A fourth-order Cartesian local mesh refinement method for the computational fluid dynamics of physiological flow in multi-generation branched vessels

Since abnormal fluid states in our body cause critical diseases, patient-specific computational fluid dynamics (CFD) probably become a standard diagnosis tool in the near future. The vessels in our body are multiple-branched tubes, which makes it difficult to obtain accurate solutions from conventional CFD methods. In this report, we propose a fourth-order local mesh refinement (LMR) method based on an interpolated differential operator scheme for simulating flow in multi-generation branched vessels. The proposed LMR method has the accuracy of fourth-order for three-dimensional advection and diffusion equations, respectively. We describe how to apply the LMR method to patient-specific pulmonary airflow simulations. In our method, the computational mesh size is determined locally by geometrical parameters: the diameter of airways and the distance from the airway wall. To demonstrate our method, an LMR model and a fine mesh model were compared for flow in the central airway, and there was no significant difference between results. We also show the applicability of the method to a maximum eleventh-generation airway model, where the number of computational nodes was reduced by 85% compared with the case using uniform fine meshes.