An implicit boundary element solution with consistent linearization for free surface flows and non‐linear fluid–structure interaction of floating bodies

Abstract

SUMMARYIn this work, a new comprehensive method has been developed which enables the solution of large, non-linear motions of rigid bodies in a uid with a free surface. The application of the modern EulerianLagrangian approach has been translated into an implicit time-integration formulation, a development which enables the use of larger time steps (where accuracy requirements allow it). Novel features of this project include: (1) an implicit formulation of the rigid-body motion in a uid with a free surface valid for both two or three dimensions and several moving bodies; (2) a complete formulation and solution of the initial conditions; (3) a fully consistent (exact) linearization for free surface ows valid for any boundary elements such that optimal convergence properties are obtained when using a NewtonRaphson solver. The proposed framework has been completed with details on implementation issues referring mainly to the computation of the complete initial conditions and the consistent linearization of the formulation for free surface ows.The second part of the paper demonstrates the mathematical and numerical formulation through numerical results simulating large free surface ows and non-linear uid structure interaction. The implicit formulation using a fully consistent linearization based on the boundary element method and the generalized trapezoidal rule has been applied to the solution of free surface ows for the evolution of a triangular wave, the generation of tsunamis and the propagation of a wave up to overturning. Fluidstructure interaction examples include the free and forced motion of a circular cylinder and the sway, heave and roll motion of a U-shaped body in a tank with a ap wave generator. The presented examples demonstrate the applicability and performance of the implicit scheme with consistent linearization.

A new method for simulating rigid body motion in incompressible two‐phase flow

“…For this example Re ≈ 8e6. For the numerical results of [29] the damping ratio is approximately 0.19, and in our numerical results it is slightly less (0.15). The damping ratio is calculated as…”

“…The liquid phase has properties of water with = 1000(kg/m 3 ), = 0.001(kg/m·s), and the gas phase has properties of air with = 1(kg/m 3 ), = 0.00002(kg/m·s). Results are shown in comparison to those from [28,29] in Figure 11 for a grid size of x = y = 0.3 m. In both the current and previous numerical studies the heave motion of the cylinder decays over a 10-s simulation period and the center of mass settles to the predicted position (indicated by the dotted line) based on buoyancy. The Reynolds number in this case can be defined [30] by…”

“…There have been analytical and numerical studies to provide benchmarks [28,29] and in this case we study a circular cylinder in a tank of water and air, with density half that of water such that the buoyant equilibrium point is approximately half submerged (the density of air being 1000 times smaller does comparatively little to change the final equilibrium position). To match the simulations of [29], which treated non-linear freesurface/rigid body interaction with an implicit boundary element technique, a cylinder with radius 2 m is positioned in a tank of 50 m in length with rigid walls and a no-slip condition at the ends (a condition that allows reflected waves). The depth of the tank is 4 m. The initial position of the cylinder's center of mass is 0.5 m above the free surface.…”

An improved low-order boundary element method for breaking surface waves

“…Two recent reviews are presented by Grilli and Subramanya [21] and by Kim et al [22]. Donescu and Virgin [23] have developed an Eulerian-Lagrangian implicit time integration formulation and applied it to 3D wave body interaction.…”

Partitioned vibration analysis of internal fluid‐structure interaction problems

“…For sloshing motions of fluid in partially filled flexible containers, various formulations and solution methods have been proposed, which include the following: velocity potential for the fluid and modal superposition for the structure [9,10], Boundary integral for the fluid and modal superposition/FEM for the structure [11][12][13][14][15][16], Eulerian-Lagrangian equations for the fluid and the finite Numerical experiments using the present partitioned continuum-based FSI formulation are carried out in Section 10, which illustrate the validity of the present partitioned FSI formulation for linearized structural vibrations due to both acoustic and sloshing phenomena, and nonlinear transient responses. Finally, a discussion of the present study, further refinements, and open problems are offered in Section 11.…”