  In this paper the projection hybrid FV/FE method presented in Busto et al.
2014 is extended to account for species transport equations. Furthermore,
turbulent regimes are also considered thanks to the $k-\varepsilon$ model.
Regarding the transport diffusion stage new schemes of high order of accuracy
are developed. The CVC Kolgan-type scheme and ADER methodology are extended to
3D. The latter is modified in order to profit from the dual mesh employed by
the projection algorithm and the derivatives involved in the diffusion term are
discretized using a Galerkin approach. The accuracy and stability analysis of
the new method are carried out for the advection-diffusion-reaction equation.
Within the projection stage the pressure correction is computed by a piecewise
linear finite element method. Numerical results are presented, aimed at
verifying the formal order of accuracy of the scheme and to assess the
performance of the method on several realistic test problems.
