Authorship：Last author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)

DOI： 10.1299/jsmekyushu.2021.74.E44

CiNii Article

Other Link： https://ci.nii.ac.jp/naid/130008092373

Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)

Purpose: This paper aims to present an improved finite element method used for achieving faster convergence in simulations of incompressible fluid flows. For stable computations of incompressible fluid flows, it is important to ensure that the flow field satisfies the equation of continuity in each element of a generally distorted mesh. The study aims to develop a numerical approach that satisfies this requirement based on the highly simplified marker-and-cell (HSMAC) method and increases computational speed by introducing a new algorithm into the simultaneous relaxation of velocity and pressure. Design/methodology/approach: First, the paper shows that the classical HSMAC method is equivalent to a Jacobi-type method in terms of the simultaneous relaxation of velocity and pressure. Then, a Gauss–Seidel or successive over-relaxation (SOR)-type method is introduced in the Newton–Raphson iterations to take into account all the derivative terms in the first-order Taylor series expansion of a nodal-averaged error explicitly. Here, the nine-node quadrilateral (Q2–Q1) elements are used. Findings: The new finite element approach based on the improved HSMAC algorithm is tested on fluid flow problems including the lid-driven square cavity flow and the flow past a circular cylinder. The results show significant improvement of the convergence property with the accuracy of the numerical solutions kept unchanged even on a highly distorted mesh. Originality/value: To the best of the author’s knowledge, the idea of using the Gauss–Seidel or SOR method in the simultaneous relaxation procedure of the HSMAC method has not been proposed elsewhere.

DOI： 10.1108/EC-02-2019-0069

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Authorship：Last author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)

Three-dimensional numerical simulation of incompressible, magnetohydrodynamic flows under traveling magnetic fields are carried out, which takes into account the coupling with the electromagnetic field in the solid and gas regions. A numerical scheme is constructed by combining the Galerkin finite element method and the edge-element based finite element method, which are applied to the discretizations of Navier-Stokes equations and the electromagnetic field equations, respectively. The solution algorithm for fluid flow is based on an explicit fractional step approach and the simultaneous relaxation of velocity and pressure to satisfy the continuity equation. The electromagnetic field equations are formulated with the use of the magnetic vector potential which is defined on the edge elements. Numerical simulations of the MHD flows in an annular channel are carried out under traveling magnetic fields. It is confirmed that the magnitude and oscillation amplitude of the z-component of the velocity becomes larger with the increase in the Hartmann number. It is also shown that the frequency of the velocity pulsation is doubled than the frequency of the externally applied traveling magnetic field.

DOI： 10.1299/jsmecmd.2019.32.028

CiNii Article

Other Link： https://ci.nii.ac.jp/naid/130007817209

Authorship：Last author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)

In our previous work, a three-dimensional numerical scheme for analyzing magnetohydrodynamic (MHD) flows under alternating-current magnetic fields was constructed, which takes into account the coupling with the electromagnetic fields in the solid and gas regions. In this study, a periodic boundary condition and an external traveling-wave magnetic field are introduced into the numerical scheme to investigate the dependences of the MHD flow in a square duct on the Hartmann number and the phase velocity of the external magnetic field. It is shown that the flow in the axial direction is encouraged with the increase in the Hartmann number or the angular frequency, while an opposite behavior is observed in terms of the oscillation amplitude of the fluid flow.

DOI： 10.1299/jsmecmd.2019.32.103

CiNii Article

Other Link： https://ci.nii.ac.jp/naid/130007817254

Authorship：Last author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)

In this study, we investigate the stability required for a two-dimensional sloshing analysis with the use of an arbitrary Lagrangian–Eulerian (ALE) method. Here, two well-known upwind methods are employed for the discretization of the kinematic condition on the free surface: SUPG and CIP methods. On the other hand, the Navier-Stokes equations are discretized by a finite element scheme without any upwind method to see whether the stability is retained solely by introducing an appropriate upwind method into the calculation on the free surface. It is shown in both primary and tertiary modes that stable results are obtained when the CIP method is employed, while unstable grid-scale oscillations are observed at some point when the SUPG method is used. This suggests that a semi-Lagrangian scheme is essential for stable computation based on the ALE formulation.

DOI： 10.1299/jsmecmd.2019.32.073

CiNii Article

Other Link： https://ci.nii.ac.jp/naid/130007817141

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In ion cyclotron range of frequency (ICRF) experiments in fusion research devices, radio frequency (RF) sheaths form where plasma, strong RF wave fields and material surfaces coexist. These RF sheaths affect plasma material interactions such as sputtering and localized power deposition, as well as the global RF wave fields themselves. RF sheaths may be modeled by employing a sheath boundary condition (BC) in place of the more customary conducting wall (CW) BC; however, there are still many ICRF computer codes that do not implement the sheath BC. In this paper we present a method for post-processing results obtained with the CW-BC. The post-processing method produces results that are equivalent to those that would have been obtained with the RF sheath BC, under certain assumptions. The post-processing method is also useful for verification of sheath BC implementations and as a guide to interpretation and understanding of the role of RF sheaths and their interactions with the waves that drive them.

