Large Eddy simulation with the immersed boundary method: implementation of an adaptive wall-modeling approach for complex turbulent flows

High Reynolds number turbulent flows dominate critical engineering applications, ranging from aircraft and other vehicles to wind turbines and turbomachinery. However, their simulation remains an open challenge: such flows are characterized by a multi-scale nature, requiring an enormous number of degrees of freedom. Wall-Modeled Large Eddy Simulation (WM-LES) addresses this problem by resolving the largest scales of the motion while modeling the smaller ones and the near-wall turbulent structures. In the present work, the Immersed Boundary Method (IBM) provides a flexible framework that avoids the complexity of body-fitted meshes. The presence of the immersed geometry is enforced in the discretized governing equations by a forcing algorithm coupled with the wall model. The initial approach for the immersed boundary forcing in the solver was based on the identification of the interface through sign changes of the level set across adjacent cell nodes, resulting in the application of the forcing to a staircase-approximated wall. To improve the approach, a refined forcing technique was developed and integrated, based on the analytical computation of the cut-cell wetted area, coupled with a flux redistribution method. This geometric characterization redefines the numerical interface, utilizing the analytically evaluated surface to accurately compute the wall-model forcing, which is then introduced into the governing equations. The result is a more uniform and consistent boundary representation that introduces no significant computational overhead. The proposed formulation was tested against two benchmarks: a canonical channel flow, demonstrating good agreement with the analytical Reichardt law, and the ERCOFTAC periodic hills, in which the solver successfully captured complex macroscopic flow topologies, including separation from a curved boundary, the formation of a free shear layer, and flow reattachment. To further assess the robustness of the numerical framework, a highly complex Airbus A320 wing-pylon-engine assembly was simulated under an inoperative engine configuration. The solver proved particularly stable under these demanding conditions, qualitatively reproducing several expected aerodynamic phenomena.