日本地球惑星科学連合2015年大会

講演情報

ポスター発表

セッション記号 P (宇宙惑星科学) » P-EM 太陽地球系科学・宇宙電磁気学・宇宙環境

[P-EM26] 宇宙プラズマ理論・シミュレーション

2015年5月24日(日) 18:15 〜 19:30 コンベンションホール (2F)

コンビーナ:*梅田 隆行(名古屋大学 太陽地球環境研究所)、天野 孝伸(東京大学 地球惑星科学専攻)、成行 泰裕(富山大学人間発達科学部)、杉山 徹(独立行政法人海洋研究開発機構 地球情報基盤センター)、中村 匡(福井県立大学)

18:15 〜 19:30

[PEM26-P02] コンパクト差分法とLAD法を用いたMHDシミュレーションコードの開発と磁気回転不安定性の非線形発展に関する計算機実験

*平井 研一郎1加藤 雄人1寺田 直樹1河合 宗司2 (1.東北大学大学理学研究科 地球物理学専攻、2.東北大学大学院工学研究科 航空宇宙工学専攻)

The magnetorotational instability (MRI) is one of the most important phenomena in the accretion disk. Turbulence generated by MRI causes the turbulent viscosity in the disk and is a strong candidate of the driver of mass accretion. Recent study suggested that the turbulence induced by MRI also plays an important role in the planetesimal formation in the protoplanetary disk. In the planetesimal formation process, both the ionized gas and dusts coexist in the disk and the motion of dusts is strongly affected by the motion of gas through collisional and/or frictional effects. Kato et al. (2010;2012) showed the possibility that meter-sized dusts are gathered locally due to the modification of the disk gas distribution through the evolution of MRI and that situations favored for the planetesimal formation are created in the localized region. In addition to the effect pointed out by this simulation, we should take into account effects through the Kelvin-Helmholtz instability (Sekiya, 1998; Barranco, 2009) and the streaming instability (Youdin & Goodman, 2005) generated by the dust-gas interaction as well as the time evolution of the global disc structure (Suzuki et al., 2010). In order to carry out the MHD simulation considering these effects, we need to develop the scheme that can accurately resolve both short wavelength waves in turbulence and discontinuity appeared in the evolution of instabilities.
In the present study, we develop an MHD simulation code using an 8th-order compact difference scheme with the local artificial diffusivity (LAD) method (Kawai, 2013). The compact difference scheme proposed by Lele (1992) enables us to solve turbulent flow accurately up to the wavenumber range corresponding to a few grid points. The LAD method for MHD simulation proposed by Kawai (2013) enables us to reduce unphysical oscillations generated in central difference type scheme like the compact difference scheme. We have also applied parallelization by MPI using the pipeline algorithm to the code in order to increase the box size with keeping the high spatial resolution. By using the pipeline algorithm, we have applied the domain decomposition to the code with maintaining the accuracy of the compact difference scheme. We carry out a series of standard test problems for MHD simulations and clarify pros and cons of the developed MHD code for the study of MRI. By conducting spatially 2-dimensional test problems, we find that the maximum value of the numerical error appeared in the computation of the divergence of the magnetic field is the order of 10-12, which is approximately consistent with the results of Kawai (2013).
We then carry out the 3-dimensional MHD simulation of MRI by the developed code. In order to realize the differential rotation, we use the shearing box boundary condition (Hawley et al., 1995) and the 9-wave method (Dedner et al, 2010) so as to suppress the divergence error caused by the interpolation in the shearing box boundary. We initially set the uniform vertical magnetic field and assume the perturbation in the three-components of the velocity vector whose amplitude is 1% of the sound speed. Our developed simulation code can solve the linear growth and nonlinear evolution of MRI. Our newly developed code enables us to solve the MRI driven turbulence accurately, which is important in solving not only a wide range of the evolution of the disk but also the fine structure of the saturation and nonlinear evolution mechanism of MRI. We show the characteristics of the developed code and study results of the 3-dimensional MHD simulation of the nonlinear evolution of MRI.