DOI： 10.1088/1361-6587/ab2f41

Kyutacar

Scopus

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Radio frequency (RF) sheaths form near surfaces where plasma and strong RF fields coexist. The effect of these RF sheaths on wave propagation near the boundary can be characterized by an effective sheath impedance that includes both resistive and capacitive contributions describing RF sheath rectification and RF power absorption in the sheath [J. R. Myra and D. A. D'Ippolito, Phys. Plasmas 22, 062507 (2015)]. Here, we define a dimensionless parameter, the ratio of incoming wave impedance to the sheath impedance, which determines the characteristics of the interaction, ranging from quasi-conducting to quasi-insulating, or in the case of matched impedances, to either perfect absorption or a sheath-plasma resonance. A semi-analytical analysis is carried out for electrostatic slow waves in the ion cyclotron range of frequencies. For the propagating slow wave case, where the incident wave is partially reflected, the fraction of power dissipated in the sheath is calculated. For the evanescent slow wave case, which admits a sheath-plasma resonance, an amplification factor is calculated. Using the impedance ratio approach, RF sheath interactions are characterized for a range of RF wave and plasma parameters including plasma density, magnetic field angle with respect to the surface, wave frequency, and wave-vector components tangent to the surface. For a particularly interesting example case, results are compared with the rfSOL code [H. Kohno and J. R. Myra, Comput. Phys. Commun. 220, 129 (2017)]. Finally, electromagnetic effects, absent from the semi-analytical analysis, are assessed.

DOI： 10.1063/1.5088343

Kyutacar

Scopus

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)

The physics of interactions between waves in plasmas and sheaths for background magnetic fields which make oblique angles with sheath surfaces is studied with the use of the self-consistent finite element code rfSOL incorporating the recently developed sheath impedance model [J. R. Myra, Phys. Plasmas 24, 072507 (2017)]. The calculation based on this model employs the generalized sheath boundary condition (sheath BC), which surpasses the previously used capacitive sheath BC in reliability by taking into account the contributions of the ion and electron currents in the sheath and the displacement current. A series of numerical simulations is carried out in two-dimensional slab geometry with a flat or curved sheath surface as part of the boundary. It is shown that the sheath-plasma wave appears when the equilibrium magnetic field line angle with respect to the sheath surface is small, the absolute value of the radio-frequency (RF) sheath voltage is large, and the plasma density is slightly higher than the lower hybrid resonance density (LHR density), all of which bring the sheath property closer to being capacitive. It is also shown that the sharp variation of the magnetic field line angle along the sheath surface can sensitively affect the maximum absolute value of the RF sheath voltage at a plasma density slightly lower than the LHR density.

DOI： 10.1063/1.5054920

Kyutacar

Scopus

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Authorship：Last author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)

Three-dimensional (3D) numerical simulation of incompressible, magnetohydrodynamic (MHD) flows under alternating-current (AC) magnetic fields are carried out, which takes into account the coupling with the electromagnetic fields in the solid and gas regions. A numerical scheme is constructed by combining the Galerkin finite element method and the edge-element based finite element method, which are applied to the discretizations of the Navier–Stokes equations and the electromagnetic field equations, respectively. The solution algorithm for fluid flow is based on an explicit fractional step approach and the simultaneous relaxation of velocity and pressure to satisfy the continuity equation. The electromagnetic field equations are formulated with the use of the magnetic vector potential which is defined on the edge elements. In the proposed numerical scheme, the advection term in the induction equation is not neglected, because the scheme needs to deal with the condition where the advection term is the same order with the diffusion term in that equation. The validity of the numerical scheme is verified through the analysis of the electromagnetic field under a direct-current magnetic field, and numerical simulations of the MHD flows under spatially uniform AC magnetic fields are carried out. It is confirmed that the spatio-temporal mean Lorentz force in the conducting fluid becomes weaker with the increase in the dimensionless frequency due to the skin effect. It is also shown that the flow pattern in a hexahedral closed domain is largely changed when the frequency is getting higher, which is associated with the change in the Lorentz force profile.

