271673 A Second-Order Accurate Immersed Boundary-Lattice Boltzmann Method for Particle-Laden Flows

Monday, October 29, 2012
Hall B (Convention Center )
Qiang Zhou, William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, OH and L. S. Fan, Chemical and Biomolecular Engineering, The Ohio State University, Columbus, OH

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.

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