Immersed boundary methods coupled with adaptive mesh refinement (AMR) are a powerful tool to solve complex viscous incompressible flow problems, especially in the presence of moving and deforming boundaries. Immersed boundary methods have been traditionally used in the framework of fractional step formulations for temporal integration and are generally coupled to logically structured grids, where the elliptic problem for the pressure is solved using fast solution techniques. In many situations, especially at large Reynolds numbers, adaptive clustering of fluid grid points on large gradient regions is desirable. This article gives an overview of currently available AMR tools, with an emphasis on block structured grids that are a natural fit to immersed boundary methods, and discusses future trends.

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