Efficient immersed-boundary lattice Boltzmann scheme for fluid-structure interaction problems involving large solid deformation

A hybrid numerical method which couples the immersed-boundary lattice Boltzmann method with the smoothed point interpolation method (S-PIM) is presented in this paper for the fluid-structure interaction problems involving large solid deformation. In the method, the lattice Boltzmann method is adopted for its advantages in modeling complex fluid flow, the S-PIM is coupled for its robustness in dealing with large solid deformation, and the immersed-boundary method is used for its efficiency in handling the interaction of fluid and solid. In the fluid-solid coupling procedure, a force correction technique based direct-forcing scheme is introduced to enforce nonslip boundary condition with high accuracy, and an averaged dual time stepping scheme is proposed to get stronger robustness of the present method. Numerical experiments are carefully carried out from benchmark problems such as cylinder Couette flow and a beam in a fluid tunnel to more challenging problems such as a flexible beam in the wake of a cylinder and the swimming of a two-dimensional fishlike body. Comparisons of the numerical results with the referenced solutions show that all desirable features of these coupled methods are inherited in the present coupling scheme, and the efficiency of the present method to model such complex problems is verified.

Figure 1

Illustration of the immersed-boundary method. The boundary is represented by the Lagrangian points and fluid points are represented by the intersection points of mesh lines. The interaction area between the solid point and the fluid points is enclosed by dashed lines.

Figure 2

Edge-based smoothing domain construction.

Figure 3

Algorithm diagram of the present coupling scheme.

Figure 4

Sketch of the cylindrical Couette flow.

Figure 5

(a) Spatial convergence properties of the fluid velocity. (b) Tangential velocity profiles alone the line $\theta =0$.

Figure 6

Sketch of a beam in a fluid tunnel.

Figure 7

Comparison of horizontal fluid velocities along the vertical plane $x=2$ cm using the direct-forcing IB-LBM [17], the bounce-back based LBM, and the present IB-LBM. Three mesh sizes $h_f=1/50\text{cm},1/100\text{cm},1/200$ cm are employed using the present method. The results by the direct-forcing IB-LBM and bounce-back based LBM are obtained on the finest mesh size.

Figure 8

Comparison of streamlines for flows over a rigid beam using the present IB-LBM [(a), (b)], the direct-forcing IB-LBM [17] [(c), (d)], and the bounce-back based LBM [(e), (f)].

Figure 9

Comparison of the tip displacement employing the present method with Zhang's results [39].

Figure 10

The convergence properties of the beam tip displacement and fluid velocity at $t=10$ s.

Figure 11

The horizontal velocity contours and the streamlines snapshots at $t=10$ s. The red dots represent the solid node positions. Results in (a), (b), and (c) are obtained by the present IB-LBM, the direct-forcing IB-LBM, and the implicit IB-LBM, respectively, with the same mesh size of $h_s=1/75\text{cm},h_f=1/100$ cm.

Figure 12

Sketch of a flexible beam in the wake of a cylinder.

Figure 13

The horizontal velocity contours at four typical time shots in an oscillating cycle. $T$ denotes the oscillating period.

Figure 14

The pressure contours at four typical time shots in an oscillating cycle. $T$ denotes the oscillating period.

Figure 15

(a) The displacement in the $y$ direction of point A. (b) The displacement in the $x$ direction of point A.

Figure 16

The temporal evolution of the beam tip with different mesh sizes: (a) tip displacement in the $y$ direction; (b) tip displacement in the $x$ direction.

Figure 17

The convergence properties of the mean value and amplitude of the beam tail point A in the $x$ and $y$ directions. The results from Turek and Hron [41] are employed as the reference solutions.

Figure 18

The time history of instantaneous and total artificial energy. The superscripts $a$ and $b$ denote the results obtained with and without employing the time-average technique, respectively.

Figure 19

Model of the fish.

Figure 20

Swimming speed against time in the $x$ direction.

Figure 21

Vorticity contours at four typical time stages.

Figure 22

Tail displacement $d_{yB}$, total FSI force $F_x$, and swimming speed $v_x$ against time in the $x$ direction.

Figure 23

Swimming speed $v_x$ against fish stiffness $E^s$ with different muscle strength $F_s$.