A lattice-Boltzmann solver coupled to an immersed boundary method with applications to fluid structure interaction.
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An immersed boundary method (IBM) is coupled to a Lattice-Boltzmann solver (ProLB) based on the Hybrid Recursive Regularized1 (HRR) collision model, and a finite element solver (Calculix) with the explicit Hilber-Hughes-Taylor method. An explicit coupling between ProLB and Calculix has been developed, in which ProLB sends the forces on each solid point to Calculix, which in return sends the displacement and velocity of the solid points to ProLB. The explicit coupling between the two solvers is analyzed, in terms of robustness and accuracy. Because of the staggered approach used here, the explicit coupling (or loosely coupled) schemes, (i.e. that only involve the solution of the fluid and the structure once per time step for instance), are known to give rise to numerical instabilities2. In order to overcome this problem and stabilize the coupling, we compare different prediction schemes for the advancement in time of the displacement and velocity of the solid points. We perform a thorough numerical study to validate and characterize the efficiency, stability and accuracy of the numerical framework using a set of test-cases of increasing complexity. The robustness and accuracy of the method are assessed first in a laminar configuration: an elastic beam attached to a fixed cylinder3. Then, we apply our solver to a 3D aortic valve on a cardiac cycle. The level of high-frequencies numerical instabilities is monitored and compared with and without the prediction schemes for the displacements and the velocities.
