Immersed boundaries in hypersonic flows with considerations about high-fidelity and massive parallelism

Summary

This paper inscribes itself in the ongoing doctoral work of the first author which aims at adapting the immersed boundary conditions (IBC) technique to three-dimensional (3D) large eddy simulations (LES) of viscous hypersonic flows around complex vehicles. The work relies on a pre-existing in-house IBC code, HYPERION (HYPERsonic vehicle design using Immersed bOuNdaries), originally developed in two dimensions (2D) as a proof of concept that it is possible to use IBC in the presence of strongly shocked flows [4]. As a first step towards the optimization of the 3D HYPERION, we discuss in this paper a novel MPI/Open MP hybrid rasterization algorithm allowing for the detection of immersed cells in record time even for very large problems. We then consider the least-square-based reconstruction algorithm from HYPERION [4]. It was shown in the original paper that the number of neighbors used in the reconstruction is directly related to the condition number of the least-square matrix and an optimum can be found when the condition number reaches an asymptote. In 3D configurations it is found that the number of neighbors has to be very high to ensure the proper conditioning of the least-square matrix. If the computation is distributed on several MPI processes (as is always the case in 3D for realistic return times), gathering the information from that many neighbors can cause obvious communication issues it amounts to covering large stencils with unrealistically large MPI halos. We therefore introduce an algorithm designed for a hybrid MPI/OpenMP environment based on migratable tasks and the consensus algorithm developed by [9] to remedy the former shortcoming. Finally, we discuss the premise of the implementation of LES capabilities in HYPERION. The last milestone of the main author's doctoral work is indeed to study the feasibility of embedding wall laws in the IBC modeling and reconstruction algorithm to try and counteract the low accuracy of the near-wall phenomena caused by the lack of body-fitted mesh.

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