Formulation and numerical benchmark of improved magneto fluid-dynamics boundary conditions for 3D nonlinear MHD code SPECYL

3D nonlinear MHD code SpeCyl is a spectral tool, operating in zero-β approximation and in cylindrical geometry to advance in time the magnetic field and the plasma flow. The traditional formulation of its boundary conditions would see the plasma as if in direct contact with an ideally conducting shell. However, a recent reformulation introduced the presence of a rigid thin shell and a tuneable-width vacuum region between the plasma and the outer conductor. With suitable parameters choice, the resistive shell can be made transparent to the magnetic field, so to simulate a free-interface between plasma and vacuum. Numerical benchmark performed in this regime against current-driven linear MHD instabilities found good agreement concerning the internal modes, yet quantitatively poor for external modes of MHD, motivating a reformulation of fluid boundary conditions, as well. We present here the resulting set of boundary conditions, which combines the chance for finite flow at plasma edge with the already present thin shell-like modelling of magnetic plasmavacuum matching conditions. We also illustrate numerical benchmarks, mainly against some well known results of the theory of linear MHD instabilities. Finally, we include a mutualbenchmark between our formulation of SpeCyl and another MHD nonlinear simulations code, Pixie3D, with analogous physical assumptions at plasma edge. This extends the nonlinear benchmark, already performed between the two codes in the past.