DOI： 10.1299/transjsme.17-00589

CiNii Article

Other Link： https://ci.nii.ac.jp/naid/130007419065

Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)

A finite element code that solves self-consistent radio-frequency (RF) sheath-plasma interaction problems is improved by incorporating a generalized sheath boundary condition in the macroscopic solution scheme. This sheath boundary condition makes use of a complex sheath impedance including both the sheath capacitance and resistance, which enables evaluation of not only the RF voltage across the sheath but also the power dissipation in the sheath. The newly developed finite element procedure is applied to cases where the background magnetic field is perpendicular to the sheath surface in one- and two-dimensional domains filled by uniform low- and high-density plasmas. The numerical results are compared with those obtained by employing the previous capacitive sheath model at a typical frequency for ion cyclotron heating used in fusion experiments. It is shown that for sheaths on the order of 100 V in a high-density plasma, localized RF power deposition can reach a level which causes material damage. It is also shown that the sheath-plasma wave resonances predicted by the capacitive sheath model do not occur when parameters are such that the generalized sheath impedance model substantially modifies the capacitive character of the sheath. Possible explanations for the difference in the maximum RF sheath voltage depending on the plasma density are also discussed.

DOI： 10.1016/j.cpc.2017.06.025

Scopus

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For applications of ICRF power in fusion devices, control of RF sheath interactions is of great importance. A sheath boundary condition (SBC) was previously developed to provide an effective surface impedance for the interaction of the RF sheath with the waves. The SBC enables the surface power flux and rectified potential energy available for sputtering to be calculated. For legacy codes which cannot easily implement the SBC, or to speed convergence in codes which do implement it, we consider here an approximate method to simulate SBCs by post-processing results obtained using other, e.g. conducting wall, boundary conditions. The basic approximation is that the modifications resulting from the generalized SBC are driven by a fixed incoming wave which could be either a fast wave or a slow wave. The method is illustrated in slab geometry and compared with exact numerical solutions; it is shown to work very well.

DOI： 10.1051/epjconf/201715703037

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A new mixed-interpolation finite element method is presented for the two-dimensional numerical simulation of incompressible magnetohydrodynamic (MHD) flows which involve convective heat transfer. The proposed method applies the nodal shape functions, which are locally defined in nine-node elements, for the discretization of the Navier–Stokes and energy equations, and the vector shape functions, which are locally defined in four-node elements, for the discretization of the electromagnetic field equations. The use of the vector shape functions allows the solenoidal condition on the magnetic field to be automatically satisfied in each four-node element. In addition, efficient approximation procedures for the calculation of the integrals in the discretized equations are adopted to achieve high-speed computation. With the use of the proposed numerical scheme, MHD channel flow and MHD natural convection under a constant applied magnetic field are simulated at different Hartmann numbers. The accuracy and robustness of the method are verified through these numerical tests in which both undistorted and distorted meshes are employed for comparison of numerical solutions. Furthermore, it is shown that the calculation speed for the proposed scheme is much higher compared with that for a conventional numerical integration scheme under the condition of almost the same memory consumption.

DOI： 10.1002/fld.4292

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Authorship：Last author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)

DOI： 10.1299/jsmekyushu.2017.70.817

CiNii Article

Other Link： https://ci.nii.ac.jp/naid/130007099690

Authorship：Last author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)

DOI： 10.1299/jsmekyushu.2017.70.816

CiNii Article

Other Link： https://ci.nii.ac.jp/naid/130007099749

Authorship：Last author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)

DOI： 10.1299/jsmekyushu.2017.70.818

CiNii Article

Other Link： https://ci.nii.ac.jp/naid/130007099682

Authorship：Last author   Language：English   Publishing type：Research paper (international conference proceedings)

Japan   Kyoto   2016.10.17  -  2016.10.22

Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)

DOI： 10.1063/1.4960384

Scopus

Authorship：Last author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)

Other Link： http://ci.nii.ac.jp/naid/110010054798

Authorship：Last author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)

Other Link： http://ci.nii.ac.jp/naid/110010054797

Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)

A new finite element method is presented for use of quadrilateral nine-node elements in the solution of the incompressible Navier-Stokes equations. In a conventional predictor-corrector scheme, the method applies the nodal averaging technique to discretize the Poisson equation used for the simultaneous relaxation of velocity and pressure. Additionally, efficient approximation procedures are devised to increase the speed of computation without deteriorating solution accuracy. The proposed numerical schemes are evaluated on two-dimensional test problems including a classical lid-driven cavity flow and a flow over a backward-facing step in a flow channel. The results show good accuracy even when distorted elements are used for calculation.

