Fluid-structure interaction problem in the framework of Arbitrary Lagrangian-Eulerian (ALE) description using a monolithic approach in 2D

The partitioned approach for solving fluid-structure interaction problems is prone to numerical instabilities, often leading to a lack of convergence. Overcoming these challenges requires stabilization techniques and reduced time steps, significantly increasing computational costs. In this study, a monolithic formulation within the Arbitrary Lagrangian-Eulerian (ALE) framework is proposed for analyzing fluid-structure interaction problems, enabling efficient tracking of moving boundaries. The Navier-Stokes equations for unsteady fluid flow and the linear elasticity equations for the structure are solved in a strongly coupled manner. Comparison with the partitioned approach revealed that the average computational time per step in the partitioned method was 51 seconds, while the proposed approach required only 7 seconds, demonstrating its computational efficiency. Furthermore, the proposed method eliminates the added mass effect, enhances solution accuracy, and prevents sudden oscillations observed in the partitioned approach.Additionally, mesh dependency analysis showed that increasing the degrees of freedom from 85,452 to 1,141,027 resulted in only a 2% increase in pressure and displacement, indicating minimal sensitivity to mesh size. This highlights the robustness and efficiency of the proposed method in solving fluid-structure interaction problems.