A multi-domain lattice Boltzmann mesh refinement method for non-Newtonian blood flow modeling

Multi-domain grid refinement is a well-established technique in lattice Boltzmann methods. However, the method is currently limited to the Newtonian flow and no established method exists for lattice Boltzmann mesh refinement in non-Newtonian fluids. This study introduces a new method for lattice Boltzmann multi-domain mesh refinement in non-Newtonian fluids, by employing rescaling, transition, and interpolation of the relaxation frequencies across the domains interface. The method also involves a correction scheme to resolve shear rate inequality across the interface, particularly in low shear rate regions of a shear-thinning flow. To adapt the method for blood flow simulations in vascular systems, it was further extended to address three dimensional (3D) cases with curved boundary interfaces, using a ghost node technique. The method was verified in two dimensions, through Hagen–Poiseuille and lid-driven cavity flows, as well as in 3D, with steady flow in an idealized stenosis, and pulsatile flow in a patient-specific aneurysm. Results were compared with fine single-resolution simulations and existing literature, showing strong agreement. The aneurysm simulation showed good agreement with wall shear stress predictions from the fine single-resolution simulation. The relative L2 norm of wall shear stress difference between the multi-domain and fine-grid simulation were 0.006 and 0.009 at end-diastole and peak-systole, respectively. Overall, the proposed method facilitates the efficient use of computational resources through mesh refinement. Combined with the high scalability of the lattice Boltzmann method for parallel simulations—attributable to the locality of computations, including shear rate calculations—this approach is well-suited for high-fidelity investigations of blood flow in arteries.