The Study Of New Schemes For Magneto-hydrodynamics Numerical Simulations

The numerical simulation of magneto-hydrodynamics(MHD)is an important means in the study of space physics,and it has also been developed rapidly in the field of space physics.A lot of space physical phenomena can be simulated by solving the MHD control equations to trace the evolutionary process of events and explore the physical mechanism inside them.The tracing of these evolutionary processes is often impossible by satellite observation,which also shows the advantages of numerical simulation.In MHD numerical simulations,the conservation element and solution element(CESE)scheme is a different numerical method which has some advantages over the usually used numerical method such as finite volume method(FVM)and finite difference method(FDM).It has been developed for and applied to hydrodynamics(HD)widely since it was first proposed by Chang.Feng firstly extended the original second-order CESE method to the MHD equations,and then it is widely used in MHD numerical simulations and well applied to study the evolution and development of the solar wind.However,to be now,the CESE scheme used in MHD only has second order accuracy.Therefore,we will extended it to higher order on the basis of the previous study to deal with multiple dimensional MHD problems.We have constructed a kind of higher order CESE scheme,especially suitable to solve problems with fine structure and perform better than the original scheme.Moreover,the spacial and temporal can reach higher order simultaneously,which is difficult to be achieved by the general numerical methods.And this is also the first time to extend the second-order CESE scheme to arbitrary much higher order for MHD.Some complex flow phenomena such as shock and other discontinuities as well as shear layers are often met with for HD and MHD problems.We combined the advantages of CESE scheme and upwind scheme,constructed a upwind CESE hybrid scheme,which can be very flexible to combine all kinds of upwind schemes and it paves the way to achieve the perfect combination of CESE and finite volume method(FVM).We also have extended it to the general curvilinear coordinate for the convenience of applying it to spherical shaped computational regions such as the Sun and the Earth.However,MHD are different from HD,controlling the magnetic field divergenceerror in each computational step is is the key aspect.Otherwise,it will bring about nonphysical forces affecting the accuracy and may lead to numerical instability as the magnetic divergence accumulating.We make the best of the characteristics of CESE method and give out a new method to clean the magnetic field divergence fundamentally based on the least-squares method.The test example results indicate that this new method is very efficient,the order of magnetic divergence error can be reduced to more than 5.Magnetic flux rope emergence and magnetic reconnection are widely regarded as the extremely important mechanisms of some solar eruptive actions.It is also very important to study these two processes by using numerical simulation.We have used our newly developed numerical method to simulate the process of emergence of magnetic field from the solar convection zone into the atmosphere and the Hall magnetic reconnection model in GEM,we have got some significant features,which makes the preparation for the study of the large scale solar eruptive actions by using these trigger mechanisms.