DOI： 10.1016/j.cpc.2015.05.002

Scopus

Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)

Interactions between propagating fast waves and radio-frequency (RF) sheaths in the ion cyclotron range of frequencies are numerically investigated based on a cold fluid plasma model coupled with a sheath boundary condition. In this two-dimensional study, the capability of the finite element code rfSOL, which was developed in previous numerical work, is extended to analyze self-consistent RF sheath-plasma interaction problems in a tokamak with a non-circular cross-section. It is found that a large sheath voltage is generated near the edges of the limiter-shaped deformation as a result of the conversion from fast to slow waves on the sheaths. The sheath voltage associated with this conversion is particularly significant in the localized region where the contact angle between the magnetic field line and the conducting wall varies rapidly along the curved sheath surface, which is consistent with the results in previous one-dimensional theoretical work. The dependences of the RF sheaths on various parameters in plasma such as the toroidal wavenumber, edge plasma density, and the degree of the RF wave absorption in the core region are also examined in detail.

DOI： 10.1063/1.4926449

Scopus

Authorship：Last author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)

DOI： 10.1299/jsmekyushu.2015.68.3

CiNii Article

CiNii Research

Other Link： https://ci.nii.ac.jp/naid/130006576105

Authorship：Last author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)

DOI： 10.1299/jsmekyushu.2015.68.1

CiNii Article

CiNii Research

Other Link： https://ci.nii.ac.jp/naid/130006575966

Language：English   Publishing type：Research paper (scientific journal)

A level set method is applied to characterize the three dimensional structures of nickel, yttria stabilized zirconia and pore phases in solid oxide fuel cell anode reconstructed by focused ion beam-scanning electron microscope. A numerical algorithm is developed to evaluate the contact angles at the triple phase boundary based on interfacial normal vectors which can be calculated from the signed distance functions defined for each of the three phases. Furthermore, surface tension force is estimated from the contact angles by assuming the interfacial force balance at the triple phase boundary. The average contact angle values of nickel, yttria stabilized zirconia and pore are found to be 143°-156°, 83°-138° and 82°-123°, respectively. The mean contact angles remained nearly unchanged after 100 hour operation. However, the contact angles just after reduction are different for the cells with different sintering temperatures. In addition, standard deviations of the contact angles are very large especially for yttria stabilized zirconia and pore phases. The calculated surface tension forces from mean contact angles were close to the experimental values found in the literature. Slight increase of surface tensions of nickel/pore and nickel/yttria stabilized zirconia were observed after operation. Present data are expected to be used not only for the understanding of the degradation mechanism, but also for the quantitative prediction of the microstructural temporal evolution of solid oxide fuel cell anode.

DOI： 10.1016/j.matchar.2014.07.020

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ICRF waves can sometimes interact with plasma-facing surfaces in tokamak fusion experiments causing degradation of core heating efficiency, impurity injection and even component damage. While presently available low dimensionality if sheath models are useful in understanding many features of these interactions, more quantitative modeling will require attention to realistic geometrical details of the boundary plasma and surfaces. In this paper, we explore the situation in which there exists a tangency point of the background magnetic field with a surface. We find that the rf interactions are strongly influenced by the generation and propagation of sheath-plasma waves (SPW) along the surface. It is found that these waves preferentially propagate towards, and accumulate at, a convex tangency point. An analytical theory of SPW propagation is developed to understand these features.

DOI： 10.1063/1.4864553

Authorship：Lead author   Language：English   Publishing type：Research paper (international conference proceedings)

Understanding the detailed physicochemical mechanisms for the electro-oxidation of fuel at the triple phase boundaries (TPBs) in solid oxide fuel cell (SOFC) anodes is a key step towards improving SOFC performance. Significant efforts have been directed toward this goal via both experimental and computational modeling studies. In particular, patterned Ni anode on a planar YSZ substrate has been examined because of its well-defined two-dimensional geometry that in principle offers the advantages of known TPB length and minimization of mass transport effects. A common formulation for such patterned anodes considers modeling of surface reactions and diffusion on both electrode and electrolyte surfaces, along with charge-transfer reactions at the TPBs based on elementary kinetics. In this study, we review the theoretical approaches proposed by several authors and offer a critique of their methods.

DOI： 10.1149/05701.2821ecst

Scopus

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Employing reactive molecular dynamics simulation, we investigated diffusion pathways of H-atoms into the bulk from the Ni(100) surface. We found that surface pathway is dominant compared to bulk pathway for H atoms diffusion. Our simulation suggests that H atoms can diffuse into the bulk Ni. From 973 to 1273 K, H atoms migration into bulk is observed, but number of H atom is influenced by the temperature. At 1273 K, 30 % H atoms move into the bulk region. Diffusion barrier of H into bulk is calculated higher than the surface pathway. Diffusion coefficient of H between bulk and surface pathway is calculated to be one order of magnitude discrepancy.

DOI： 10.1149/05701.2649ecst

Language：English   Publishing type：Research paper (international conference proceedings)

High SOFC operating temperature allows direct internal reforming (DIR) of methane within the SOFC anode. However, carbon formation reduces considerably the performance and durability of the cells. A key step towards improving SOFC performance is to understand the detailed surface kinetics and electrochemistry for DIR of methane at the triple phase boundaries (TPBs) in SOFC anodes. In this study, we have performed kinetic simulations with a numerical model on Ni pattern anode, combined with surface reactions, charge transfer reactions, and diffusions for DIR of methane. The I-V characteristics of SOFC near TPBs are discussed.

