The C-CUP method suitable for both compressible and incompressible fluids is extended to the general curvilinear coordinate system. In this paper, a staggered square grid in the transformed space is used, and the numerical viscosity, which does not depend on the change of metrics due to the rotation of the grid, is proposed. The equation of pressure is solved by the iteration method. As numerical examples, a shock-tube problem, a two-fluid flow and a flow field around a two-dimensional wing were calculated. Numerical results of the shock-tube problem show that the proposed numerical viscosity for the curvilinear coordinate system is effective to stabilize the solution. For the viscous two-fluid flow, the sharp interface between the two fluids is traced by using the density function.

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シンプレクティック解法による高精度分子動力学法によりモデル粒子系の結晶-ヘキサティックスメクティックB(HexB)-スメクティックA(SmA)相転移を調べた。それぞれの相におけるダイナミックスの観察にとどまらず、相対エントロピーや比熱などの熱力学量の考察も行った。熱力学的な平衡状態に相当するHexB相に加えて、複数の準安定状態が広い温度範囲にわたって見つかった。これらの準安定なHexB状態は、６回ボンド対称性の秩序変数が異なる離散的な値をとる。

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現在までに様々な格子生成法が提案されている. 中橋が提案した Building-Cube Method（BCM）は，物体適合格子法のひとつで， 簡易なアルゴリズムで格子が生成でき，精度のよいスキームを適応できる．また，計算領域を単純な規則に従って分割するので, 並列型電算機との相性がよいなどの特徴をもつ. 簡易な方法による格子生成は，複雑形状物体周りの流れの計算に有用である.
本発表では，基本的な流れ場のひとつである2次元円柱周りの数値シミュレーションを行い, BCMの有用性を確認する

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The Smoothed Particle Method is applied to the gas dynamics in the astrophysical problems and the radiative transfer problem for the direct visualization of gas flows. The fluid is treated as an ensemble of spatially extended Lagrangian particles, which have density distribution of the Gaussian kernel. The Smoothed Particle Hydrodynamics (SPH) describes the motion of each particle in the Lagrangian approach and then calculates the physical quantities from the distribution of particles. Hence SPH is particularly suited for the simulation of highly distorted flow. The Smoothed Particle Rendering (SPR) integrates the ray equation through the opaque medium and calculates the contribution of scattered light. The opacity represents the density scalar and the emissivity is derived by the temperature field. The validity of SPR indicates the possibility to simulate the radiation hydrodynamics. We will show four SPH applications visualized by SPR.

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The flow between concentric cylinders is numerically studied by means of a finite difference method. A third-order upwind scheme is applied to the advection terms of the Navier-Stokes equations. The outer cylinder is at rest and the inner cylinder rotates at a constant speed. The ratio of the radii of inner and outer cylinders is fixed at 1. 14 and the height of the cylinders, twenty times longer than the gap between the two concentric cylinders. Cyclic boundary condition is applied in the axial direction. The computation is carried out at the Reynolds numbers, 0. 92R_c, 1. 1R_c, 1. 5R_c and 2. 0R_c, where R_c is the theoretical critical Reynolds number of the Couette flow between the concentric cylinders of infinite length. In the present study, Couette flow is realized at the Reynolds number of 0. 92R_c and steady Taylor vortex flow is obtained for the cases with Re ≥ 1. 1R_c when impulsive start from the rest is employed. Wavy Taylor vortex flow is attained for the cases with 1. 5R_c and 2. 0R_c if small amplitude of random disturbances is added in the Taylor vortex flow solution as an initial condition. Present numerical results are in qualitative consistency with the previously reported studies, and this will give credence to the utilization of present numerical method.

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Reentrant liquid crystals are low ordered phases, which reappear at lower temperatures than that of higher ordered phases. We investigate the possibility of reentrant liquid crystals appearing when the volume is kept constant, even when the chemical interaction among the molecules are the same. The method of canonical hydrostatic molecular dynamics simulation is used for this purpose. Canonical hydrostatic simulation results are compared with simulation results of isobaric-isothermal ensemble. Reentrant smectic A and hexatic smectic phases appear in several model systems.

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Reentrant liquid crystals are low ordered phases, which reappear at lower temperatures than that of higher ordered phases. The possibility of reentrant liquid crystals appearing when the volume is kept constant is investigated, using the same interaction among all molecules. The method of canonical hydrostatic molecular dynamics simulation is used for this purpose. Canonical hydrostatic simulation results are compared with simulation results of isobaric-isothermal ensemble. Reentrant smectic A and hexatic smectic B phases appear in several model systems. Elastic instabilities and elastic oscillations in these systems are reported.

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