Direct numerical simulation for lid-driven cavity under various Reynolds numbers in fully staggered grid

Finite difference method in a fully staggered grid is applied to solve the incompressible Navier-Stokes equation with direct numerical simulations. Without a turbulent or transient model, lid-driven cavity simulations are conducted with various Reynolds numbers from 102 to 106. The fluid property is fixed, and a lid velocity is changed to set the Reynolds number condition. Time steps are adjusted to keep the consistency of Courant number conditions. Simulation results are compared with the experimental measurements for a Reynolds number of 104 condition, in which the result shows relatively larger values of non-dimensional root mean square (RMS) compared to the other Reynolds number conditions. Vertical and horizontal velocity components show comparably higher RMS distributions around a downstream eddy region and above a bottom surface region, respectively, when the Reynolds number is 104. Time-averaged and RMS distributions show reasonable agreement with the experimental results, and a velocity spectral analysis shows the Kolmogorov spectrum of -5/3 slope for all velocity components. Taylor-Gortler-like (TGL) vortices are observed clearly in the downstream jet region. When the Reynolds number increases, the size of the TGL vortical structure in the spanwise direction decreases and numerous small-scale vortices occur.

Automated summary

The finite difference method in a fully staggered grid is used to solve the incompressible Navier-Stokes equation through direct numerical simulations. Lid-driven cavity simulations are conducted with different Reynolds numbers, and the results are compared to experimental measurements. The study reveals that at a Reynolds number of 104, there are higher RMS distributions of vertical and horizontal velocity components, and clearly observed TGL vortices in the downstream jet region.