The present work extends the conservative convective scheme proposed by Charnyi et al. (2017) [13], originally formulated for mixed finite elements and tested in laminar flows, to equal order finite elements. A non-incremental fractional-step method is used to stabilise pressure, allowing the use of finite element pairs that do not satisfy the inf-sup conditions, such as equal order interpolation for the velocity and pressure used in this work. The final scheme preserves momentum and angular momentum at the discrete level; the error in the conservation of kinetic energy introduced by this stabilisation is of O (dt,h^2) in the case of linear finite elements. The low dissipation strategy is tested on a set of relevant turbulent cases. First, by using direct numerical simulation on the inviscid and viscous Taylor-Green vortex problem at Re =1600 and later, coupled with the Vreman (2004) [25]sub-grid stress model for performing large-eddy simulations on a turbulent channel flow at Ret=950, the flow past a sphere at ReD=10^4 and the flow around an Ahmed body at ReH=2 ×10^5. In all cases the performance of the presented formulation is fairly good and it has been capable of reproducing the reference results with good accuracy.

Peer Reviewed