  In this paper, we clarify reconstruction-based discretization schemes for
unstructured grids and discuss their economically high-order versions, which
can achieve high-order accuracy under certain conditions at little extra cost.
The clarification leads to one of the most economical approaches: the
flux-and-solution-reconstruction (FSR) approach, where highly economical
schemes can be constructed based on an extended kappa-scheme combined with
economical flux reconstruction formulas, achieving up to fifth-order accuracy
(sixth-order with zero dissipation) when a grid is regular. Various economical
FSR schemes are presented and their formal orders of accuracy are verified by
numerical experiments.
