Magnetospheres of many astrophysical objects can be accurately described by the low-inertia (or “force-free”) limit of MHD. We present a new numerical method for solution of equations of force-free relativistic MHD based on the finite-difference time-domain (FDTD) approach with a prescription for handling spontaneous formation of current sheets. We use this method to study the time-dependent ev...

A complete solution is obtained for nonaxisymmetric resonant vibrations of a free cylinder or disk involving infinite sums. For axisymmetric longitudinal vibrations an alternative to previous solutions is included. In principle, the solutions satisfy exactly the stress-free boundary conditions, in contrast to the approximate bending-mode solutions due to Pickett or approximate solutions based o...

A free surface problem arising in the Czochralski (CZ) crystal growth process is considered. A mathematical model accounting for the interaction of the molten material with applied and induced magnetic fields, temperature-induced convection, rotating boundaries and a free surface is given. The model described avoids some common simplifying assumptions and allows for more general geometries, and...

The generation of the mesh consists of diierent steps: Calculation of neighbouring cells { procedure NEICELL For a given cell K i this procedure calculates the cell coordinates K j i of the neighbouring cells K j i. Checking of a cell { procedure CHKCELL For a given cell K j this procedure calculates the coordinates L k of the 2 m vertices of the cell and checks whether the cell has to be creat...

A new moving mesh approach is used for numerical simulation of incompressible flow problems involving freesurfaces. The divergence form of the Navier-Stokes equation is discretized using an unstructured staggered mesh method. This method exploits the inherent advantages of the DelaunayVeronoi co-volumes, which exhibit an orthogonal behavior. The paper also describes the semi-Lagrangian mesh ada...

Abstract A fully conservative overset mesh method is proposed and applied to overcome the metric singularity at symmetry line for blunt bodies, e.g., capsules blunted cones, in general curvilinear coordinates. The placed automatically by avoiding collapse of grid lines using a hexahedral structure contrast prismatic body-orientated mesh. In addition, points coincide with those avoid interpolati...

Using the fluid-magnetofluid formalism, we obtain axisymmetric stability criteria for a composite disc system consisting of stellar and gaseous magnetized singular isothermal discs (MSIDs). Both (M)SIDs are presumed to be razor-thin and are gravitationally coupled in a self-consistent axisymmetric background equilibrium with power-law surface mass densities and flat rotation curves. The gaseous...