We describe a new algorithm for the solution of the laminar, incompressible Navier-Stokes equations for steady, two-dimensional flows. The basis of the method is a robust and efficient multigrid algorithm. A novel feature of our approach is that it dynamically adapts the grid as part of the solution process. Special interpolation operators have been used to ensure exact mass conservation. This technique can give significant savings in both CPU time and memory usage. The code has been implemented on a global shared-memory architecture, and speedups of over 13 have been observed on 20 processors. This implies that less than 2% of the code is intrinsically serial.