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Attitude control for small satellites is crucial to enable high value missions. Active attitude control is challenging for nanosatellites, due to their small mass and power budgets. On the other hand, the air in low Earth orbit is a promising resource for passive aero-stabilisation of a satellite's orientation. Potential has increased with the development of miniaturised deployable aeroshells for atmospheric entry. The EGG nanosatellite, released into space from the ISS in 2017, is one example of an aeroshell-equipped satellite with no means of active attitude control. Flight data from the EGG mission is a convenient resource to evaluate the concept of passive aero-stabilisation. In this work, a comprehensive coupled atmosphere-orbit-attitude simulation platform for small satellites was developed. The objectives are: (i) to validate the simulation against EGG mission data, and (ii) to evaluate the impact of attitude disturbances on robustness of passive aero-stabilisation. The results provide qualitative validation of the simulation platform, and show that passive attitude control with aeroshell deployed is highly sensitive to initial spin and spacecraft geometric asymmetry. These findings suggest the need for hybrid active control to turn aeroshell-equipped capsules into a viable means of trans-atmospheric transport.
Maximilien Berthet; Kazuhiko Yamada; Yasunori Nagata; Kojiro Suzuki. Feasibility assessment of passive stabilisation for a nanosatellite with aeroshell deployed by orbit-attitude-aerodynamics simulation platform. Acta Astronautica 2020, 173, 266 -278.
AMA StyleMaximilien Berthet, Kazuhiko Yamada, Yasunori Nagata, Kojiro Suzuki. Feasibility assessment of passive stabilisation for a nanosatellite with aeroshell deployed by orbit-attitude-aerodynamics simulation platform. Acta Astronautica. 2020; 173 ():266-278.
Chicago/Turabian StyleMaximilien Berthet; Kazuhiko Yamada; Yasunori Nagata; Kojiro Suzuki. 2020. "Feasibility assessment of passive stabilisation for a nanosatellite with aeroshell deployed by orbit-attitude-aerodynamics simulation platform." Acta Astronautica 173, no. : 266-278.
The compressible and non-expanding (CNE) fluid model was applied to the numerical simulation of the high-speed impact of the regolith-like granular material. Assuming the different speeds of sound for the irreversible compression and reversible elastic unload/recompression processes, this model can describe the following features: (1) high-density fluid remains after all the motion stops, (2) the absence of the fluid, that is, the vacuum is allowed to exist, and (3) the crack can be formed in place of the expansion wave. The fundamental solutions of the Riemann problem, which are necessary for Godunov’s method, are composed of the shock waves in the elastic process, the shock waves with the irreversible compression, the contact discontinuities, and the contact surfaces with the vacuum. The shock wave in the elastic process appears as the precursor to the irreversible compression. The numerical results of the one-dimensional regolith-on-regolith impact problems revealed that the phenomena are divided into the penetration stage and the bounce back stage. The ejection velocity decreases with the increase in the speed of sound for the unload process. In the two-dimensional oblique shock wave problems, the two-stage shock wave structure composed of the precursor wave and the irreversible compression wave was numerically simulated, and the relation between the wedge angle and the wave angles was obtained.
K. Suzuki. Application of Riemann Solver for Compressible and Non-Expanding Fluid to Impact on Regolith. 31st International Symposium on Shock Waves 2 2019, 343 -350.
AMA StyleK. Suzuki. Application of Riemann Solver for Compressible and Non-Expanding Fluid to Impact on Regolith. 31st International Symposium on Shock Waves 2. 2019; ():343-350.
Chicago/Turabian StyleK. Suzuki. 2019. "Application of Riemann Solver for Compressible and Non-Expanding Fluid to Impact on Regolith." 31st International Symposium on Shock Waves 2 , no. : 343-350.
