Flow problems with moving boundaries and interfaces include fluid–structure interaction (FSI) and a number of other classes of problems, have an important place in engineering analysis and design, and offer some formidable computational challenges. Bringing solution and analysis to them motivated the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) method and also the variational multiscale version of the Arbitrary Lagrangian–Eulerian method (ALE-VMS). Since their inception, these two methods and their improved versions have been applied to a diverse set of challenging problems with a common core computational technology need. The classes of problems solved include free-surface and two-fluid flows, fluid–object and fluid–particle interaction, FSI, and flows with solid surfaces in fast, linear or rotational relative motion. Some of the most challenging FSI problems, including parachute FSI, wind-turbine FSI and arterial FSI, are being solved and analyzed with the DSD/SST and ALE-VMS methods as core technologies. Better accuracy and improved turbulence modeling were brought with the recently-introduced VMS version of the DSD/SST method, which is called DSD/SST-VMST (also ST-VMS). In specific classes of problems, such as parachute FSI, arterial FSI, ship hydrodynamics, fluid–object interaction, aerodynamics of flapping wings, and wind-turbine aerodynamics and FSI, the scope and accuracy of the FSI modeling were increased with the special ALE-VMS and ST FSI techniques targeting each of those classes of problems. This article provides an overview of the core ALE-VMS and ST FSI techniques, their recent versions, and the special ALE-VMS and ST FSI techniques. It also provides examples of challenging problems solved and analyzed in parachute FSI, arterial FSI, ship hydrodynamics, aerodynamics of flapping wings, wind-turbine aerodynamics, and bridge-deck aerodynamics and vortex-induced vibrations.

Engineering Analysis and Design with ALE-VMS and Space–Time Methods

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.

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

URANS studies of hydrodynamic performance and slamming loads on high-speed planing hulls in calm water and waves for deep and shallow conditions

Usually gravity can be neglected for planing vessels at very high planing speed. However, if the planing speed becomes lower, the influence of gravity must be considered. A 2D+t theory with gravity effects is applied to study the steady performance of planing vessels at moderate planing speeds. In the framework of potential theory, a computer program based on a boundary-element method (BEM) in two dimensions is first developed, in which a new numerical model for the jet flow is introduced. The spray evolving from the free surface is cut to avoid the plunging breaker to impact on the underlying water. Further, flow separation along a chine line can be simulated. The BEM program is verified by comparing with similarity solutions and validated by comparing with drop tests of V-shaped cylinders. Then the steady motion of prismatic planing vessels is studied by using the 2D+t theory. The numerical results are compared with the results by Savitsky’s empirical formula and the experiments by Troesch. Significant nonlinearities in the restoring force coefficients can be seen from the results. Three-dimensional effects are discussed to explain the difference between the numerical results and the experimental results. Finally, in the comparison of results at high planing speed and moderate planing speed, it is shown that the gravity not only affects the free-surface profile around the hull, but also influences the hydrodynamic force on the hull surface.

The influence of gravity on the performance of planing vessels in calm water

The dynamic response of planing vessels in regular head seas is investigated numerically. Nonlinear time domain simulations were performed using a 2D + t theory (two-dimensional plus time dependent theory). A prismatic hull form was assumed. We employed a two-dimensional (2D) boundary element method to solve the initial boundary value problems in 2D cross planes, in which nonlinear free-surface conditions and exact body boundary conditions were satisfied. At each time step, the total force and moment on the hull could be obtained by using the sectional forces calculated in those 2D planes. Heave and pitch motions were then acquired by solving the equations for those motions. The calculated heave and pitch responses were compared with the experiments by Fridsma (A systematic study of the rough-water performance of planing boats. Davidson Laboratory Report R-1275, 1969) for two different Froude numbers. Three-dimensional (3D) corrections at the transom stern were applied to show the influence of the 3D effect at the stern on the numerical results. Ship motions were affected by the 3D corrections, especially near the resonance frequency, while the phase angles were slightly affected and the acceleration peaks at the bow near the resonance frequency were sensitive to the 3D corrections. Other error sources in the theoretical results are also mentioned.

Dynamic motions of planing vessels in head seas

: A series of constant-deadrise models, varying in length, was tested in smooth water and regular waves to define the effects of deadrise, trim, loading, speed, length-beam ratio, and wave proportions on the added resistance, on heave and pitch motions, and on impact accelerations at the bow and center of gravity. Each of these parameters was varied independently of the others so as to obtain a proper evaluation of the effects of changing a single quantity. The results, presented in the form of response characteristics, cover a wide range of operating conditions; and show, quantitatively, the importance of design parameters on the rough-water performance of planing hulls.

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Gerald Fridsma

Papers

A systematic study of the rough-water performance of planing boats