A note on the general multi-moment constrained flux reconstruction formulation for high order schemes

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) [3] by imposing not only the continuity constraint conditions on the flux function at the cell boundary, but also other types of constraints which may include those on the spatial derivatives or the point values. This formulation can be also interpreted as a blend of Lagrange interpolation and Hermite interpolation, which provides a numerical framework to accommodate a wider spectrum of high order schemes. Some representative schemes will be presented and evaluated through Fourier analysis and numerical tests.