This paper describes the world's first successful simulation for lateral cutoff phenomena of sonic boom far from the flight path due to variation in atmospheric temperature with altitude. A flow field around an axi-symmetric paraboloid has been analyzed by the full-field simulation method that solves the three-dimensional Euler equations with a gravity term to create a horizontally stratified atmosphere. A solution-adapted structured grid is constructed to align the grid lines with the front and rear shock-wave surfaces in the entire domain, including the near field around a supersonic body and far field reaching the ground beyond lateral cutoff. The flight is assumed to have a speed of Mach 1.2 at an altitude of 10 km, and the computational domain ranges over a distance of 30 km from the axis of symmetry. The computational results show that the evanescent wave in the shadow zone beyond lateral cutoff decays exponentially and changes into a progressive rounding waveform. The characteristics of the waveform transition are in good agreement with those observed in the flight tests. Therefore, the full-field simulation is recognized as a promising approach for investigating sonic boom strength in the full extent of sonic boom noise, including lateral cutoff and evanescent waves. Moreover, the computational results clarify that sonic boom focusing occurs above the ground, except for the vicinity of the ground, and the focusing strength along the lateral cutoff curve detected from the three-dimensional shock-wave surface increases with altitude. The results of ray tracing analysis collaborate the reasonability of the simulation results, and the caustic of downward convex agrees well with the lateral cutoff curve. In the shadow zone, the magnitude of exponential decay increases with altitude, and the lateral distance where the pressure rise decreases rapidly shortens with altitude.
Rei Yamashita; Kojiro Suzuki. Lateral cutoff analysis of sonic boom using full-field simulation. Aerospace Science and Technology 2019, 88, 316 -328.
AMA StyleRei Yamashita, Kojiro Suzuki. Lateral cutoff analysis of sonic boom using full-field simulation. Aerospace Science and Technology. 2019; 88 ():316-328.
Chicago/Turabian StyleRei Yamashita; Kojiro Suzuki. 2019. "Lateral cutoff analysis of sonic boom using full-field simulation." Aerospace Science and Technology 88, no. : 316-328.
Hisaichi Shibata; Yasumasa Watanabe; Ryosuke Yano; Kojiro Suzuki. Numerical Study on Fundamental Characteristics of Electro-Hydrodynamic Thruster for Mobility in Planetary Atmosphere. TRANSACTIONS OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES, AEROSPACE TECHNOLOGY JAPAN 2014, 12, 1 .
AMA StyleHisaichi Shibata, Yasumasa Watanabe, Ryosuke Yano, Kojiro Suzuki. Numerical Study on Fundamental Characteristics of Electro-Hydrodynamic Thruster for Mobility in Planetary Atmosphere. TRANSACTIONS OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES, AEROSPACE TECHNOLOGY JAPAN. 2014; 12 (ists29):1.
Chicago/Turabian StyleHisaichi Shibata; Yasumasa Watanabe; Ryosuke Yano; Kojiro Suzuki. 2014. "Numerical Study on Fundamental Characteristics of Electro-Hydrodynamic Thruster for Mobility in Planetary Atmosphere." TRANSACTIONS OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES, AEROSPACE TECHNOLOGY JAPAN 12, no. ists29: 1.
Ryosuke Yano; Kojiro Suzuki. Uniform shear flow under thermally relativistic limit: Case of zero Lorentz contraction. Physica A: Statistical Mechanics and its Applications 2013, 392, 4222 -4230.
AMA StyleRyosuke Yano, Kojiro Suzuki. Uniform shear flow under thermally relativistic limit: Case of zero Lorentz contraction. Physica A: Statistical Mechanics and its Applications. 2013; 392 (19):4222-4230.
Chicago/Turabian StyleRyosuke Yano; Kojiro Suzuki. 2013. "Uniform shear flow under thermally relativistic limit: Case of zero Lorentz contraction." Physica A: Statistical Mechanics and its Applications 392, no. 19: 4222-4230.
The autocorrelation of density fluctuations for thermally relativistic fluids is formulated on the basis of the relativistic Navier-Stokes-Fourier equation under the static equilibrium state. The autocorrelation of density fluctuations for thermally relativistic fluids, obtained theoretically, is compared with the autocorrelation of density fluctuations for thermally relativistic fluids, calculated using the stochastic relativistic Boltzmann equation on the basis of the direct simulation Monte Carlo method. The theoretical result of the autocorrelation of density fluctuations for thermally relativistic fluids on the basis of the relativistic Navier-Stokes-Fourier equation gives good agreement with the numerical result of the autocorrelation of density fluctuations for thermally relativistic fluids in the lowest wave number, because we calculated the autocorrelation of density fluctuations for thermally relativistic fluids under the transition regime between the rarefied and continuum regimes.
Ryosuke Yano; Kojiro Suzuki; Hisayasu Kuroda. Autocorrelation of density fluctuations for thermally relativistic fluids. Physical Review D 2013, 88, 1 .
