CIP/multi-moment finite volume method with arbitrary order of accuracy
  This paper presents a general formulation of the CIP/multi-moment finite volume method (CIP/MM FVM) for arbitrary order of accuracy. Reconstruction up to arbitrary order can be built on single cell by adding extra derivative moments at the cell boundary. The volume integrated average (VIA) is updated via a flux-form finite volume formulation, whereas the point-based derivative moments are computed as local derivative Riemann problems by either direct interpolation or approximate Riemann solvers. 
Feng Xiao and Satoshi Ii
physics.comp-ph physics.ao-ph physics.flu-dyn physics.geo-ph