In this paper, a new numerical scheme of Total Variation Diminishing (TVD) MacCormack type for MagnetoHydroDynamic (MHD) equations is proposed by taking into account of the characteristics such as convergence, stability, resolution. This new scheme is established by solving the MHD equations with a TVD modified MacCormack scheme for the purpose of developing a scheme of quick convergence as well as of TVD property. To show the validation, simplicity and practicability of the scheme for modelling MHD problems, a self-similar Cauchy problem with the discontinuous initial data consisting of constant states, and the collision of two fast MHD shocks, and two-dimensional Orszag and Tang's MHD vortex problem are discussed with the numerical results conforming to the existing results obtained by the Roe type TVD, the high-order Godunov scheme,and Weighted Essentially Non-Oscillatory (WENO) scheme. The numerical tests show that this two-step TVD MacCormack numerical scheme for MHD system is of robust operation in the presence of very strong waves, thin shock fronts, thin contact and slip surface discontinuities.
FENG Xueshang WEI Fengsi ZHONG Dingkun(Center for Space Science and Applied Research, The Chinese Academy of Sciences, Beijing 100080)
By proposing a two-dimensional triggering model with concentrically circular closed magnetic field line structure,numerical research is made on the asymmetric propagation feature of coronal mass ejection (CME) in two cases emerging at the solar northern latitudes 10° and 45° respectively.The numerical results can qualitatively explain some features of CME event observed by the spacecraft SOHO and show that:(i) In these two cases,the triggering model can initiate CME with an asymmetric closed magnetic field structure.(ii) Closed magnetic structure of CME event will keep deflecting to the current sheet when it propagates away from the sun and this deflecting effect mostly happens within tens of solar radii before CME travels finally along the current sheet.(iii) The triggering model emerging at different locations can introduce CME events with different magnetic shapes.This shape happens to be circular and crescent when the triggering model emerges at the northern latitudes 10° and 45°,respectively.
During Ulysses’ first rapid pole-to-pole transit from September 1994 to June 1995, its observations showed that middle- or high-speed solar winds covered all latitudes except those between ?20° and +20° near the ecliptic plane, where the velocity was 300―450 km/s. At poleward 40°, however, only fast solar winds at the speed of 700―870 km/s were observed. In addition, the transitions from low-speed wind to high-speed wind or vice versa were abrupt. In this paper, the large-scale structure of solar wind observed by Ulysses near solar minimum is simulated by using the three-dimensional numerical MHD model. The model com- bines TVD Lax-Friedrich scheme and MacCormack II scheme and decomposes the calculation region into two re- gions: one from 1 to 22 Rs and the other from 18 Rs to 1 AU. Based on the observations of the solar photospheric magnetic field and an addition of the volumetric heating to MHD equations, the large-scale solar wind structure mentioned above is reproduced by using the three-dimensional MHD model and the numerical results are roughly consistent with Ulysses’ observations. Our simulation shows that the initial magnetic field topology and the addition of volume heating may govern the bimodal structure of solar wind observed by Ulysses and also demonstrates that the three-dimensional MHD numerical model used here is efficient in modeling the large-scale solar wind structure.
FENG Xueshang, XIANG Changqing, ZHONG Dingkun & FAN Quanlin SIGMA Weather Group, Key Laboratory of Space Weather
