Systematic construction of upwind constrained transport schemes for MHD

The constrained transport (CT) method reflects the state of art numerical technique for preserving divergence-free condition magnetic field to machine accuracy in multi-dimensional MHD simulations performed with Godunov-type, or upwind, conservative codes. evolution different components, located at zone interfaces using a staggered representation, is achieved by calculating electric components cell edges, way that has be consistent Riemann solver used update cell-centered fluid quantities interfaces. Albeit several approaches have been undertaken, purpose this work is, on one hand, compare existing methods terms robustness and and, other, extend \emph{upwind contrained transport} (UCT) Londrillo \& Del Zanna (2004) et al. (2007) systematic construction new averaging schemes. In particular, we propose general formula upwind fluxes induction equation which simply involves information available from base employed part, provided it does not require full spectral decomposition, 1D reconstructions velocity nearby intercell faces edges. Our results are presented here context second-order schemes classical MHD, but they can easily generalized higher than second order schemes, either based finite volumes differences, other physical systems retaining same structure equations, such as relativistic MHD.