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_/ 流体力学セミナー ２００５ No. ３
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_/ 日 時 : ０５年 ５月 ３０日 (月) １５：００〜１６：３０
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_/ 場 所 : 京大数理研 ００９号室
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_/ 講 師 : Aiguo Xu 氏（京大大学院 人間・環境学研究科）
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_/ 題 目 : Finite-difference lattice Boltzmann methods for binary fluids
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_/ 内 容 :
_/ Lattice Boltzmann Method (LBM) has become a viable and promising numerical
_/ scheme for simulating fluid flows. There are several options to discretize
_/ the Boltzmann equation: (i) Standard LBM (SLBM); (ii) Finite-Difference LBM
_/ (FDLBM); (iii) Finite-Volume LBM; (iv) Finite-Element LBM; etc. These kinds
_/ of schemes are expected to be complementary in the LBM studies. For
_/ multicomponent fluids, (i) most existing methods belong to the SLBM, and/or
_/ based on the single-fluid theory; (ii)nearly all the studies are focused on
_/ isothermal and nearly incompressible systems. In our study, a two-fluid
_/ kinetic model, first proposed by L. Sirovich, is clarified and
_/ extended. Based on this kinetic model, FDLBMs for binary Euler
_/ equations and Navier-Stokes equations are formulated.
_/ We consider a binary mixture with two components, $A$ and $B$. The based
_/ discrete velocity model (DVM) is described by two indexes, $k$ and $i$,
_/ where $k$ denotes the $k$th group of discrete velocities with the same size
_/ $v_k$, $i$ indicates the direction of the discrete velocity. The basic
_/ ideas in the formulation procedure of the FDLBMs are as follows:
_/ (i) The Chapman-Enskog analysis shows what properties the discrete
_/ Maxwellian distribution function $f_{ki}^{A¥left( 0¥right)}$ should follow;
_/ (ii) Those requirements tell the lowest order of the flow velocity
_/ ${¥bf u}^A$ in the Taylor expansion of $f_{ki}^{A¥left( 0¥right) }$;
_/ (iii) The highest rank of tensors of the particle velocity ${¥bf v}^A$ in
_/ the requirements on the truncated $f_{ki}^{A¥left( 0¥right) }$ determines
_/ the needed isotropy of the DVM. The present approach works for binary
_/ neutral fluid mixtures. One possibility to introduce interfacial tension is
_/ to modify the pressure tensors, which is implemented by changing the force
_/ terms. For binary fluids with disparate-mass components, say $m^A¥ll m^B$,
_/ only if the total masses and temperatures of the two species are not
_/ significantly different, Sirovich’s kinetic theory works, so do the
_/ corresponding FDLBMs. When the masses and/or the temperatures of the two
_/ components are greatly different, the two-fluid kinetic theory should be
_/ modified. In those cases, the Navier-Stokes equations and the FDLBMs are
_/ not symmetric about the two components, but the formulation procedure is
_/ straightforward.
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世話人：大木谷 耕司(京大数研)、藤 定義(京大理)、松本 剛(京大理)、
山田 道夫(京大数研)
アドバイザー：河原 源太(京大工)、小森 悟（京大工）、藤坂博一（京大情報学）、
船越 満明（京大情報学）、水島 二郎(同志社大工)、余田 成男（京大理）
連絡先：ohkitani@kurims.kyoto-u.ac.jp
メールリスト連絡先： semi-adm@kyoryu.scphys.kyoto-u.ac.jp
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