A projection hybrid high order finite volume/finite element method for incompressible turbulent flows

In this paper the projection hybrid FV/FE method presented in [1] is extended to account for species transport equations. Furthermore, turbulent regimes are also considered thanks to the k–ε 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. •Development of a projection hybrid FV/FE method for turbulent incompressible flows.•Extension of the CVC Kolgan-type scheme to solve 3D Navier–Stokes equations.•Introduction of LADER methodology to reach 2nd order of accuracy in space and time.•Performance of stability and accuracy analysis for the transport-diffusion equation.•Numerical results in 3D: order of accuracy assessed, realistic test problems solved.