A parallel and adaptative Nitsche immersed boundary method to simulate viscous mixing

In this study, we present a parallel immersed boundary strategy that uses Nitsche's method (noted NIB) to weakly impose on a given fluid the boundary conditions associated with a solid of arbitrary shape and motion. Specific details of the software implementation, as done in the software Lethe, are discussed. We verify the NIB method and compare it with other methods in the literature on the well-established test cases of Taylor-Couette flow and von Karman vortex street. Then, we validate the NIB method through simulations of the mixing of fluid in a stirred tank, which is a process central to industries as diverse as polymer manufacturing, food processing, pharmaceutical or chemicals. Simulation results show excellent agreement with experimental data available in the literature for a large range of Reynolds numbers (Re ∈ 1, 2 × 10³), for baffled and unbaffled tanks with a pitched-blade turbine (PBT) impeller. Lastly, the versatility of the NIB method is demonstrated with simulations of a mixing rig with two off-centered impellers with overlapping swept volumes, a case that is either unpractical or impossible to simulate with many other techniques. The software as well as all the files that we used for the simulations are available in the public domain for ease of reproducibility.