A cell-centered adaptive projection method for the incompressible Navier–Stokes equations in three dimensions

We present a method for computing incompressible viscous flows in three dimensions using block-structured local refinement in both space and time. This method uses a projection formulation based on a cell-centered approximate projection, combined with the systematic use of multilevel elliptic solvers to compute increments in the solution generated at boundaries between refinement levels due to refinement in time. We use an L0-stable second-order semi-implicit scheme to evaluate the viscous terms. Results are presented to demonstrate the accuracy and effectiveness of this approach.