A new 3D MHD algorithm: the distribution function method

A new three-dimensional (3D) magnetohydrodynamic (MHD) algorithm is describ ed. The 3D MHD equations are solved in conservative form using a finite vol ume scheme. The hydrodynamic variables in a cell are updated bq calculating fluxes across the cell inter faces. The fluxes of mass, momentum and energ y across cell interfaces are calculated by integrating a Boltzmann-like dis tribution function over velocity space. The novel feature of the method is that the distribution function incorporates most of the electromagnetic ter ms. In addition, the electric field along cell edges, which is used to upda te the magnetic field at cell faces, is also calculated using the Boltzmann -like distribution funct ion. An important aspect of the method is that it provides a theoretical framework to incorporate additional terms in the 3D MHD equations (e.g. an anisotropic ion stress tensor and anisotropic temper ature distributions).