In this work, a local adaptive mesh refinement (AMR) embedded incompressible flow solver is developed for biomedical flows. This AMR technique is based on the block-structured mesh and adapted from an in-house numerical solver for the Navier-Stokes equations with immersed-boundary method embedded, which is suitable for flows with complex and moving boundaries in biomedical applications. Flow behavior of the human upper airway under various head-neck postures is evaluated using the developed AMR technique, where the head-neck posture is hypothesized to change the cross-sectional area of the airway, therefore the airflow and aerodynamic behavior. The anatomically accurate three-dimensional human upper airway model is reconstructed from human magnetic resonance images (MRI) with measurements from the literature. Analyses were performed on vortex dynamics and pressure fluctuations in the pharyngeal airway. It was found that the vortex formation and aerodynamic pressure were affected by the airway bending. The sniffing position or the head-neck junction extension posture tend to facilitate the airflow through the upper human airway.