A two-probe approach for hydrodynamic load evaluation in immersed boundary methods

In this work we propose a method to accurately evaluate hydrodynamic loads in fluid-structure interaction problems. The approach builds upon the probe method used within the direct-forcing immersed boundary method, introducing key improvements. Specifically, we relax the assumption of constant shear stress and employ two normal probes to enable a linear reconstruction of viscous stresses on the solid surface without relying on wall models. The method is validated against classical benchmark test cases for fluid-structure interaction in both two and three dimensions. Numerical results demonstrate that the proposed approach achieves second-order convergence rate in the evaluation of hydrodynamic loads, while also providing increased accuracy and a smoother stress distribution on solid surfaces. Furthermore, we show that the method is applicable to elastic, deformable structures with zero thickness.