3.1 Solving Magnetic Induction and Electric Potential Equations

The magnetic induction equation and the electric potential equations are solved through user-defined scalar transport equations. For the magnetic induction equation a set of 2 or 3 scalar equations are solved, each representing a Cartesian component of the induced magnetic field vector in a 2-D or 3-D case. For the electric potential equation a single scalar equation is solved.

The convection and the diffusion terms of the scalar equations are defined using user functions DEFINE_UDS_FLUX(mhd_flux, ..., ns) and DEFINE_DIFFUSIVITY (mhd_magnetic_diffusitivity, ..., ns) respectively. The user-defined scalar equation is identified by the scalar index ns.

The source terms to the induction equations and the potential equation are implemented using user function DEFINE_SOURCE(mhd_mag_source, ..., eqn) and DEFINE_SOURCE(mhd_phi_source, ..., eqn) respectively, where eqn identifies the scalar equations.

For transient cases, the additional unsteady source term is introduced through the user function DEFINE_UDS_UNSTEADY(mhd_unsteady_source, ..., ns), where ns identifies the scalar being solved.

The induction and potential equations can also be solved in solid zones, in which case the fluid velocity terms in the equations are not considered. For multiphase flows, the MHD equations are solved in the mixture domain only.

The wall boundary conditions are implemented through user profile functions ( DEFINE_PROFILE(mhd_bc_...), and are applied to the Cartesian components of the induced magnetic field vector or to the electric potential. For external wall boundaries, three types of boundary conditions, i.e. electrically insulating, conducting and 'thin wall', can be applied. The 'thin wall' type boundary refers to an external wall where a 1-D magnetic or electric potential diffusion normal to the boundary is assumed, and the wall material and the thickness are specified for the boundary. For internal wall boundaries, that is the boundaries between fluid/solid or solid/solid zones, a coupled boundary condition is applied.