DOI： 10.1149/05701.2865ecst

Language：English   Publishing type：Research paper (international conference proceedings)

Microstructural change of porous electrodes in SOFC caused by sintering affected by materials and impurities is one of the main factors of the long-term degradation. Since it is difficult to clarify the effects of materials and impurities on sintering by experiments, atomistic scale simulation is important. In this study, we performed molecular dynamics (MD) simulation of porous structure of Ni and analyzed sintering properties of porous structure by employing master sintering curve theory. We have succeeded to obtain the sintering activation energy and its size dependency and to identify the dominant sintering mechanism by comparing sintering activation energy with activation energy of surface diffusion on each facet.

DOI： 10.1149/05701.1407ecst

Language：English   Publishing type：Research paper (international conference proceedings)

The anodic reactions of solid oxide fuel cells are examined by density functional theory method under different oxygen coverage on the Ni(111) surface. The oxidation reactions H, OH and CO are calculated and the reaction barriers are affected by the oxygen potential. The concept of oxygen potential is introduced to discuss the effect of the surface chemical potential to the oxidation reactions. The results are valuable for estimating the reaction rate of anodic reactions under different oxygen potential near the anodic three phase boundary.

DOI： 10.1149/05701.2429ecst

Language：English   Publishing type：Research paper (international conference proceedings)

We analyzed the dependence of X-ray absorption spectra for Co 2p orbital of LaCoO3 on the Hubbard U and lattice parameters by using the density functional theory (DFT) method. The X-ray absorption spectra and partial density of states (PDOS) are studied with the different U parameters ranging from 2.5 to 7.8. The characteristic peak position of X-ray absorption spectra is also investigated for different structures: i.e., the O atom positions assuming the displacement by thermal vibrations, the lattice expansion and the crystalline lattice distortion. The effect of the above parameters on the X-ray absorption spectra are discussed on the basis of theoretical calculation results.

DOI： 10.1149/05701.2655ecst

Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)

Computer simulations of radio-frequency (RF) waves propagating across a two-dimensional (2D) magnetic field into a conducting boundary are described. The boundary condition for the RF fields at the metal surface leads to the formation of an RF sheath, which has previously been studied in one-dimensional models. In this 2D study, it is found that rapid variation of conditions along the sheath surface promote coupling of the incident RF branch (either fast or slow wave) to a short-scale-length sheath-plasma wave (SPW). The SPW propagates along the sheath surface in a particular direction dictated by the orientation of the magnetic field with respect to the surface, and the wave energy in the SPW accumulates near places where the background magnetic field is tangent to the surface.

DOI： 10.1063/1.4818991

Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)

We present a novel numerical method for solving the advection equation for a level set function. The new method uses hierarchical-gradient truncation and remapping (H-GTaR) of the original partial differential equation (PDE). Our strategy reduces the original PDE to a set of decoupled linear ordinary differential equations with constant coefficients. Additionally, we introduce a remapping strategy to periodically guarantee solution accuracy for a deformation problem. The proposed scheme yields nearly an exact solution for a rigid body motion with a smooth function that possesses vanishingly small higher derivatives and calculates the gradient of the advected function in a straightforward way. We will evaluate our method in one- and two-dimensional domains and present results to several classical benchmark problems.

DOI： 10.1016/j.cpc.2013.02.002

Scopus

Language：English   Publishing type：Research paper (international conference proceedings)

The prediction of long-term durability of SOFC anode is important to understand the sintering phenomena in the anode, which are affected by microstructure, materials, and impurities. To understand the sintering phenomena considering the effects of materials and chemical species, molecular dynamics (MD) simulation is one of the most effective computational methods. In this study, we developed a theoretical methodology based on the master sintering curve to analyze the sintering property. We performed MD simulation for the densification of both Ni and YSZ porous structures. The sintering activation energy obtained from our proposed method was in reasonable agreement with the experimental result.

DOI： 10.1149/05030.0001ecst

Language：English   Publishing type：Research paper (scientific journal)

DOI： 10.2477/jccj.2012-0017

Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)

A numerical code that solves self-consistent radio-frequency (RF) sheath-plasma interactions in the ion cyclotron range of frequencies is developed based on a nonlinear finite element technique. The present code solves for plasma waves based on the cold plasma model subject to a sheath boundary condition. The finite element procedure has been implemented for one- and two-dimensional analyses using simplified models for the poloidal plane of a tokamak. The results show good accuracy and generalize previous analytical calculations. The present algorithmic approach shows promise for developing a code to predict RF sheath potentials in the scrape-off layer of RF-heated fusion experiments.

