(142df) A Second-Order Accurate Immersed Boundary-Lattice Boltzmann Method for Particle-Laden Flows

A new and efficient direct numerical method with second-order accuracy is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles. The method combines the state-of-the-art immersed boundary method (IBM), the multi-direct forcing method and the lattice Boltzmann method (LBM). Previously the combination of IBM and LBM could only achieve first-order accuracy though LBM is a second order method. The IBM was recently improved based on the traditional solver of incompressible Navier-Stokes equations. First, the multi-direct forcing method is adopted in the improved IBM to better approximate the no-slip/no-penetration (ns/np) condition on the surface of the particles. Second, a slight retraction of the Lagrangian grid from the surface towards the interior of the particles with a fraction of the Eulerian grid spacing helps increase the accuracy of the method. These two improvements are adopted in the present IB-LBM. The method is further improved by: 1) an over-relaxation technique in the procedure of multi-direct forcing method; and 2) an implementation of the classical fourth order Runge-Kutta scheme in the coupled fluid-particle interaction. The over-relaxation technique is demonstrated to yield higher orders of convergence when the retraction distance is fixed. The use of the classical fourth order Runge-Kutta scheme helps the overall IB-LBM achieve the second order accuracy and provides more accurate predictions of the translational and rotational motion of the particle. A novel finding of this study is the demonstration that the retraction allows a super-convergence of the method, which is around fourth order, with a proper range of the retraction distance. The new method has been validated by several benchmark applications and promises to be a very efficient and high-fidelity technique for fluid-particle interaction problems. More challenging problems with larger numbers of particles will be tested in the near future.