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In this paper we propose and test the validity of simple andeasy-to-implement algorithms within the immersed boundary framework gearedtowards large scale simulations involving thousands of deformable bodies inhighly turbulent flows. First, we introduce a fast moving least squares(fast-MLS) approximation technique with which we speed up the process ofbuilding transfer functions during the simulations which leads to considerablereductions in computational time. We compare the accuracy of the fast-MLSagainst the exact moving least squares (MLS) for the standard problem ofuniform flow over a sphere. In order to overcome the restrictions set by theresolution coupling of the Lagrangian and Eulerian meshes in this particularimmersed boundary method, we present an adaptive Lagrangian mesh refinementprocedure that is capable of drastically reducing the number of required nodesof the basic Lagrangian mesh when the immersed boundaries can move and deform.Finally, a coarse-grained collision detection algorithm is presented which candetect collision events between several Lagrangian markers residing on separatecomplex geometries with minimal computational overhead.

A fast moving least squares approximation with adaptive Lagrangian mesh refinement for large scale immersed boundary simulations