This research is about the flow behaves under the turbulent effect. Depending on the flow condition (Reynolds number), the flow characteristic is changed, and this research shows how the flow characteristic changes using the Computational Fluid Dynamics method. Because it is fundamental research, the simulations are performed with the simple and cubical geometry which is so called the Lid-driven cavity. But it is applicable with a curved surface in 3 dimensions with the coordinate transformation because this CFD research does not use a Spectral method.

## Why is it important?

Since the Navier-Stock equation is developed in the 19th century, there has been a lot of progress for understanding how the fluid flows. However, mankind cannot find the solution for the Navier-Stock equation yet, and even still do not know whether the solution is unique or not. Thus, peoples have tried to solve the equation numerically, which is a CFD and it is widely used nowadays to understand how the fluid flows. However, CFD still has a fundamental problem because of its non-linear convection term. When the convection term is solved numerically, the numerical oscillation and diffusion are inevitable, thus it is impossible to capture all the flow behaves with very high resolutions using a ‘normal’ grid. To overcome this fundamental CFD problem, turbulence models have been studied for several decades by employing some artificial variables like a turbulent kinetic energy and dissipation rate. But it is based on the Boussinesq assumption, and each turbulent model shows all different results that makes us continuously keep comparing the simulation results with experiment data. A Direct Numerical Simulation (DNS) is the way that can resolve the flow behaves with a very high resolution, but it is still used with a very limited condition and low Reynolds number. DNS does not use the turbulence model. Instead, it is using a high-order convection scheme like a 5th order WENO scheme. However, to capture the flow behaves with very high resolution, it still needs extremely large number of grid points that might be too expansive for the people who cannot afford to use a supercomputing machine, and the electric power consumption with carbon emissions are too large. For the most normal people, such kind of large grid is ‘abnormal’ grid. In this research, DNS is performed with ‘normal’ grid. The ‘normal’ is not a scientific word, but used here because conventional DNS research are conducted with ‘abnormal’ grid previously in the earth.