讲座内容：

As an important branch of modern physics, Magnetohydrodynamics (MHD) has close connections in technical sciences such as plasma physics, metal liquids, astrophysics, metallurgy, aerospace, and controlled thermonuclear fusion. Especially in recent years, MHD  has received great attention as a research foundation in multiple key cutting-edge application fields. This report mainly introduces some recent works on advanced models of incompressible MHD and their numerical methods, including the modeling and analysis of physical preserving MHD , two-phase MHD, thermally driven MHDs as well as  some challenging computational problems driven by applications.