Hall Magnetohydrodynamics on Adaptive Grids

Summary form only given. Numerical scheme for system of MHD equations with Hall term using adaptive grid in 2D case is presented. The field of application of the scheme is the description of Z-pinch plasma compression. Magnetic field is calculated using generalized Ohm law received from motion equation of massless electrons. Magnetic field generation by gradient of electron pressure is also considered. Adaptive Euler grid, refined in the regions of large gradients of gasdynamic values, is used. Total system of equations is divided into 3 subsystems in accordance with physical processes and type of: (1) adiabatic motion plus changing of magnetic field, frozen into plasma; (2) magnetic field evolution accounting the diffusion, existing due to finite conductivity, Hall term and generation of magnetic field by electron pressure gradient; (3) changing of electrons and ions temperature due to heat conductivity plus Joule energy release. Equations of magnetic field dynamics is solved using nonconservative form of Hall term, which allows apply implicit scheme. Numerical test results are compared with known analytical solutions, obtained in the approach of electron magnetic gasdynamics