A scalable immersed boundary method for large scale simulations with moving geometries

The constraint based immersed boundary (cIB) method has been shown to be accurate for low Reynolds number (Re) flows. In our studies of flow around immersed bodies at moderate and high Re, we found that cIB is not able produce accurate results. High Re flows typically result in large pressure gradient across fluid-IB interface. This jump in pressure is more pronounced when IB is an interface and has zero-thickness. The jump in pressure leads to incorrect pressure gradient evaluation near the fluid-IB interface leading to inaccuracies in the boundary layer around the IB, and it can also lead to leakage of flow across the fluid- interface. A numerical formulation that avoids jump in pressure through a modified pressure gradient operator will be presented. The pressure gradient operator is modified through a WENO based stencil penalization.  The numerical method is implemented in a software based on a hierarchical meshing technique known as building cube method (BCM). A Lagrangian-Eulerian framework, with the immersed body/structure on the Lagrangian mesh and the fluid on an Eulerian mesh, is used for the immersed boundary method.  The information exchange between the two meshes is typically achieved through appropriate interpolation/interaction operators. In the framework of unstructured meshes, or block structured meshes like BCM the interpolation is an expensive proposition and its scalability poor. In this context, we present a block structured Lagrangian data structure that minimizes the cost of interpolation and improves the scalability of the Lagrangian- Eulerian methods.  Validation of the numerical method for standard benchmark cases like the flow past a sphere and also for complex geometries like full vehicle with ʼdirtyʼ CAD geometry data will be presented. Strong scaling results of the numerical software with and without the immersed boundary method will also be presented