Adaptive Mesh Refinement Strategies for Immersed Boundary Methods

In the present study we propose an adaptive mesh refinement (AMR) strategy which can be coupled with embedded boundary methods in a straightforward manner. The building-block of the AMR solver is a structured Cartesian solver employed on a hierarchy of sub-grids. A fractional-step formulation is used for the time advancement, and all spatial derivatives are discretized on a staggered grid using second-order, central finite-differences. The boundary conditions on an arbitrary body immersed in the AMR grid are imposed using a direct-forcing, embedded boundary formulation. The overall method is second order accurate both in space and time. The accuracy and robustness of the approach are demonstrated for the flow around a sphere and a flow around a sphere bouncing off a wall.