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. Copyright © 2010 John Wiley & Sons, Ltd.