A Projection Hybrid Finite Volume-ADER/Finite Element Method for Turbulent Navier-Stokes

We present a second order finite volume/finite element projection method for low-Mach number flows. Moreover, transport of species law is also considered and turbulent regime is solved using a k - epsilon standard model. Starting with a 3D tetrahedral finite element mesh of the computational domain, the momentum equation is discretized by a finite volume method associated with a dual finite volume mesh where the nodes of the volumes are the barycenter of the faces of the initial tetrahedra. The resolution of Navier- Stokes equations coupled with a k - epsilon turbulence model requires the use of a high order scheme. The ADER methodology is extended to compute the flux terms with second order accuracy in time and space. Finally, the order of convergence is analysed by means of academic problems and some numerical results are presented.