Consistency and accuracy in the simulation of two-phase flows with phase change using sharp interface capturing methods

•Consistent phase-change procedure are proposed and investigated for any interface capturing method.•Accurate and second-order discretizations for diffusion operator with flux jump are presented.•Second-order accurate gradients from any interface representation are obtained.•VOF and Level-Set framework for evaporating flows are limited to first-order convergence with important errors in 3D.