Current work presents a monolithic method for the solution of fluid-structure interaction problems involving flexible structures and free-surface flows. The technique presented is based upon the utilization of a Lagrangian description for both the fluid and the structure. A linear displacement-pressure interpolation pair is used for the fluid whereas the structure utilizes a standard displacement-based formulation. A slight fluid compressibility is assumed that allows to relate the mechanical pressure to the local volume variation. The method described features a global pressure condensation which in turn enables the definition of a purely displacement-based linear system of equations. A matrixfree technique is used for the solution of such linear system, leading to an efficient implementation. The result is a robust method which allows dealing with FSI problems involving arbitrary variations in the shape of the fluid domain. The method is completely free of spurious added-mass effects.

SUMMARY We propose a technique for improving mass‐conservation features of fractional step schemes applied to incompressible flows. The method is illustrated by using a Lagrangian fluid formulation, where the mass loss effects are particularly apparent. However, the methodology is general and could be used for fixed grid approaches. The idea consists in reflecting the incompressibility condition already in the intermediate velocity. This is achieved by predicting the end‐of‐step pressure and using this prediction in the fractional momentum equation. The resulting intermediate velocity field is thus much closer to the final incompressible one than that of the standard fractional step scheme. In turn, the predicted pressure can be used as the boundary condition necessary for the solution of the pressure Poisson equation in case a continuous Laplacian matrix is employed. Using this approximation of the end‐of‐step incompressible pressure as the essential boundary condition considerably improves the conservation of mass, specially for the free surface flows of fluids with low viscosity. The pressure prediction does not require the resolution of any additional equations system. The efficiency of the method is shown in two examples. The first one shows the performance of the method with respect to mass conservation. The second one tests the method in a challenging fluid–structure interaction benchmark, which can be naturally resolved by using the presented approach. Copyright © 2012 John Wiley & Sons, Ltd.

h i g h l i g h t sWe model the droplet dynamics on a PEFC cathode gas channel with a novel technique. A simple method to obtain interface curvature in two dimensions is given. Dynamic contact angle condition for droplets on rough surfaces is presented. Results can predict several variables of interest and agree with experimental data. a b s t r a c tAn embedded Eulerian-Lagrangian formulation for the simulation of droplet dynamics within a polymer electrolyte fuel cell (PEFC) channel is presented. Air is modeled using an Eulerian formulation, whereas water is described with a Lagrangian framework. Using this framework, the gas-liquid interface can be accurately identified. The surface tension force is computed using the curvature defined by the boundary of the Lagrangian mesh. The method naturally accounts for material property changes across the interface and accurately represents the pressure discontinuity. A sessile drop in a horizontal surface, a sessile drop in an inclined plane and droplets in a PEFC channel are solved for as numerical examples and compared to experimental data. Numerical results are in excellent agreement with experimental data. Numerical results are also compared to results obtained with the semi-analytical model previously developed by the authors in order to discuss the limitations of the semi-analytical approach.

An embedded formulation for the simulation of immiscible multi-fluid problems is proposed. The method is particularly designed for handling gas-liquid systems. Gas and liquid are modeled using the Eulerian and the Lagrangian formulation, respectively. The Lagrangian domain (liquid) moves on top of the fixed Eulerian mesh. The location of the material interface is exactly defined by the position of the boundary mesh of the Lagrangian domain. The individual fluid problems are solved in a partitioned fashion and are coupled using a Dirichlet-Neumann algorithm. Representation of the pressure discontinuity across the interface does not require any additional techniques being an intrinsic feature of the method. The proposed formulation is validated and its potential applications are shown.