DOI： 10.1016/j.cpc.2012.05.014

Scopus

Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)

A new finite element numerical scheme for analyzing self-consistent radio-frequency (RF) sheath-plasma interaction problems in the ion cyclotron range of frequencies is applied to various problems represented by simplified models for the tokamak scrape-off layer. The present code incorporates a modified boundary condition, which is called a sheath boundary condition, that couples the radio-frequency waves and sheaths at the material boundaries by treating the sheath as a thin vacuum layer. A series of numerical analyses in one- and two-dimensional domains show several important physical properties, such as the existence of multiple roots, hysteresis effects, presence and characteristics of the sheath-plasma waves, and the phase shift of a reflected slow wave, some of which are newly identified by introducing a spatially varying plasma density and background magnetic field.

DOI： 10.1063/1.3677262

Scopus

Language：English   Publishing type：Research paper (international conference proceedings)

A new quantitative approach for computing the rf sheath potential is described, which incorporates plasma dielectric effects and the relative geometry of the magnetic field and the material boundaries. The new approach uses a modified boundary condition ("rf sheath BC") that couples the rf waves and the sheaths at the boundary. It treats the sheath as a thin vacuum region and matches the fields across the plasma-vacuum boundary. When combined with the Child-Langmuir Law (relating the sheath width and sheath potential), the model permits a self-consistent determination of the sheath parameters and the rf electric field at the sheath-plasma boundary. Semi-analytic models using this BC predict a number of general features, including a sheath voltage threshold, a dimensionless parameter characterizing rf sheath effects, and the existence of sheath plasma waves with an associated resonance. Since the sheath BC is nonlinear and dependent on geometry, computing the sheath potential numerically is a challenging computational problem. Numerical results will be presented from a new parallel-processing finite-element rf wave code for the tokamak scrape-off layer (called "rfSOL"). The code has verified the physics predicted by analytic theory in 1D, and extended the solutions into model 2D geometries. The numerical calculations confirm the existence of multiple roots and hysteresis effects, and parameter studies have been carried out. Areas for future work will be discussed.

DOI： 10.1063/1.3664959

Scopus

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A finite element wave-packet procedure is presented to solve problems of wave propagation in multiscale behavior. The proposed scheme combines the advantages of the finite element and spectral methods. The basic formulation is presented, and the capabilities of the procedure are demonstrated through the solution of some illustrative problems, including a problem that characterizes the mode-conversion behavior in plasmas.

DOI： 10.1016/j.compstruc.2009.05.001

Scopus

Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)

In this paper the interfacial instability in aluminium reduction cells under a uniform, vertical magnetic field is investigated by means of numerical simulation. Shallow-water equations governing the wave motion and the electric field at the interface between two electrically conducting fluids are discretized using a finite element scheme which employs quadratic interpolation functions. For a sufficiently high magnetic field, it is observed that one global maximum and one global minimum of the interface elevation are formed in closed symmetrical and asymmetrical domains irrespective of shape. By taking account of this, an asymptotic expression for the evaluation of the growth rate and the frequency of instability is constructed. The effectiveness of the proposed model is validated through comparison with the numerical results.

DOI： 10.1016/j.ijengsci.2007.03.016

Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)

Interfacial instability in a two-fluid system under a vertical magnetic field with a transverse gradient to the sidewall is studied with reference to aluminium reduction cells. Analytical, asymptotic and numerical solutions are obtained for the semi-bounded domain. It is shown that for the magnetic field increasing from a sidewall instability is dominated by the boundary mode, as for the uniform field. In contrast, for the magnetic field decreasing from the sidewall, the most unstable mode is determined mainly by the gradient of the magnetic field.

DOI： 10.1016/j.physleta.2006.12.074

Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)

We propose a nine-node flow-condition-based interpolation (FCBI) finite element for the analysis of 2D incompressible flows. Emphasis in the FCBI approach is on obtaining an element that is stable and can be used in rather coarse meshes even when considering high Reynolds number flows. The formulation of the element is presented and the results obtained in the solution of some test cases are given.

DOI： 10.1002/cnm.861

Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)

A flow-condition-based interpolation finite element scheme is presented for use of triangular grids in the solution of the incompressible Navier-Stokes equations. The method provides spatially isotropic discretizations for low and high Reynolds number flows. Various example solutions are given to illustrate the capabilities of the procedure.

