日本航空宇宙学会関西支部分科会）

日時： 平成27年4月9日（木）　16:30-17:30
場所： 京都大学 桂キャンパスCクラスタ総合研究棟III（C3棟）　3階　b3n03室（航空宇宙工学専攻会議室）
講演： Sub-shock formation in gas mixtures
Prof. Fiammetta Conforto
(Dipartimento di Mathematica e Informatica, Universita degli Studi di Messina, Italy)
要旨：  Abstract

分科会「非平衡現象の流体力学」（第13回）

平成26年度第13回講演会（日本航空宇宙学会関西支部分科会）

日時： 平成27年2月9日（月）　14:40-15:40
場所： 京都大学 桂キャンパスCクラスタ総合研究棟III（C3棟）　3階　b3n03室（航空宇宙工学専攻会議室）
講演： Global Solutions of the Boltzmann Equation over R^D near Global Maxwellians with Small Mass
(joint work with Claude Bardos, Irene M. Gamba, and C. David Levermore)
Prof. François Golse
(Centre de mathématiques Laurent Schwartz, Ecole Polytechnique, France)
要旨：  We study the dynamics defined by the Boltzmann equation set in the Euclidean space R^D in the vicinity of global Maxwellians with finite mass. A global Maxwellian is a special solution of the Boltzmann equation for which the collision integral vanishes identically. In this setting, the dispersion due to the advection operator quenches the dissipative effect of the Boltzmann collision integral. As a result, the large time limit of solutions of the Boltzmann equation in this regime is given by noninteracting, freely transported states and can be described with the tools of scattering theory.

分科会「非平衡現象の流体力学」（第12回）

平成26年度第12回講演会（日本航空宇宙学会関西支部分科会）

日時： 平成27年1月13日（火）　14:40-16:20
場所： 京都大学 桂キャンパスCクラスタ総合研究棟III（C3棟）　3階　b3n03室（航空宇宙工学専攻会議室）
講演1：
(1 hour)		 From Stochastic Differential Games and Kinetic Theory Methods To the Modeling of Behavioral Social Crowds
Prof. Nicola Bellomo
(Department of Mathematical Sciences, Politecnico di Torino, Italy)
要旨1：  Abstract
講演2：
(30 min)		 A Monte Carlo simulation on the basis of the kinetic theory for chemo-tactic bacteria
Prof. Shugo Yasuda
(Graduate School of Simulation Studies, University of Hyogo, Japan)
要旨2：  Abstract

分科会「非平衡現象の流体力学」（第11回）

平成26年度第11回講演会（日本航空宇宙学会関西支部分科会）

日時： 平成27年1月6日（火）　16:10-17:10
場所： 京都大学 桂キャンパスCクラスタ総合研究棟III（C3棟）　3階　b3n03室（航空宇宙工学専攻会議室）
講演：
On Coagulation-Fragmentation Models with Spatial Diffusion
(joint work with Laurent Desvillettes, J. A. Canizo, J. A. Carrillo)
Prof. Klemens Fellner
(Institute for Mathematics and Scientific Computing, University of Graz, Austria)
要旨：
We consider existence, large-time behaviour and fast-reaction limits of coagulation-fragmentation models with spatial diffusion, which share many formal and structural  similarities with kinetic equations. As continuous-in-size model, we study Smoluchowski’s equation with constant coefficients and prove explicit convergence to equilibrium also in the case of degenerate diffusion coefficients.
Discrete-in-size models are considered with more general coefficients. The diffusion coefficients are also allowed to degenerate in size.
The main techniques include a-priori estimates based on the dissipation of an  entropy functional, entropy entropy-dissipation methods, moment bounds and  duality methods.