A flow-reconstruction based approach for the computation of hydrodynamic stresses on immersed body surface

This study focuses on obtaining reliable hydrodynamic stresses on the surface of rigid bodies in the simulation of fluid-solid interactions using the diffuse-interface immersed boundary method (IBM). In order to obtain the pressure and velocity gradient information on the immersed boundary, we employ a model to reconstruct the near-boundary fluid flow along the surface normal direction. Different from most existing flow reconstruction models in diffuse-interface IBMs based on the boundary layer approximation, we propose a new reconstruction model relying only on the non-slip velocity and local flow information. With this improvement, the present reconstruction model is theoretically applicable to fluid flows with intermediate Reynolds numbers (with the existence of a laminar boundary layer) and low Reynolds numbers (in the absence of a boundary layer). To examine the validity of the present reconstruction model, we conduct a series of simulations, including the uniform flow past a fixed body and the settling of a rigid body in a quiescent fluid. It is demonstrated that the present reconstruction model has a better performance than existing models in predicting hydrodynamic stresses on the immersed boundary within a wide range of Reynolds numbers from O(1) to O(100). The capability and robustness of the proposed model demonstrate its potential to address fluid-solid interaction problems with a-priori unknown or time-varying Reynolds numbers, such as fully resolved simulations of particle laden flows.