Three-dimensional MHD Modeling Of Solar Corona

Not only the transient interplanetary disturbances from coronal mass ejections(CMEs)influence space weather,the ambient solar wind flows and corona magnetic fields also affect the space weather.Therefore,simulations on the solar wind ambient are also important parts of space weather researches.This paper focuses on the studies of so-lar corona by using the three-dimensional path-conservative magnetohydrodynamics(MHD)model.The model advances the equations of single-fluid solar wind plasma MHD in time by using a Godunov-type finite volume method(FVM).The methods used in this paper are path-conservative,which is employed based on a path-dependent numerical integration connecting the left and right states of the interface.The path in-tegral is evaluated on a simple straight line segment path by a high-order numerical Gauss-Legendre quadrature.The codes are programmed in FORTRAN language with Message Passing Interface(MPI)parallelization on the six-component composite grid system in spherical coordinates with hexahedral cells of quadrilateral frustum type.For the first time,we established two solar wind models,Osher-Solomon-MHD and HLLEM-MHD,by using path-conservative numerical methods.The Riemann solution of the path-conservative Osher-Solomon-MHD model is a full-wave numerical scheme,which contains all characteristic waves of MHD system,and different characteristic fields correspond to different numerical viscosities.The generalized Osher-Solomon scheme possesses the attractive features:it is nonlinear,free of entropy-fix,differen-tiable,and complete.During the implementation of the Osher-Solomon-MHD model,we use minmod limiter for spatial oscillation control and the second-order Runge-Kutta or one-step MUSCL-type time integrations.Thus the path-conservative Osher-Solomon scheme reaches to second-order in space and time.Compare with the original HLLEM method,the novel,simple,low-cost and universal formulation of the path-conservative HLLEM Riemann solver in this paper can accommodate any intermediate wave as long as its eigenstructure is known,and it has a broader applicability.The Riemann solver inherits the good positivity preserving,entropy enforcement and robust properties be-cause it is built on top of the path conservative formulation of HLL method.The one-step MUSCL-type time relaxation method together with the logarithmic space-time recon-struction makes the HLLEM-MHD model second-order in space and time.The Osher-Solomon-MHD and HLLEM-MHD models can be implemented under both conserva-tive and non-conservative hyperbolic equations.Specifically,it can be realized for the generalized Lagrange multiplier(GLM)formulation,the extended generalized Lagrange multiplier(EGLM)formulation and the EGLM formulation with Galilean invariance(G-EGLM)of solar wind MHD systems.The Osher-Solomon-MHD model is validated in modeling the time-dependent large-scale structure of the solar corona,driven continuously by the Global Oscillation Net-work Group(GONG)data updated every six hours.To demonstrate the suitability of this code for the simulation of solar wind,we present the selected results from 2009 October 9 to 2009 December 29 to show its capability of producing a structured so-lar corona in agreement with solar coronal observations.We have also implemented to solve the solar wind MHD systems of G-EGLM MHD equations with a path conser-vative HLLEM FVM.Using the method,Carrington rotations(CRs)2048,2069,2097 and 2121 have been studied to model the large-scale structure of solar corona with the line-of-sight(LOS)magnetic field given by GONG.Numerical results show its capa-bility of producing structured solar wind of different phases coinciding well with the observations.