Application of multi-block approach in the immersed boundary–lattice Boltzmann method for viscous fluid flows

The immersed boundary–lattice Boltzmann method was presented recently to simulate the rigid particle motion. It combines the desirable features of the lattice Boltzmann and immersed boundary methods. It uses a regular Eulerian grid for the flow domain and a Lagrangian grid for the boundary. For the lattice Boltzmann method, as compared with the single-relaxation-time collision scheme, the multi-relaxation-time collision scheme has better computational stability due to separation of the relaxations of various kinetic models, especially near the geometric singularity. So the multi-relaxation-time collision scheme is used to replace the single-relaxation-time collision scheme in the original immersed boundary–lattice Boltzmann method. In order to obtain an accurate result, very fine lattice grid is needed near the solid boundary. To reduce the computational effort, local grid refinement is adopted to offer high resolution near a solid body and to place the outer boundary far away from the body. So the multi-block scheme with the multi-relaxation-time collision model is used in the immersed boundary–lattice Boltzmann method. In each block, uniform lattice spacing can still be used. In order to validate the multi-block approach for the immersed boundary–lattice Boltzmann method with multi-relaxation-time collision scheme, the numerical simulations of steady and unsteady flows past a circular cylinder and airfoil are carried out and good results are obtained.