The aim of this work is to present a sencond-order projection method which solves the time dependent Navier-Stokes equations of a viscous, incompressible flow with constant density on a block-structured computational mesh. This projection method is obtained by coupling a second-order fractional-step variation of the original Chorin's projection method to an adaptive mesh refinement technique. In  this approach,  regions of the flow containing special features (e.g., boundary layers) are covered by a sequence of nested, progressively finer rectangular grid patches, concentrating in this way the computational effort to where it is most needed. A quite "standard" second order spatial discretization of the nonlinear advection terms, suitable for flows at low Reynolds numbers, is used, allowing for the development of the rest of the algorithm in the simplest possible setting. The numerical results obtained for simple model problems discretized on  block-structured computational meshes show that for smooth flows the method preserves its second order behavior and that for flows with special features the method, by appropriate refining the computational domain, achieves the same accuracy as if the whole computation had been performed on an uniform mesh with the resolution of the finest grid patches that are used.
 

Roma, A.M.: A projection method for the Navier-Stokes equations on adaptively refined meshes, Proceedings of the II Pan-American Workshop of Computational and Applied Mathematics, p.45, Gramado, RS, Brazil, 09/08-12, 1997.