Impaired respiration capabilities or a reduced sense of smell and taste are common for pathologically shaped nasal cavities. To analyze the flow in the human nasal cavity, simulations with a Lattice-Boltzmann Method (LBM) are carried out. This method is particularly suited to simulate flows in intricate geometries, it is efficient compared to solvers based on the Navier-Stokes equations, and straight forward to parallelize. A surface of the nasal cavity is extracted from Computer Tomography (CT) images and is used to automatically generate a hierarchically refined computational grid. Wall-bounded shear layers are highly resolved in contrast to regions of lower velocity gradients. In this way the overall number of cells is reduced and the computational efficiency is improved. A mean volume flux of 125 ml/sec is prescribed, which results in a Reynolds number of Re = 766 based on the averaged velocity and the averaged hydraulic diameter of the nostrils of the nasal cavity. Different nasal cavities are investigated, previously selected from medical analysis. A performance analysis of the algorithm is carried out to show the scalability of the code. The findings verify that the LBM is a valuable tool to predict and analyze the flow in the human nasal cavity for the individual patient and that it is suited for High Performance Computing (HPC) due to its good scalability.