Finite difference time domain algorithm for electromagnetic problems involving material movement

An Eulerian MHD model for the analysis of magnetic flux compression by expanding diamagnetic fusion plasma sphere

“…The diffusion equation for the radial step is obtained by dropping axial terms form Eq. (15). The advection terms in each direction are treated separately during remap step.…”

“…The electrical conductivity of a mixed cell (cell containing plasma and vacuum/background medium) is determined using a volume weighted average [15] ( = m f m m ), where the volume fraction of each material, f m in a mixed cell is calculated using volume-of-fluid algorithm [22] (discussed in later sections). The conductivity at the cell edge is the average of these cell centered quantities.…”

“…Next, a magnetic convective-diffusion problem [15,[40][41][42][43] is chosen for the validation of magnetic field diffusion into a moving conductor. The flux compression problem [15,40] is formulated in a cylindrical co-ordinate system.…”

“…For MFC problems with imperfectly known boundary conditions, complex geometries and materials having large variations in electrical conductivity (materials from insulator to conductor); the finite difference time-domain (FDTD) method for electromagnetics [15][16][17][18] may be the best suited method to calculate the amplified field in the compression volume and the diffused magnetic flux into the liner. This method can be coupled to a suitable hydrodynamic algorithm to obtain the evolution of density, pressure, temperature, etc.…”

“…Detailed discussions on the advantages and disadvantages of such approach are given in Refs. [15][16][17][18] (also, see Refs. therein).…”