AMA StyleRyosuke Yano, Kojiro Suzuki, Hisayasu Kuroda. Autocorrelation of density fluctuations for thermally relativistic fluids. Physical Review D. 2013; 88 (2):1.
Chicago/Turabian StyleRyosuke Yano; Kojiro Suzuki; Hisayasu Kuroda. 2013. "Autocorrelation of density fluctuations for thermally relativistic fluids." Physical Review D 88, no. 2: 1.
The ultrarelativistic shock layer around the triangle prism is numerically analyzed using the relativistic Boltzmann equation to investigate the dissipation process under two types of ultrarelativistic limits: namely, the Lorentz contraction limit, in which the uniform flow velocity approximates to the speed of light, and the thermally relativistic limit, in which the temperature of the uniform flow approximates to infinity. The relativistic Boltzmann equation is numerically solved using the direct simulation Monte~Carlo method. We discuss dissipation process in the flow field by focusing on profiles of the dynamic pressure and heat flux along the stagnation streamline under the Lorentz contraction limit or the thermally relativistic limit. Our numerical results confirm that profiles of the dynamic pressure and heat flux along the stagnation streamline strongly depend on the Lorentz contraction and thermally relativistic effects under their ultrarelativistic limits, as predicted by Chapman-Enskog expansion on the basis of the generic Knudsen number.
Ryosuke Yano; Kojiro Suzuki. Kinetic analysis of ultrarelativistic flow with dissipation. Physical Review D 2012, 86, 1 .
AMA StyleRyosuke Yano, Kojiro Suzuki. Kinetic analysis of ultrarelativistic flow with dissipation. Physical Review D. 2012; 86 (8):1.
Chicago/Turabian StyleRyosuke Yano; Kojiro Suzuki. 2012. "Kinetic analysis of ultrarelativistic flow with dissipation." Physical Review D 86, no. 8: 1.
Ryosuke Yano; Kojiro Suzuki. Coarsely grained stochastic Boltzmann equation and its moment equations. Physica A: Statistical Mechanics and its Applications 2012, 391, 2291 -2299.
AMA StyleRyosuke Yano, Kojiro Suzuki. Coarsely grained stochastic Boltzmann equation and its moment equations. Physica A: Statistical Mechanics and its Applications. 2012; 391 (7):2291-2299.
Chicago/Turabian StyleRyosuke Yano; Kojiro Suzuki. 2012. "Coarsely grained stochastic Boltzmann equation and its moment equations." Physica A: Statistical Mechanics and its Applications 391, no. 7: 2291-2299.
Katsutoshi Hamasaki; Ryosuke Yano; Kojiro Suzuki. Numerical Study on Application of Knudsen Pump to Thruster of Spacecraft. TRANSACTIONS OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES, AEROSPACE TECHNOLOGY JAPAN 2012, 10, Pe_73 -Pe_80.
AMA StyleKatsutoshi Hamasaki, Ryosuke Yano, Kojiro Suzuki. Numerical Study on Application of Knudsen Pump to Thruster of Spacecraft. TRANSACTIONS OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES, AEROSPACE TECHNOLOGY JAPAN. 2012; 10 (ists28):Pe_73-Pe_80.
Chicago/Turabian StyleKatsutoshi Hamasaki; Ryosuke Yano; Kojiro Suzuki. 2012. "Numerical Study on Application of Knudsen Pump to Thruster of Spacecraft." TRANSACTIONS OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES, AEROSPACE TECHNOLOGY JAPAN 10, no. ists28: Pe_73-Pe_80.
Ryosuke Yano; Kojiro Suzuki. Kinetic description of finite-wall catalysis for monatomic molecular recombination. Physics of Fluids 2011, 23, 117101 .
AMA StyleRyosuke Yano, Kojiro Suzuki. Kinetic description of finite-wall catalysis for monatomic molecular recombination. Physics of Fluids. 2011; 23 (11):117101.
Chicago/Turabian StyleRyosuke Yano; Kojiro Suzuki. 2011. "Kinetic description of finite-wall catalysis for monatomic molecular recombination." Physics of Fluids 23, no. 11: 117101.
