An immersed boundary method coupled with a dynamic overlapping-grids strategy

An immersed-boundary method is devised within an existing finite-volume dynamic overlapping-grids solver. The immersed-boundary approach allows improved flexibility, removing the constraint of the Eulerian grid to conform to the geometry of solid bodies within the fluid domain. This is beneficial to the regularity of the grid, especially in the near wall regions, improving the stability and accuracy of the overall method. Furthermore, grid generation, which is a very time-consuming, non-automated task in body-fitted techniques, requiring a significant effort in terms of human work-hours, is dramatically simplified. Here the immersed-boundary strategy is utilized together with curvilinear grids capabilities, which are useful to keep cells count under control, a major issue in more conventional immersed-boundary methods using Cartesian grids. The main advantage of the proposed approach is the coupling with a dynamic overlapping-grids methodology. This is especially convenient in presence of moving bodies, since the grid attached to a moving immersed-boundary can follow the body during its motion, with no need to update the position of the Lagrangian grid, discretizing the body surface, relative to the associated Eulerian grid, discretizing the fluid domain in the vicinity of the body. A distance function is defined at each node of the computational grid, based on the position relative to the surface of the immersed-boundary, which is utilized to enforce no-slip boundary conditions via reconstruction of the solution in the vicinity of the body. Thanks to the dynamic overlapping grids, the distance function is computed only once in preprocessing, with no additional cost due to the motion of the immersed-boundary. Here the methodology is discussed in detail and test-cases are presented, featuring both stationary and moving bodies, also in relative motion. Results from present immersed-boundary computations are compared with body-fitted solutions by the same solver and with data from the literature as well. (C) 2019 Elsevier Ltd. All rights reserved.