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.
2 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. Figure 1. Initial Particle Distribution of the 50x50 Case
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 2 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. Figure 2. Profiles of the Re=100 Case Figure 3. Profiles of the Re=1000 Case Figure 4. Profiles of the Re=10000 Case
1 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.
2 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.
