Simulation of Wave Breaking Impact Forces on Walls Using the Cahn-Hilliard Navier-Stokes Equations

In this paper, we address the numerical simulation of wave-breaking impact forces on walls in the context of membrane LNG sloshing applications. Traditional front-tracking (ALE) methods provide a precise representation of the free surface under moderate deformations, yet can struggle with topological changes such as droplet formation, merging, and fragmentation. To capture these complex interface dynamics, we propose and validate a Cahn–Hilliard–Navier–Stokes (CHNS) formulation integrated into the finite element solver CADYF. By comparing the results of both approaches—front-tracking and diffuse-interface—on key test cases (including Rayleigh–Taylor instability, a large gas-pocket impact scenario, and a piston-generated breaking wave), we demonstrate consistent predictions in terms of free-surface shapes. The CHNS method naturally accommodates strong topological changes but requires careful calibration of parameters and local mesh refinement for high accuracy. The front-tracking approach, on the other hand, excels at sharply imposing jump conditions whenever the interface remains continuous. Overall, the two strategies exhibit complementary strengths, and their agreement in wave-impact benchmarks underlines the reliability of CADYF for sloshing-related flows. Ongoing and future work will refine the CHNS approach using adaptive remeshing, extend validations against experimental data, and further explore free-surface instabilities and fragmentation phenomena to enhance predictions of impact loads in LNG membrane tanks and related applications.General Context. The general context of this study is the sloshing assessment of membrane LNG tanks on floating structures thanks to sloshing model tests. The flows of liquid and gas within the model tank are not in complete similarity with the flows within the LNG tank because the fluids properties, other than their densities, do not match the right values to comply with the relevant similarity laws. Therefore, it is important to understand the influence of the different biases on the long-term statistics of pressure measurements when a complete similarity is assumed to enable up-scaling the pressures by dimensional analysis.