日本航空宇宙学会関西支部分科会「非平衡の流体力学と分子運動論」（第5回）

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日時： 2024年5月2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1： Finite-volume methods for cross-diffusion systems and discrete chain rules
  Prof. Ansgar Jüngel (Institute of Analysis and Scientific Computing, Technische Universität Wien, Austria)
要旨1：

Many thermodynamic mixture and biological multicomponent models can be described by cross-diffusion systems. Although the diffusion matrices are generally neither symmetric and nor positive definite, the systems often possess an entropy (or free energy) structure. We aim to “translate” this entropy structure to finite-volume discretizations. The main difficulty is to adapt the nonlinear chain rule to the discrete level.
In this talk, we present two strategies to define a discrete chain rule, assuming either that the total entropy is the sum of individual entropies or that the entropy describes volume-filling models. Both strategies use suitable mean formulas, based on the mean-value theorem and the convexity of the entropy functional. This leads to convergent and structure-preserving numerical schemes. Examples include models for segregating populations and Maxwell-Stefan systems for gas mixtures.

 

日本航空宇宙学会関西支部分科会「非平衡の流体力学と分子運動論」（第4回）

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日時： 2023年11月9日（木）16:45-17:45
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： A High-Order Flux Reconstruction Method for the Polyatomic Boltzmann-BGK equation
  Prof. Freddie Witherden (Department of Ocean Engineering, Texas A&M University, USA)
要旨1： In this work, we will present a positivity-preserving high-order flux reconstruction method for the polyatomic Boltzmann-BGK equation augmented with a discrete velocity model that ensures the scheme is discretely conservative. Moreover, we will show how the approach can be extended to polyatomic molecules and hence is able to encompass arbitrary constitutive laws. We will show validation data on a series of large-scale complex numerical experiments, ranging from shock-dominated flows computed on unstructured grids to direct numerical simulation of three-dimensional compressible turbulent flows, the latter of which is the first instance of such a flow computed by directly solving the Boltzmann equation. In particular, we will showcase the ability of our proposed scheme to directly resolve shock structures without any ad-hoc numerical shock capturing method and correctly approximate turbulent flow phenomena in a consistent manner with the hydrodynamic equations.

日本航空宇宙学会関西支部分科会「非平衡の流体力学と分子運動論」（第3回）

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日時： 2023年8月18日（金）14:30-16:30
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1： Green’s function and surface wave
  Prof. Hung-Wen Kuo (Department of Mathematics, National Cheng Kung University, Taiwan)
要旨1：
In this talk, we will introduce a systematic scheme for explicitly constructing Green’s function for an initial-boundary value problem of evolutionary partial differential equations. To illustrate our approach, we first solve some basic PDEs such as the heat equation, the wave equation, and the damped wave equation, in a half-space and a quarter plane with various boundary conditions. Moreover, we will introduce the forming of the surface wave for these equations with particular boundary conditions. Then we will construct the complete representations of Green’s functions for the convection-diffusion equation and the drifted wave equation in a half-space with various boundary conditions. Finally, we will provide some ideas for constructing Green’s function of hyperbolic-dissipative system such as the compressible Navier-Stokes equations.
講演2： On the small data Cauchy problem for the Boltzmann equation
  Prof. Jin-Cheng Jiang (Department of Mathematics, National Tsing Hua University, Taiwan)
要旨2： We will review the result on the Cauchy problem for the Boltzmann equation with small initial data which including our recent progress on the soft potential model when the initial data is small in $L^3_{x,v}$ space.
    Then we will  provide some heuristic thinking about the possible result for the hard potential model. Part of talk is based on the joint work with Ling-Bing He.

