  In this paper we propose and test the validity of simple and
easy-to-implement algorithms within the immersed boundary framework geared
towards large scale simulations involving thousands of deformable bodies in
highly turbulent flows. First, we introduce a fast moving least squares
(fast-MLS) approximation technique with which we speed up the process of
building transfer functions during the simulations which leads to considerable
reductions in computational time. We compare the accuracy of the fast-MLS
against the exact moving least squares (MLS) for the standard problem of
uniform flow over a sphere. In order to overcome the restrictions set by the
resolution coupling of the Lagrangian and Eulerian meshes in this particular
immersed boundary method, we present an adaptive Lagrangian mesh refinement
procedure that is capable of drastically reducing the number of required nodes
of the basic Lagrangian mesh when the immersed boundaries can move and deform.
Finally, a coarse-grained collision detection algorithm is presented which can
detect collision events between several Lagrangian markers residing on separate
complex geometries with minimal computational overhead.
