In this manuscript, the injection of a homogeneous jet in a numerical tank is considered to revolve around discussing the limitation of the direct numerical simulation (DNS), to resolve the equations governing the problem of a jet emitted from the bottom of a numerical tank. The investigation has been made in the context of an unsteady, viscous, and incompressible fluid. The numerical resolution of the equations governing the problem is made by the compact Hermitian finite differences method

more »

... DM) high accuracy. First, the numerical code used in this work is validated by comparing the profiles of the velocity components at the median of the lid-driven cavity with the results of the literature. Furthermore, to confirm the validity of the present numerical code, an evaluation of mesh domain sensitivity is assessed by comparing the numerical vertical velocity profiles for different steps of y-direction (flow direction) with the analytical solution. Afterward, the aim is to perform the nonlinear simulations of the Navier–Stokes equations in a large computational domain. Next, the goal is to characterize the instabilities associated with high Reynolds numbers when a jet is emitted from the bottom of the numerical tank.