UCLA Global MHD model

UCLA Global magnetohydrodynamic (MHD) magnetosphere-ionosphere code is based on a single fluid description
of the interaction between the solar wind and Earth’s magnetosphere. A detailed description of the MHD model can be
found in [Frank et al., 1995] and Raeder et al. [1998; 2001] and El-Alaoui [2001]. In the MHD simulation, the total
electric field includes convective and resistive terms. Explicit resistivity is necessary in our code for reconnection
to occur. The MHD equations are solved on a non-uniform Cartesian computational grid that is computed prior to
the run by using continuous functions to distribute the grid points in the simulation system. The size of each
grid cell is defined by three continuous functions that allow us to distribute grid points so as to increase the
grid resolution in the region of interest without excessively degrading the resolution in the rest of the simulation
domain. The minimum grid spacing for this event was about 0.12 RE in each direction. The dimensions of the
simulation box are 20 RE in the sunward direction, 300 RE along the tail, and 55 RE in each transverse direction.
With such a large simulation domain, all flows at the external boundaries are in the super-magnetosonic regime.
The time step in the simulations is determined by the Courant condition tau=Delta/VA where Delta is the minimum grid spacing and
VA is the maximum Alfvén velocity in the simulation domain. The ionospheric part of the model takes into account
three sources of ionospheric conductance: solar EUV ionization modeled by using an empirical model, diffuse auroral
precipitation modeled by assuming strong pitch-angle scattering, and the accelerated electron precipitation
associated with upward field-aligned currents modeled in accordance with the approach of Knight [1972]. We
use the empirical relations developed by Robinson et al. [1987] to calculate ionospheric conductances from
mean electron energies and energy fluxes. A detailed description of the MHD model can be found in Raeder et al.
[1998; 2001] and El-Alaoui et al., 2001.

El-Alaoui, M. (2001), Current disruption during November 24, 1996, substorm, Journal of Geophysical Research-Space Physics, 106(A4), 6229-6245, doi:10.1029/1999ja000260.

Frank, L.A., M. Ashour Abdalla, J. Berchem, J. Raeder, W. R. Paterson, S. Kokubun, T. Yamamoto, R. P. Lepping, F. V. Coroniti, D. H. Fairfield, and K. L. Ackerson (1995), Observations of plasmas and magnetic fields in Earth's distant magnetotail: Comparison with a global MHD model, J. Geophys. Res., 100(A10), 19177–19190, doi:10.1029/95JA00571.

Knight, S. (1973), Parallel Electric-Fields, Planetary and Space Science, 21(5), 741-750, doi:10.1016/0032-0633(73)90093-7.

Raeder, J., and R.L. McPherron (1998), Global MHD simulations of the substorm current wedge and dipolarization, in SUBSTORMS-4, edited by S. Kokubun, and Y. Kamide, pp. 343-348, Terra Scientific Pub. Co. and Kluwer Academic Publishers, Lake Hamana, Japan.

Raeder, J., Y.L. Wang, T.J. Fuller-Rowell, and H.J. Singer (2001), Global simulation of magnetospheric space weather effects of the Bastille Day storm, Solar Physics, 204(1-2), 325-338, doi:10.1023/A:1014228230714.

Robinson, R.M., R.R. Vondrak, K. Miller, T. Dabbs, and D. Hardy (1987), On Calculating Ionospheric Conductances from the Flux and Energy of Precipitating Electrons, Journal of Geophysical Research-Space Physics, 92(A3), 2565-2569, doi:10.1029/JA092iA03p02565.

加州大学洛杉矶分校的全球磁流体动力学（MHD）磁层-电离层代码，基于对太阳风与地球磁层相互作用的单流体描述。该MHD模型的详细描述可参阅Frank等（1995年）、Raeder等（1998年；2001年）以及El-Alaoui（2001年）的研究。在MHD模拟中，总电场包括对流和电阻项。为了实现磁层重连接，我们的代码中必须引入显式电阻率。MHD方程在非均匀笛卡尔计算网格上求解，该网格在运行前通过连续函数计算网格点分布于模拟系统。每个网格单元的大小由三个连续函数定义，这些函数允许我们在感兴趣的区域增加网格分辨率，同时不过度降低模拟域其余部分的分辨率。该事件的最低网格间距约为0.12地球半径。模拟盒的尺寸为太阳风方向20地球半径，尾部300地球半径，横向每个方向55地球半径。由于模拟域如此之大，外部边界上的所有流动均处于超磁音速状态。模拟的时间步长由Courant条件确定，即tau=Delta/VA，其中Delta是最低网格间距，VA是模拟域内的最大阿尔芬速度。模型中的电离层部分考虑了三种电离层电导率来源：使用经验模型模拟的太阳极端紫外线（EUV）电离、假设强极角散射的弥漫性极光降水以及与向上场向电流相关的加速电子降水，后者根据Knight（1972年）的方法进行模拟。我们采用Robinson等（1987年）开发的经验关系，从平均电子能量和能量通量计算电离层电导率。关于MHD模型的详细描述，可参阅Raeder等（1998年；2001年）和El-Alaoui等（2001年）的研究。