A square cavity with a side length of L°= 1e-3° m is filled with water
(density: 1000 kg/m3, dynamic viscosity: 1e-3 kg/m/s). The
upper wall is moved with a constant velocity U0 imposing a rotational
movement of the fluid in the cavity. Here, the configurations with Re°=°100,
Re°=°1000 and Re°=°10000 are simulated by adjusting the velocity of the lid
correspondingly. The highly-resolved Finite-Difference calculations by Ghia et al.
#reference_fql_tlv_s2b__fn_fbf_tmv_s2b with a grid resolution of 257x257 are taken as reference.
Numerical Setup
Three different resolutions of 50x50, 100x100 and 200x200 fluid particles are used
for each Reynolds-Number. Figure 1 shows the initial particle distribution for the coarsest
resolution where wall boundary conditions are imposed by three rows of particles.
The simulation is run until a fully developed flow is achieved.
Results
The velocity profiles in the horizontal and vertical centerlines are shown in Figure 2 to Figure 4 for each
Reynolds-Number. For the Re = 100 case, all the profiles show very good agreement
with the reference profiles by Ghia et al. Velocity profiles at Re = 1000 and Re =
10000 match those of #reference_fql_tlv_s2b__fn_fbf_tmv_s2b at finer resolutions of 100x100 and 200x200,
respectively. This is expected as higher Reynolds numbers results in finer
structures and requires more particles to resolve.
S. Adami, H. Hu and N. Adams, "A generalized wall boundary condition
for smoothed particle hydrodynamics," Journal of Computational Physics, vol.
231, pp. 7057-7075, 2012.
U. Ghia and K. S. C. Ghia, "High-Re solutions for incompressible flow
using the Naview-Stokes equations and a multigrid method," Journal of
Computational Physics, vol. 48, pp. 387-411, 1982.