The immersed boundary-lattice Boltzmann method for solving fluid–particles interaction problems

A new computational method, the immersed boundary-lattice Boltzmann method, is presented. This method is a combination and utilizes the most desirable features of the lattice Boltzmann and the immersed boundary methods. The method uses a regular Eulerian grid for the flow domain and a Lagrangian grid to follow particles that are contained in the flow field. The rigid body conditions for the fluid and the particles are enforced by a penalty method, which assumes that the particle boundary is deformable with a high stiffness constant. The velocity field of the fluid and particles is solved by adding a force density term into the lattice Boltzmann equation. This novel method preserves the advantages of LBM in tracking a group of particles and, at the same time, provides an alternative and better approach to treating the solid–fluid boundary conditions. The method also solves the problems of fluctuation of the forces and velocities on the particles when the “bounce-back” boundary conditions are applied. This method enables one to simulate problems with particle deformation and fluid–structure deformation. Its results are validated by comparison with results from other methods.