Systematic construction of upwind constrained transport schemes for MHD

•With this work we assess the validity of novel UCT schemes for the solution of the MHD equations in multiple dimensions.•The proposed schemes improve on the original formulation of Londrillo & Del Zanna (2004) [22] by providing more general guidelines allowing different Riemann solvers to be incorporated.•This approach offers enhanced flexibility allowing new upwind techniques to be incorporated in CT-MHD schemes at the modest cost of storing transverse velocity, weight coefficients for the fluxes and diffusion terms for the magnetic field.