\begin{thebibliography}{} \bibitem[\protect\astroncite{Guermond and Minev}{2006}]{guermond06} Guermond, J. and Minev, P. (2006). \newblock {An overview of projection methods for incompressible flow}. \newblock {\em {Comput. Methods Appl. Mech. Engrg.}}, 195:6011--6045. \bibitem[\protect\astroncite{Leveque}{2002}]{leveque02} Leveque, R.~J. (2002). \newblock {\em Finite Volume Methods for Hyperbolic Problems}. \newblock Cambridge University Press. \bibitem[\protect\astroncite{Sapsis and Lermusiaux}{2009}]{sapsis09} Sapsis, T. and Lermusiaux, P. (2009). \newblock {Dynamically orthogonal field equations for continuous stochastic dynamical systems}. \newblock {\em {Physica D}}, 238:2347--2360. \bibitem[\protect\astroncite{Sapsis and Lermusiaux}{2011}]{sapsis_lermusiaux_PhysD2011} Sapsis, T.~P. and Lermusiaux, P. F.~J. (2011). \newblock {Dynamical criteria for the evolution of the stochastic dimensionality in flows with uncertainty}. \newblock {\em {Physica D}}, In. Press. \bibitem[\protect\astroncite{Van~Leer}{1977}]{leer77} Van~Leer, B. (1977). \newblock {Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection}. \newblock {\em {J. Comput. Phys.}}, 23(3):276 -- 299. \end{thebibliography}