A multi-domain lattice Boltzmann method for mesh refinement with curved boundary interfaces

Multi-domain grid refinement is a well-known method for mesh refinement in Lattice Boltzmann Methods (LBM). However, the method in three-dimensional cases is currently limited to problems in which the interface between domains can only be surfaces with straight boundaries, and no 3D multi-domain LBM method is specifically tailored for cases with domain interface on a complex curved boundary. Complex geometries like this are frequently observed in blood flow in cardiovascular systems. In this paper, an LBM multi-domain method was developed for grid refinement with curved boundary interfaces. The proposed method is based on using an interpolative second-order wall boundary condition in conjunction with a new image-based ghost node method for near-wall treatment at the interface. The method was verified to show second-order accuracy in space at the domain interface in a circular Poiseuille flow. The methodology was further employed in three different cases: steady idealized stenosis flow, pulsatile flow in the carotid bifurcation, and pulsatile flow in an intracranial aneurysm. The results were compared to single-resolution simulations for each case. For the resolutions used in these cases, the relative L2 norm of the difference between the multi-domain and fine single-resolution simulation had the following values: 0.005 for velocity magnitude at the stenosis center, 0.002 for mass flowrate splitting in the bifurcation, and 0.008 for wall shear stress in peak systole in the aneurysm dome. For these examples, the method demonstrated up to 65 % speedup for the bifurcation simulation and 39 % speedup for the aneurysm simulation compared to single-resolution simulations.