We present an efficient parallelized multidomain algorithm for solving the 3D Navier–Stokes equations in cylindrical geometries. The numerical method is based on fourth-order compact schemes in the two non-homogeneous directions and Fourier series expansion in the azimuthal direction. The temporal scheme is a second-order semi-implicit projection scheme leading to the solution of five Helmholtz/Poisson equations. To handle the singularity appearing at the axis in cylindrical coordinates, while being able to have a thinner or conversely a coarser mesh in this zone, parity conditions are imposed at r=0r=0 for each flow variable and azimuthal Fourier mode. To simulate flows in irregularly shaped cylindrical geometries and benefit from a hybrid OpenMP/MPI parallelization, an accurate perfectly free-divergence multidomain method based on the influence matrix technique is proposed. First, the accuracy of the present solver is checked by comparison with analytical solutions and the scalability is then evaluated. Simulations using the present code are then compared to reliable experimental and numerical results of the literature showing good quantitative agreements in the cases of the axisymmetric and 3D unsteady vortex breakdowns in a cylinder and turbulent pipe flow. Finally to show the capability of the algorithm to deal with more complex flows relevant of turbomachineries, the turbulent flow inside a simplified stage of High-Pressure compressor is considered.