Thermally relativistic flow with dissipation was analyzed by solving the rarefied supersonic flow of thermally relativistic matter around a triangle prism by Yano and Suzuki [Phys. Rev. D 83, 023517 (2011)], where the Anderson-Witting (AW) model was used as a solver. In this paper, we solve the same problem, which was analyzed by Yano and Suzuki, using the relativistic Boltzmann equation (RBE). To solve the RBE, the conventional direct simulation Monte~Carlo method for the nonrelativistic Boltzmann equation is extended to a new direct simulation Monte~Carlo method for the RBE. Additionally, we solve the modified Marle (MM) model proposed by Yano-Suzuki-Kuroda for comparisons. The solution of the thermally relativistic shock layer around the triangle prism obtained using the relativistic Boltzmann equation is considered by focusing on profiles of macroscopic quantities, such as the density, velocity, temperature, heat flux and dynamic pressure along the stagnation streamline (SSL). Differences among profiles of the number density, velocity and temperature along the SSL obtained using the RBE, the AW and MM. models are described in the framework of the relativistic Navier-Stokes-Fourier law. Finally, distribution functions on the SSL obtained using the RBE are compared with those obtained using the AW and MM models. The distribution function inside the shock wave obtained using the RBE does not indicate a bimodal form, which is obtained using the AW and MM models, but a smooth deceleration of thermally relativistic matter inside a shock wave.
Ryosuke Yano; Jun Matsumoto; Kojiro Suzuki. Kinetic analysis of thermally relativistic flow with dissipation. II. Relativistic Boltzmann equation versus its kinetic models. Physical Review D 2011, 83, 1 .
AMA StyleRyosuke Yano, Jun Matsumoto, Kojiro Suzuki. Kinetic analysis of thermally relativistic flow with dissipation. II. Relativistic Boltzmann equation versus its kinetic models. Physical Review D. 2011; 83 (12):1.
Chicago/Turabian StyleRyosuke Yano; Jun Matsumoto; Kojiro Suzuki. 2011. "Kinetic analysis of thermally relativistic flow with dissipation. II. Relativistic Boltzmann equation versus its kinetic models." Physical Review D 83, no. 12: 1.
Ryosuke Yano; Kojiro Suzuki. Erratum: Kinetic analysis of thermally relativistic flow with dissipation [Phys. Rev. D83, 023517 (2011)]. Physical Review D 2011, 83, 1 .
AMA StyleRyosuke Yano, Kojiro Suzuki. Erratum: Kinetic analysis of thermally relativistic flow with dissipation [Phys. Rev. D83, 023517 (2011)]. Physical Review D. 2011; 83 (4):1.
Chicago/Turabian StyleRyosuke Yano; Kojiro Suzuki. 2011. "Erratum: Kinetic analysis of thermally relativistic flow with dissipation [Phys. Rev. D83, 023517 (2011)]." Physical Review D 83, no. 4: 1.
Nonequilibrium flow of thermally relativistic matter with dissipation is considered in the framework of the relativistic kinetic theory. As an object of the analysis, the supersonic rarefied flow of thermally relativistic matter around the triangle prism is analyzed using the Anderson-Witting model. Obtained numerical results indicate that the flow field changes in accordance with the flow velocity and temperature of the uniform flow owing to both effects derived from the Lorentz contraction and thermally relativistic effects, even when the Mach number of the uniform flow is fixed. The profiles of the heat flux along the stagnation streamline can be approximated on the basis of the relativistic Navier-Stokes-Fourier (NSF) law except for a strong nonequilibrium regime such as the middle of the shock wave and the vicinity of the wall, whereas the profile of the heat flux behind the triangle prism cannot be approximated on the basis of the relativistic NSF law owing to rarefied effects via the expansion behind the triangle prism. Additionally, the heat flux via the gradient of the static pressure is non-negligible owing to thermally relativistic effects. The profile of the dynamic pressure is different from that approximated on the basis of the NSF law, which is obtained by the Eckart decomposition. Finally, variations of convections of the mass and momentum owing to the effects derived from the Lorentz contraction and thermally relativistic effects are numerically confirmed.
Ryosuke Yano; Kojiro Suzuki. Kinetic analysis of thermally relativistic flow with dissipation. Physical Review D 2011, 83, 1 .
AMA StyleRyosuke Yano, Kojiro Suzuki. Kinetic analysis of thermally relativistic flow with dissipation. Physical Review D. 2011; 83 (2):1.
Chicago/Turabian StyleRyosuke Yano; Kojiro Suzuki. 2011. "Kinetic analysis of thermally relativistic flow with dissipation." Physical Review D 83, no. 2: 1.
