| Solar corona is the upper region for the space-weather events. The diversestructures and evolutions in the corona are fundamental for the space physics. Ina data-driven corona model, the dynamic evolution of the corona is simulated bycontinuously inputting the observed data (e.g., the magnetic fleld) at the coronalbottom to drive the model. It provides a powerful numerical tool for study ofthe large-scale coronal structures and the solar eruptions. In this thesis withthe bias on numerical-technique aspect, we have developed a new adaptive solarcorona-solar wind model basing on the space-time conservation-element/solution-element (CESE) scheme and the adaptive-mesh-reflnement (AMR) technique.Then by combining with a photospheric magnetic-flux transport model, we de-velop the flrst dynamic model for the evolution of the global corona driven bythe time-varying photospheric magnetogram.As a novel and high-performance numerical scheme, the CESE method hasalready been successfully applied to the fleld of space-physic simulation. Basingon the theory of general curvilinear coordinates, in this thesis we flrst establish acurvilinear-coordinate version of the CESE method for MHD, by transform thegoverning MHD equations from the physical space (x,y,z) to the computationalspace (ξ,η,ζ) while retaining the form of conservation. Then utilizing a parallel-AMR package PARAMESH and overcoming various incompatibles of the CESEscheme with the AMR grid system (e.g., the problems of space-time staggeringand the Courant number sensitive), we present the flrst implementation of theCESE method on block-AMR grid for MHD (the AMR-CESE-MHD code) inboth Cartesian and curvilinear coordinates.To precisely characterize the bottom sphere of the global corona and avoidthe grid-convergence problems at two poles, a new kind of overlapping grid, theso-called Yin-Yang grid, is borrowed here to overcome various weaknesses of othergrid systems. High-accuracy interpolation is used for transparent transferring ofsolution information at the overlapping boundaries. The adaptive model of the solar corona-solar wind is built on the AMR-CESE-MHD code and the Yin-Yanggrid under the framework of PARAMESH.The time-varying and self-consistent boundary conditions at the coronalbottom is based on the projected-characteristic method and a surface transport(SFT) model. With observed synoptic map as input, the SFT model can repro-duce well the long-term evolution of the photospheric fleld for several months,and avoid the inconsistency of using directly the global magnetogram from obser-vation. By modeling the dynamic evolution for a long time interval of three Car-ringtion rotation (from CR1913 to CR1915) and comparing with multi-observedcoronal images, we show that the model is able to simulate the general structuresof the global corona, e.g., the coronal streamers, the locations of coronal holes,the magnetic fleld of the active regions and their evolutions.Besides, magnetic fleld extrapolation is a common and accurate way to over-come the problem of unavailable direct measurement of the three-dimensionalfleld in the corona. In this thesis, we also present a new implementation ofthe MHD relaxation method for reconstruction of the nearly force-free coronalmagnetic fleld from a photospheric vector magnetogram. Unlike most of the ex-trapolation methods that focus on a nonlinear force-free-fleld model, we solve thefull MHD equations directly by using the CESE method. The bottom boundarycondition is prescribed in a similar way as in the stress-and-relax method, i.e., bychanging the transverse fleld incrementally to match the magnetogram, and otherboundaries of the computational box are set by the nonreflecting boundary con-ditions. Applications to the well-known benchmarks for nonlinear force-free-fleldreconstruction, the Low & Lou force-free equilibria, validate the method and con-flrm its capability for future practical application, with observed magnetogramsas inputs.
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