Toward free-surface modeling of planing vessels: simulation of the Fridsma hull using ALE-VMS

In this paper we focus on a class of applications involving surface vessels moving at high speeds, or "planing". We introduce a Fridsma planing hull benchmark problem, and simulate it using the finite-element-based ALE-VMS (Bazilevs et al. in Math Models Methods Appl Sci 2012; Takizawa et al. in Arch Comput Methods Eng 19:171-225, 2012) approach. The major reasons for selecting this problem is the relative simplicity of the hull geometry and the existence of high-quality experimental data used for the purposes of validation. The ALE-VMS approach is formulated in the context of the Mixed Interface-Tracking/Interface-Capturing Technique (MITICT) (Tezduyar in Arch Comput Methods Eng 8:83-130, 2001; Akin et al. in Comput Fluids 36:2-11, 2007; Cruchaga et al. in Int J Numer Methods Fluids 54:1021-1031, 2007), where the level set technique is used for capturing the air-water interface, and the Arbitrary Lagrangian Eulerian (ALE) method is employed to track the interface between the fluid and structure. In this work, the planing hull structure is treated as a six-degree-of-freedom rigid object. The computational results obtained for the Fridsma hull, which include convergence of the trim angle and drag under mesh refinement, match well with the experimental data.