A comparison of force computations for modeling fluid - structure interaction problems with the lattice Boltzmann volume penalisation method

Figure 1.  Discrete velocities of the D2Q9 model

Figure 2.  Curved interface on a square lattice: example of a fluid boundary node $ \mathbf{x}_f $, its image in the solid domain $ \mathbf{x}_s $, and the intersection point $ \mathbf{ x}_\Gamma $ located on the interface

Figure 3.  Scheme of the computational domain around the NACA airfoil

Figure 4.  Lift and Drag coefficient versus angle. The VP-LBM's results computed with Stress Integration and Momentum Exchange methods are compared with those in the literature

Figure 5.  Streamlines around NACA 0012 for various angles

Figure 6.  Comparison of the power extractor coefficient (equation (25)) obtained using the VP-LBM method and the literature reference

Figure 7.  Comparison of the vorticity field obtained by [17] and by the LBM-VP for $ t/T = 0.25 $

Figure 8.  Comparison of the vorticity field obtained by [17] and by the LBM-VP for $ t/T = 0.45 $

Figure 9.  Scheme of particle sedimentation

Figure 10.  Results obtained using the VP-LBM approach and compared with Tao et al's results [24]

Figure 11.  Rotational velocity obtained using the VP-LBM approach and compared with reference's results [24,21]

Figure 12.  Fluid velocity magnitude at times t = 0.4, 06, 1.0 and 3.0 seconds in lattice units

Figure 13.  Fluid vorticity at times t = 0.4, 06, 1.0 and 3.0 seconds in lattice units