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 mom...
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.
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.
Citation
Lehmkuhl, O. [et al.]. A low-dissipation finite element scheme for scale resolving simulations of turbulent flows. "Journal of computational physics", 1 Agost 2019, vol. 390, p. 51-65.