  This paper presents a general formulation to construct high order numerical
schemes by using multi-moment constraint conditions on the flux function
reconstruction. The new formulation, so called multi-moment constrained flux
reconstruction (MMC-FR), distinguishes itself essentially from the flux
reconstruction formulation (FR) of Huynh (2007) by imposing not only the
continuity constraint conditions on the flux function at the cell boundary, but
also other types constraints which may include those on the spatial derivatives
or the point values. This formulation can be also interprated as a blend of
Lagrange interpolation the Hermite interpolation, which provides a numerical
framework to accomodate a wider spectrum of high order schemes. Some
representative schemes will be presented and evaluated through Fourier analysis
and numerical tests.
