Lagrangian vs. Eulerian: An Analysis of Two Solution Methods for Free-Surface Flows and Fluid Solid Interaction Problems

As a step towards addressing scarcity of references on this topic, we compared the Eulerian and Lagrangian Computational Fluid Dynamics (CFD) approaches for solution free-surface Fluid–Solid Interaction (FSI) problems. The approach uses Finite Element Method (FEM) to spatially discretize Navier–Stokes equations. free surface is handled via volume-of-fluid (VOF) level-set (LS) equations; an Immersed Boundary (IBM) in conjunction with Nitsche’s technique were applied resolve fluid–solid coupling. For approach, smoothed particle hydrodynamics (SPH) method meshless discretization choice; no additional equations are needed handle or FSI We two flow around cylinder. dam break test was used gauge performance flows. Lastly, problems—one floating rigid body dropped into fluid one elastic gate interacting flow. conclude discussion robustness, ease model setup, versatility approaches. solvers study open-source available public domain.