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A Cell-Centered Adaptive Projection Method for the Incompressible Euler Equations

We present an algorithm to compute adaptive solutions for incompressible flows using block-structured local refinement in both space and time. This method uses a projection formulation based on a cell-centered approximate projection, which allows the use of a single set of cell-centered solvers. Because of refinement in time, additional steps are taken to accurately discretize the advection and projection operators at grid refinement boundaries using composite operators which span the coarse and refined grids. This ensures that the method is approximately freestream preserving and satisfies an appropriate form of the divergence constraint.