DOI： 10.1002/fld.1246

Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)

The flow-condition-based interpolation (FCBl) finite element approach is Studied in the solution of advection-diffusion problems. Two FCBI procedures are developed and tested with the original FCBI method: in the first scheme, a general solution of the advection-diffusion equation is embedded into the interpolation, and in the second scheme, the link-cutting bubbles approach is used in the interpolation. In both procedures, as in the original FCBI method, no artificial parameters are included to reach stability for high Peclet number flows. The procedures have been implemented for two-dimensional analysis and the results of some test problems are presented. These results indicate good stability and accuracy characteristics and the potential of the FCBI Solution approach.

DOI： 10.1002/nme.1276

Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)

This paper presents an efficient numerical scheme for the analysis of coupled natural and Marangoni convection encouraged by the thermal radiation. The novel feature of the proposed algorithm is the introduction of the jump quantity on the free surface into the boundary integration term in the Navier-Stokes equation discretized by the finite element method (FEM). In addition, the generalized simplified marker and cell (GSMAC) method is applied to the solution of the velocity field, which realizes high-speed computation. In order to verify the validity of the present scheme, two-dimensional (2D) and three-dimensional (3D) numerical simulation of coupled natural and Marangoni convection in a square cavity is performed for a wide range of Marangoni number and Grashof number: Numerical results obtained here are in good agreement with the experimental data, and the dominance of Marangoni convection is clearly shown with the increase of Marangoni number.

DOI： 10.1080/10618560500032764

Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)

Numerical simulation of the thermal melt flow coupled with moving melt/solid interfaces in the floating zone (FZ) method under low gravity is carried out. The novel feature of the proposed algorithm is the application of the arbitrary Lagrangian-Eulerian (ALE) method to the moving melt/solid interface problem. The governing equations are discretized by the finite element method (FEM), and the velocity field is solved by the generalized simplified marker and cell (GSMAC) method. The developed scheme is employed to investigate the two-dimensional (2D) melt flow and melt/solid interface shapes in various conditions of gravity and surface tension. Through computation, it is revealed that the melt/solid interface shape is greatly affected by the flow configuration and the intensity of convection, Moreover, coupled natural and Marangoni convection reduces the stability of the melt zone; for the conditions in the present study, the flow configuration and the melt/solid interface shape are suddenly changed as soon as natural convection is merged into Marangoni convection as a consequence of increased gravity. The usefulness of the transverse magnetic field in control of the melt flow is also clarified through the comparison with the vertical magnetic field.

DOI： 10.1080/10618560500032772

Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)

A novel numerical scheme for the analysis of large deformation of electrically conducting liquid under alternating current magnetic fields is presented. The main features are characterized by two numerical tools; the level set method to calculate deformed free surface stably and the hybrid finite element method and boundary element method to discretize the electromagnetic field efficiently. Two-dimensional numerical simulation of conducting drop deformation is carried out to demonstrate the effectiveness of the present scheme, and the oscillatory behaviour, which depends on the magnitude of surface tension and Lorentz force, is investigated.

DOI： 10.1002/fld.793

Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)

A novel numerical scheme is developed by coupling the level set method with the adaptive mesh refinement in order to analyse moving interfaces economically and accurately. The finite element method (FEM) is used to discretize the governing equations with the generalized simplified marker and cell (GSMAC) scheme, and the cubic interpolated pseudo-particle (CIP) method is applied to the reinitialization of the level set function. The present adaptive mesh refinement is implemented in the quadrangular grid systems and easily embedded in the FEM-based algorithm. For the judgement on renewal of mesh, the level set function is adopted as an indicator, and the threshold is set at the boundary of the smoothing band. With this criterion, the variation of physical properties and the jump quantity on the free surface can be calculated accurately enough, while the computation cost is largely reduced as a whole. In order to prove the validity of the present scheme, two-dimensional numerical simulation is carried out in collapse of a water column, oscillation and movement of a drop under zero gravity. As a result, its effectiveness and usefulness are clearly shown qualitatively and quantitatively. Among them, the movement of a drop due to the Marangoni effect is first simulated efficiently with the present scheme.

DOI： 10.1002/fld.715

Authorship：Lead author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)

A novel numerical scheme for the analysis of conducting fluid flow under the alternating current magnetic field is presented. In this scheme, the large deformation problem of a free surface is stably calculated by using the level set method, and the computation of the electromagnetic field is economically carried out by discretizing the governing equations formulated by the A - φ method with hybrid FEM-BEM. With this scheme, the deformation problem of a silicon liquid bridge is analyzed in the non-gravity field. As a result, it is confirmed numerically that the deformation caused by the Lorentz force depends on the relative coil position, number of turns, and the magnitude of surface tension. Moreover, in the real condition, it is observed that the deformation of the free surface is kept small, which corresponds to the theory.

