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?C225, 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?C130, 2001; Akin et?al. in Comput Fluids 36:2?C11, 2007; Cruchaga et?al. in Int J Numer Methods Fluids 54:1021?C1031, 2007), where the level set technique is used for capturing the air?Cwater 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.