In the present paper a computational algorithm suitable for large-eddy simulations of fluid/structure problems that are commonly encountered in biological flows is presented. It is based on a mixed Eurelian-Lagrangian formulation, where the governing equations are solved on a fixed grid, which is not aligned with the body surface, and the non-slip conditions are enforced via local reconstructions of the solution near the solid interface. With this strategy we can compute the flow around complex stationary/moving boundaries and at the same time maintain the efficiency and optimal conservation properties of the underlying Cartesian solver. A variety of examples, that establish the accuracy and range of applicability of the method are included.

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