日本航空宇宙学会関西支部分科会「非平衡の流体力学と分子運動論」（第2回）

今回の講演会は，対面形式で開催します．ご参加される方は下記の講義室へお越し下さい（事前申込は不要です）．

日時： 2023年3月31日（金）14:30-16:30
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）　1階　b1N01室（講義室1）
講演1： A two-scale reduced-order model for two-phase flows with polydisperse deformed droplets relying on Hamilton’s principle and a geometric method of moments
  Prof. Marc Massot (Centre de Mathématiques Appliquées, Ecole Polytechnique, France)
要旨1： Two-scale multi-fluid models with diffuse interface, amenable to realistic computational time, can be predictive for atomization, as long as they rely on the proper modeling of the small-scale interface dynamics below a given length threshold.
    The derivation of this two-scale model relies on three ingredients: 1- Large- and small-scale energies and conserved variables describing the physics, 2- the Hamilton’s Stationary Action Principle (SAP), 3- the second principle of thermodynamics that provide together with SAP the framework for consistent momentum and energy equations.
    Instead of solving capillarity at all physical length-scales with a phase-field model, this work proposes a two-scale model where a large-scale diffuse interface model interacts with a small-scale model under the chosen threshold, where the flow structure is simplified. The capillarity at large scale is here treated with a “Continuum Surface Force” (CSF), while the small-scale is modelled with a method of moment on a spray of droplets relying on a kinetic level of description. The resulting set of geometric moments allows geometric exchanges between scales to preserve the consistency of the interface geometry.
    The resulting unified model naturally degenerate into a Eulerian method of moments in the polydisperse spray region downward the flow, while matching the usual multi-fluid model in the separated flow region near the injector and offers an interesting entropy-consistant framework for the transfer of scales.
講演2： Small-scale modelling of interface dynamics in two-phase flows: a kinetic approach based on a geometric method of moments
  Mr. Arthur Loison (PhD student at Centre de Mathématiques Appliquées, Ecole Polytechnique, France)
要旨2： In the context of multi-scale two-phase flows such as liquid atomization or bubbly flows, the small-scale dynamics of the interface are computationally unaffordable with classic DNS with interface tracking, yet they are necessary to predict the right size distribution of the spray downstream the flow or the bubble polydispersity. Two-scale models avoid this bottleneck by modeling the small-scale unresolved dynamics of the interface.
    We expect such a small-scale model to be defined for any flow regime, while being consistent with reduced-order models based on methods of moments and the kinetic modelling of the disperse regime. This requires using specific quantities related to the average geometry of the unresolved interface that are the foundation of a geometric method of moments.
    In this presentation, we start by reviewing an averaged approach of interface dynamics [Pope 1988] [Essadki et al 2018] providing criteria for choosing appropriate geometric variables that are defined in every flow regime. Then, the small-scale model is closed with a geometric method of moments consistent with the disperse regime. Finally, we overview several closures and extensions of this method that allows the description of geometric polydispersion in size, shape, and internal dynamics in the disperse regime while providing dynamics for averaged geometrical variables for any flow regimes.

日本航空宇宙学会関西支部分科会「非平衡の流体力学と分子運動論」（第1回）

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日時： 2023年3月7日（火）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： Kinetic shear flow governed by the Boltzmann equation
  Prof. Renjun Duan (Department of Mathematics, The Chinese University of Hong Kong, Hong Kong)
要旨： For a rarefied gas, a uniform shear flow is characterized at a macroscopic level as a state where the horizontal velocity is linear along its normal direction while the density and temperature remain spatially uniform. Due to the shearing motion that induces the viscous heat, the total energy and hence temperature monotonically increase in time. It is more fundamental to understand the change of energy under the effect of shear forces at the kinetic level where the gas motion is governed by the nonlinear Boltzmann equation. In this context, the state is defined as the one that is spatially homogeneous when the velocities of particles are referred to a Lagrangian frame moving with the given macro shearing velocity. In the talk I will present recent results on uniform shear flow via the Boltzmann equation.

分科会「非平衡流体への運動学的アプローチ」（第9回）

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日時： 2022年12月22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： Modeling and experiments on thermophoresis in microfluidic systems
  Prof. Tetsuro Tsuji (Department of Advanced Mathematical Sciences, Kyoto University, Japan)
辻徹郎 准教授（京都大学大学院 情報学研究科 先端数理科学専攻）
要旨： Thermophoresis is the motion of tiny particles induced by the temperature gradient of surrounding fluids. Recent advances in experimental techniques to produce a steep temperature gradient in fluids have developed novel manipulation methods of nano- and microscale materials using thermophoresis. In the present talk, some trials to understand thermophoresis and its applications to microfluidics will be presented. More specifically, in the first part of the talk, a kinetic model on thermophoresis of Brownian particles is introduced to elucidate the mass effect on thermophoretic mobility. Furthermore, a molecular dynamics simulation is carried out to investigate the effect of interaction potential on the direction of thermophoretic motion. The second part of the talk will include the results of some microfluidic experiments. The aims of the experiments are two-fold: one is to obtain fundamental characteristics of thermophoresis and the other is to apply thermophoresis in microfluidic devices for concentration and separation. Some ongoing trials to investigate the origin of thermophoresis will be also presented.

