Application of an Upwind integration method to plane parallel Hall-MHD

We study the impact of an Upwind scheme on numerical convergence simulations Hall and Ohmic effect in neutron stars crusts. While these effects have explored a variety geometries wide ranges physical parameters, they are limited to relatively low values parameter, playing role magnetic Reynolds number, which should be not exceed few hundred for convergence. evolution field plane-parallel Cartesian geometry. discretise induction equation using finite difference then integrate it via Euler forward method. Two different approaches used integration advective terms appearing equation: Forward Time Central Space (FTCS) scheme. compare them accuracy performance. explore method according ratio planar vertical parameter. In limit strength use provides vast improvement leading where parameter is 2 orders magnitude higher than that FTCS. still better if stronger, yet, maximum value reached within factor 10 or few. Moreover, we notice schemes diverge their behaviour very different, with FTCS producing infinite energy, while only temporarily increasing overall energy. Overall, enhances efficiency allowing exploration environments electric conductivity getting us closer before realistic environmental conditions magnetars.