DOI： 10.1299/kikaib.69.1746

Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)

The characteristics of the melt convection and the melt deformation process in two crystal growth techniques, Czochralski (CZ) and floating zone (FZ) methods, are investigated with three-dimensional numerical simulation using generalized simplified marker and cell-finite element method (GSMAC-FEM). Large eddy simulation (LES) with the Smagorinsky model is applied to calculate the melt convection with high Rayleigh numbers in the CZ method, and level set method (LSM) is adopted for the computation of liquid bridge deformation. First, the CZ (LSM) melt convections are investigated with the boundary conditions in terms of the free surface and the rotational rate changed. As a result, it is found that the heat radiation and the Marangoni effect on the free surface encourage the instability of flows, and the Coriolis' force can largely suppress the natural convection. Second, a series of simulations in terms of liquid bridge deformation are carried out with the coil position, coil shape, and the magnitude of surface tension varied. After that, it turns out that those are important factors in the melt shape. Moreover, it is proved numerically that the deformation of the liquid bridge is kept small by the skin effect and large surface tension in the real FZ crystal growth.

DOI： 10.1016/S0377-0427(02)00543-5

Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)

DOI： 10.1007/BF03182323

Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)

Three-dimensional numerical simulations in the large-scale CZ method are carried out to investigate the complicated melt flow. Large Eddy Simulation (LES) is adopted to calculate unsteady, turbulent buoyancy-driven flow fields. When the crucible and the crystal keep static, the melt flow becomes non-axisymmetrical as the temperature of the crucible wall increases because of the instability of the potential energy, and finally it turns out to be turbulent. The oscillation of velocity in the circumferential direction is also observed near the free surface, and it causes the mode transition in the temperature field. On the other hand, when the crucible and the crystal rotate constantly, the natural convection driven by the buoyancy is greatly suppressed because of the large magnitude of Coriolis' force, and the forced convection dominates the flow field.

DOI： 10.1299/kikaib.68.1044

Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)

This paper presents an improved level set method (LSM) for the analysis of a free surface deformed in an alternating current magnetic field. Three-dimensional numerical simulations are carried out based on the generalized simplified marker and cell-finite element method (GSMAC-FEM) algorithm to investigate the deformation processes of a Silicon liquid bridge similar to the floating zone (FZ) configuration with the coil position, width. and the magnitude of surface tension changed Under microgravity. The A-phi method is adopted to calculate the physical quantities of the magnetic field, and it is solved by the hybrid finite element method-boundary element method (FEM-BEM). The liquid part at the coil position becomes largely squeezed by the Lorentz force if the magnitude of surface tension is small. and the radius of a liquid bridge varies when a coil moves from the Upper position in height to the middle one. However. the deformation becomes greatly suppressed if the magnitude of surface tension is large because the outward force in proportion to the magnitude of curvature increases. From these results. it is expected that the deformation quantity of a liquid bridge will be rather small in the real FZ process because of large surface tension and a high frequency which causes the skin effect.

DOI： 10.1016/S0022-0248(01)02206-0

Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)

This paper presents the hybrid finite element and boundary element method (FEM-BEM) with a level set method (LSM) for the analysis of a free surface deformed in the alternating current magnetic field. Three-dimensional numerical simulations In the floating zone (FZ) method under microgravity are carried out to investigate the deformation process of a silicon liquid bridge with two types of coil positions, the upper case and the middle case. The results clearly show the deformation processes. The liquid parts which are the same position as each coil yield to pressure caused by strong Lorentz force and both ends swell out. This phenomenon conforms well to behavior of melt in the real growing process qualitatively.

DOI： 10.1299/kikaib.67.1408

Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)

Three-dimensional (3D) unsteady numerical simulations are carried out by means of the finite element method (FEM) with the generalized simplified marker and cell (GSMAC) method in silicon melt with a non-deformable free surface with Prandtl number Pr = 1.8534 x 10(-2), Marangoni number Ma = 0.0 - 6.2067 x 10(2), Grashof number Gr = 7.1104 x 10(6), and the aspect ratio As = 1.0 in the Czochralski (CZ) method. The flow state becomes unstable earlier by increasing the absolute value of the thermal coefficient of surface tension in the range of sigma (T) = 0.0 - 1.5 x 10(-5)N/mK. Although the velocity distribution in the circumferential direction is isotropy in any direction first, its magnitude becomes periodic and has the wavelength equal to 1/8 of the circumference. Then the wavelength doubles, and the flow pattern becomes finally asymmetrical. Moreover, the oscillation of the velocity distribution is observed just under the single crystal, and the amplitude is found to depend on the value of sigma (T). After imposing the vertical magnetic field more than 0.05T to the melt from 50s, the flow pattern becomes restored to symmetry. But the instability remains under the single crystal and it indicates that the influence of Marangoni convection can not be neglected in the crystal growing process.

DOI： 10.3970/cmes.2001.002.155

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1年次必修科目「基礎物理学・同演習」の講義が選出され，表彰