A simple and scalable Immersed Boundary Method for high-fidelity simulations of fixed and moving objects on a Cartesian mesh

A simple and scalable Immersed Boundary Method based on cubic spline reconstructions is presented for high-fidelity simulations of immersed objects in a turbulent flow on a Cartesian mesh. The novelty of the proposed IBM lies in its simplicity, accuracy, scalability and its ability to simulate both fixed and moving immersed objects. The new IBM is thoroughly validated against a 1D benchmark, with the 2D flow around a cylinder at Re = 40 and 300 and the 3D flow around a sphere at Re = 300 and Re = 3700. Convergence studies and detailed error maps showing the spatial distribution of the velocity L2-Norm error compared to a spectral reference solution for the cylinders at Re = 40 show the robustness of the proposed method. The cost and performance of the method are also presented for multi-billion mesh node simulations with up to 65,536 computational cores. The potential of the method in handling multiple moving objects for practical applications is demonstrated with the control of a square bluff body wake by two rear pitching flaps