Investigation of direct forcing immersed boundary method

The direct forcing immersed boundary method (DF-IBM) is very popular in direct numerical simulation of rigid particulate flows. However, most simulations are limited to spherical particles. The current theory relies upon matching the Eulerian mesh (fluid) velocity and the Lagrangian markers (particles) velocity to correctly model the interaction between the fluid and particles. This approach poses two main difficulties in its extension to irregular particles, one to generate Lagrangian markers in accordance to the Eulerian mesh, the other to assign to each marker a proper weight. Here, analyses show that the interaction force modeling in DF-IBM is actually seeking the least-square error solution for the fluid-particle system, which can also been seen as a reflective projection of unperturbed fluid force field over the fluid-particle interface region. Through investigating the projection subspace, an unexpected conclusion is that the marker distribution can be chosen freely to a great extent, without noticeable impact on the results. On the other hand, the weight proves to be a relaxation factor, whose optimal value is the largest limited by a stability condition. Numerical examples are provided to support the new theories.