In this paper, we consider on the thermally relativistic nonequilibrium flows in the flat or curved spacetime. In the flat spacetime, the supersonic thermally relativistic flow around the prism is numerically analyzed using the Anderson‐Witting model. Obtained numerical results show that the flowfield is remarkably different from that obtained by the Bhatnagar‐Gross‐Krook equation, which is the nonrelativistic limit of the Anderson‐Witting model. Additionally, the sign of the dynamic pressure is opposite to that obtained by the Navier‐Stokes‐Fourier law on the basis of the Eckart decomposition. Finally, the thermally relativistic flow in the curved spacetime is numerically analyzed by solving the general relativistic Anderson‐Witting model and the Einstein’s equation simultaneously. In curved spacetime, nongravitational flow is induced owing to the local dependency of the equilibrium function on the local metric of curved spacetime. Such a flow is confirmed by the nongravitational initial cluster inside the stuffed black hole.
Ryosuke Yano; Kojiro Suzuki. Kinetic analyses of thermally relativistic nonequilibrium flows. 27TH INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS 2011, 1 .
AMA StyleRyosuke Yano, Kojiro Suzuki. Kinetic analyses of thermally relativistic nonequilibrium flows. 27TH INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS. 2011; ():1.
Chicago/Turabian StyleRyosuke Yano; Kojiro Suzuki. 2011. "Kinetic analyses of thermally relativistic nonequilibrium flows." 27TH INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS , no. : 1.
Thermally relativistic flows in the early Universe can be characterized by the emergence of flows induced by gravitational-force-free particle motion in curved spacetime as well as induced by the gravitational force. In this paper, thermally relativistic flows induced by gravitational-force-free particle motion in curved spacetime are discussed on the basis of the general relativistic Boltzmann equation. As an object of analysis, we consider the flow from the static state inside the Schwarzschild radius of a thermally relativistic stuffed black hole induced by such motion. Analytical results obtained using the collisionless, nongravitational general relativistic Boltzmann equation reveal that the initial cluster is induced by gravitational-force-free particle motion. Numerical results obtained using the nongravitational general relativistic Anderson-Witting model confirm the presence of an initial cluster inside the thermally relativistic stuffed black hole, which is induced by gravitational-force-free particle motion.
Ryosuke Yano; Kojiro Suzuki; Hisayasu Kuroda. Thermally relativistic flows induced by gravitational-force-free particle motion in curved spacetime. Physical Review D 2009, 80, 123506 .
AMA StyleRyosuke Yano, Kojiro Suzuki, Hisayasu Kuroda. Thermally relativistic flows induced by gravitational-force-free particle motion in curved spacetime. Physical Review D. 2009; 80 (12):123506.
Chicago/Turabian StyleRyosuke Yano; Kojiro Suzuki; Hisayasu Kuroda. 2009. "Thermally relativistic flows induced by gravitational-force-free particle motion in curved spacetime." Physical Review D 80, no. 12: 123506.
Ryosuke Yano; Kojiro Suzuki; Hisayasu Kuroda. Formulation and numerical analysis of vibrationally coupled recombination of monatomic molecules using Boltzmann kinetic equation. Physics of Fluids 2009, 21, 127101 .
AMA StyleRyosuke Yano, Kojiro Suzuki, Hisayasu Kuroda. Formulation and numerical analysis of vibrationally coupled recombination of monatomic molecules using Boltzmann kinetic equation. Physics of Fluids. 2009; 21 (12):127101.
Chicago/Turabian StyleRyosuke Yano; Kojiro Suzuki; Hisayasu Kuroda. 2009. "Formulation and numerical analysis of vibrationally coupled recombination of monatomic molecules using Boltzmann kinetic equation." Physics of Fluids 21, no. 12: 127101.
Nonequilibrium relaxation by the simplified Fokker–Planck equation is studied by calculating the relaxation of Grad’s moments. From calculated relaxation of moments, we propose two simplified Fokker–Planck-type equations. For the quantitative validation of nonequilibrium relaxation by using the simplified Fokker–Planck-type equations, we solve a rarefied shock layer problem. To study the stronger diffusion of the distribution function than the simplified Fokker–Planck-type equation, we consider diffusion of the distribution function due to the gain term of the Boltzmann equation, because the Boltzmann equation can be described by a partial differential equation with higher-order terms than the simplified Fokker–Planck equation. The effect of the gain term of the Boltzmann equation is discussed based on comparisons with our proposed Bhatnagar–Gross–Krook equation with velocity-dependent collision frequency.
