A high-resolution Navier–Stokes solver for direct numerical simulation of free shear flow

Abstract

A high-resolution, Navier–Stokes solver is developed for direct numerical simulation (DNS) of free shear flow. All terms in Navier–Stokes equations are discretized using higher order methods. Diffusion term is discretized using fourth order central difference scheme while second order Adams–Bashforth is used for time derivative. Advecting velocity is approximated using fourth order Lagrangian interpolation. For the approximation of advected velocity, a blended fifth order-upwind scheme is proposed. Developed high resolution solver is used for DNS of round jet in transitional and turbulent regimes. A novel open outlet boundary condition (OOBC) is proposed which has the ability to dynamically adjust according to prevailing local condition at the outlet thereby minimizing reflections from outlet. Ability of blended fifth order upwind scheme and fifth order WENO is assessed in terms of algorithmic efficiency as well as fidelity of simulations. It is demonstrated that the proposed blended fifth order upwind scheme outperforms the WENO scheme in terms of algorithmic efficiency. Assessment of fidelity of simulations reveals that WENO displays a tendency to over-predict momentum advection in transitional as well as fully turbulent regime of the round jet. In contrast, the proposed advection scheme is not faced with such limitation.

Funding

The authors would like to acknowledge the financial assistance provided by Sardar Vallabhbhai National Institute of Technology, Surat, towards development of the Advanced Fluid Dynamics Laboratory where the present work has been carried out.

Notes

1 x, y and $z-$staggered control volume sizes are given by $\Delta x_i·\Delta y_{\mathbb{j}}·\Delta z_{\mathbb{k}};$ $\Delta x_{\mathbb{i}}·\Delta y_j·\Delta z_{\mathbb{k}};$ and $\Delta x_{\mathbb{i}}·\Delta y_{\mathbb{j}}·\Delta z_k,$ respectively.

Additional information

Funding

The authors would like to acknowledge the financial assistance provided by Sardar Vallabhbhai National Institute of Technology, Surat, towards development of the Advanced Fluid Dynamics Laboratory where the present work has been carried out