The Study On High Resolution Entropy Stable Schemes For Ideal Magnetohydrodynamics Equations

Magnetohydrodynamics(MHD)equation is a very important numerical model in space physics,which can well describe the movement of space plasma and is a powerful tool in the research of space physics.The numerical simulation of the MHD equations can be used to calculate the movement of the flow field and the magnetic field.It can effectively make up for the limitation of the observation method and the inconvenience caused by the complexity of the theoretical analysis,and widely used in space physics.Therefore,the study on the efficient numerical method of MHD equations is an important topic.In this thesis,a high resolution entropy stable scheme for MHD equations was constructed and then extended to two-dimensional space.Details are as follows:1.Entropy stable scheme for MHD equations was constructed.Based on the relationship between MHD equations and hyperbolic conservation laws,the entropy stabilization theory of hyperbolic conservation law was extended to MHD equations and obtained the entropy stable scheme.The scheme is closely linked with the concept of physics.It has a sufficient theoretical basis and can effectively avoid the appearance of non-physical phenomena.2.By embedding suitable flux limiter,we obtained a high resolution entropy stable scheme.The new scheme was based on the entropy conservation scheme.By embedding suitable flux limiter to the entropy conserved flux,the new scheme can automatically adds numerical dissipation to the discontinuity to avoid the appearance of nonphysical phenomena.Simultaneously,smoothing was effectively suppressed to achieve high-resolution results.Several classical numerical examples was calculated with the high resolution entropy stable scheme.The results show the versatility,robustness and high resolution of the new scheme.3.The high resolution entropy stable scheme was simply extended to two-dimensional space.The Orszag-Tang turbulence problem and the two-dimensional Riemann problem were calculated by entropy stable and high resolution entropy stable scheme.Numerical results also show the high resolution and non-oscillation characteristics of the new scheme.