Ryosuke Yano; Kojiro Suzuki; Hisayasu Kuroda. Analytical and numerical study on the nonequilibrium relaxation by the simplified Fokker–Planck equation. Physics of Fluids 2009, 21, 047104 .
AMA StyleRyosuke Yano, Kojiro Suzuki, Hisayasu Kuroda. Analytical and numerical study on the nonequilibrium relaxation by the simplified Fokker–Planck equation. Physics of Fluids. 2009; 21 (4):047104.
Chicago/Turabian StyleRyosuke Yano; Kojiro Suzuki; Hisayasu Kuroda. 2009. "Analytical and numerical study on the nonequilibrium relaxation by the simplified Fokker–Planck equation." Physics of Fluids 21, no. 4: 047104.
The relativistic shock layer problem was numerically analyzed by using two relativistic Boltzmann-kinetic equations. One is Marle model, and the other is Anderson-Witting model. As with Marle model, the temperature of the gain term was determined from its relation with the dynamic pressure in the framework of 14-moments theory. From numerical results of the relativistic shock layer problem, behaviors of projected moments in the nonequilibrium region were clarified. Profiles of the heat flux given by Marle model and Anderson-Witting model were quite adverse to the profile of the heat flux approximated by Navier-Stokes-Fourier law. On the other hand, profiles of the heat flux given by Marle model and Anderson-Witting model were similar to the profile approximated by Navier-Stokes-Fourier law. Additionally we discuss the differences between Anderson-Witting model and Marle model by focusing on the fact that the relaxational rate of the distribution function depends on both flow velocity and molecular velocity for Anderson-Witting model, while it depends only on the molecular velocity for Marle model.
Ryosuke Yano; Kojiro Suzuki; Hisayasu Kuroda. Numerical Analysis of Relativistic Boltzmann-kinetic Equations to Solve Relativistic Shock Layer Problems. 2008, 1 .
AMA StyleRyosuke Yano, Kojiro Suzuki, Hisayasu Kuroda. Numerical Analysis of Relativistic Boltzmann-kinetic Equations to Solve Relativistic Shock Layer Problems. . 2008; ():1.
Chicago/Turabian StyleRyosuke Yano; Kojiro Suzuki; Hisayasu Kuroda. 2008. "Numerical Analysis of Relativistic Boltzmann-kinetic Equations to Solve Relativistic Shock Layer Problems." , no. : 1.
The previously developed Flux-Vector-Splitting (FVS) method was formulated here for the first-order version of Z4 formalism. Then, the characteristics of this method formulated for Z4 formalism were studied by numerically analyzing the evolution of two types of black holes (free and stuffed). Finally, these numerical results from the FVS method were compared with those from the Local Lax Friedrichs and Modified Local Lax Friedrichs methods to reveal the dependency of numerical solution by Z4 formalism on the choice of numerical scheme.
Ryosuke Yano; Kojiro Suzuki; Hisayasu Kuroda. Flux-Vector-Splitting (FVS) method for Z4 formalism and its numerical analysis. 2008, 1 .
AMA StyleRyosuke Yano, Kojiro Suzuki, Hisayasu Kuroda. Flux-Vector-Splitting (FVS) method for Z4 formalism and its numerical analysis. . 2008; ():1.
Chicago/Turabian StyleRyosuke Yano; Kojiro Suzuki; Hisayasu Kuroda. 2008. "Flux-Vector-Splitting (FVS) method for Z4 formalism and its numerical analysis." , no. : 1.
Ryosuke Yano; Kojiro Suzuki; Hisayasu Kuroda. Formulation and numerical analysis of diatomic molecular dissociation using Boltzmann kinetic equation. Physics of Fluids 2007, 19, 017103 .
AMA StyleRyosuke Yano, Kojiro Suzuki, Hisayasu Kuroda. Formulation and numerical analysis of diatomic molecular dissociation using Boltzmann kinetic equation. Physics of Fluids. 2007; 19 (1):017103.
Chicago/Turabian StyleRyosuke Yano; Kojiro Suzuki; Hisayasu Kuroda. 2007. "Formulation and numerical analysis of diatomic molecular dissociation using Boltzmann kinetic equation." Physics of Fluids 19, no. 1: 017103.