分科会「非平衡流体への運動学的アプローチ」（第8回）

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日時： 2022年10月28日（金）16:30-17:30
場所： 京都大学 吉田キャンパス 工学部総合校舎 111講義室 （キャンパスマップ53番の建物です）
講演： Kinetic description of polyatomic gases undergoing resonant collisions
  Prof. Francesco Salvarani (Pôle Universitaire Léonard de Vinci, France & Dipartimento di Matematica, Università di Pavia, Italy)
要旨： This talk is devoted to the study of a kinetic model describing a polyatomic gas in which the microscopic internal and kinetic energies are separately conserved during a collision process (resonant collisions). This behaviour has been observed in some physical phenomena, for example in the collisions between selectively excited CO2 molecules. After describing the model itself, we prove the related H-theorem and show that, at the equilibrium, two temperatures are expected. We moreover prove a compactness property of the corresponding linearized Boltzmann operator. The peculiar structure of resonant collision rules allows to tensorize the problem and separately treat the internal energy contributions. We also propose a geometric variant of Grad’s proof of the compactness property in the monatomic case.

分科会「非平衡流体への運動学的アプローチ」（第7回）

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日時： 2022年9月9日（金）　17:30-18:30
場所： オンライン開催
講演： Spectroscopy of the asteroid Ryugu: Access to the records of our ancient Solar System
  Dr. Eri Tatsumi (Instituto de Astrofísica de Canarias, Spain)
巽 瑛理 氏 （カナリア天体物理学研究所）
要旨： Asteroids are building blocks of planets and keep the compositional information of the early Solar System. Especially the primitive asteroids, which are characterized by dark surfaces, are the key for water and organics on the Earth. My approach to constrain the composition and its evolusion on asteroids is the telescopic and remote-sensing observations. Recently the Hayabusa2 spacecraft by JAXA brought the sample materials from the primitive asteroid (162173) Ryugu. The sample return mission can connect the spectroscopic information to the compositional information directly, which gives strong constrains to our knowledge of the ancient Solar System.
In this talk, the spectroscopic results of Ryugu from the Hayabusa2 remote-sensing observations and ground-based observations will be discussed. The Hayabusa2 spacecraft equipped the multi-band Optical Navigation Camera (ONC) which mapped the whole surface of Ryugu up to 5 cm/pix in visible wavelengths. Using the images obtained by ONC, we could extract the evolutional history of Ryugu such as the parent body history, the impact history, and the recent trajectry changes. Besides, it is important to put the asteroid in the context of the Solar System. To do this, we investigated the distribution of the asteroids which have the similar spectral feature to Ryugu. Especially the UV region is useful to characterize hydrated minerals on asteroids. We found the very peculiar distribution of the asteroid with the spectral feature similar to Ryugu. Connecting the spectra to the material information which will be brought from the Ryugu sample analyses will make a new compositional map of the Solar System.

分科会「非平衡流体への運動学的アプローチ」（第6回）

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日時： 2021年10月25日（月）　16:45-17:45
場所： オンライン開催
講演： New lattice Boltzmann model for simulating compressible flows
  Prof. Takeshi Kataoka (Department of Mechanical Engineering, Kobe University, Japan)
片岡 武 准教授 （神戸大学大学院 工学研究科 機械工学専攻）
要旨： We have developed a new type of simple lattice Boltzmann (LB) model for the compressible Euler and NS equations based on the kinetic-equation approach proposed by Sone in 2002. The model uses the kinetic equation of the free-molecular type in the streaming process, and modifies the distribution function to its Chapman-Enskog type in the collision process. Compared with the conventional LB models which solve the kinetic equation of the BGK type, the proposed model is superior in the following two points: (i) any flow parameters, including the specific-heat ratio and three transport coefficients, can be chosen freely according to our convenience; (ii) there are no inherent errors associated with the Knudsen number. Numerical tests and error estimates confirm these merits.

分科会「非平衡流体への運動学的アプローチ」（第5回）

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日時： 2021年8月11日（水）　16:30-17:30
場所： オンライン開催
講演： Mathematical analysis of Chorin’s projection method
  Prof. Kohei Soga (Department of Mathematics, Faculty of Science and Technology, Keio University, Japan)
曽我 幸平 准教授 （慶應義塾大学 理工学研究科 基礎理工学専攻）
要旨： Chorin’s projection method, originally introduced by Alexandre Joel Chorin in 1969, is a numerical technique of computational fluid dynamics. The method can be seen as the most elementary and direct approach to solve the incompressible Navier-Stokes equations in a general setting. Nowadays, many versions of the original method are known. In this talk, we revisit Chorin’s original projection method and discuss its potential to be a mathematical tool beyond a computational technique for smooth solutions. We first observe that the method yields a Leray-Hopf weak solution. Then, we apply the method to investigate time-periodic solutions, which is an attempt to capture qualitative features of flows through discrete approximation. Finally, we investigate the accuracy of the method.