Fully Nonlinear Potential Flow Research Articles

Simulation of floating structure dynamics in waves by implicit coupling of a fully non-linear potential flow model and a rigid body motion approach

We demonstrate the accuracy and convergence of a new numerical model solving wave-structure interactions based on the fully non-linear potential flow (FNPF) theory coupled to a rigid body motion approach. This work extends an earlier model proposed by Guerber et al. (Eng Anal Bound Elements 36(7):1151–1163, 2012), restricted to fully submerged structures, by allowing to solve for freely floating bodies on the free surface. Although we are currently extending the model to three dimensions (3D), the work reported here only considers two-dimensional (2D) problems. We first introduce the FNPF model, originally developed in 2D by Grilli et al. (Eng Anal Bound Elements 6(2):97–107, 1989), Grilli and Subramanya (Comput Mech 17(6):374–391, 1996), and later extended to 3D by Grilli et al. (Int J Numer Methods Fluids 35(7):829–867, 2001). We present the implementation by Guerber et al. (Eng Anal Bound Elements 36(7):1151–1163, 2012) in the 2D-FNPF model of van Daalen’s implicit method for fluid-structure interactions [see van Daalen (Numerical and theoretical studies of water waves and floating bodies, PhD thesis, Universiteit Twente, The Netherlands 1993) and Tanizawa (Proceedings of 4th Osaka colloquium on seakeeping performance of ships 2000)]. We then detail the numerical scheme used for coupling the FNPF model to the motion of a floating rigid body. Moreover, we propose a new numerical strategy for advancing the free surface front inspired by symplectic integrators, which achieves a much better performance for energy conservation. The developed algorithm is first applied to forced motion cases, for which analytical and experimental results can be found in the literature and used as benchmarks. The accuracy of the numerical solution for the fluid and applied forces is then discussed for cases with small or large amplitude motion. In the latter case, a preliminary investigation of non-linear effects is performed for the classical application of a semi-circular heaving cylinder, by comparing the computed hydrodynamic force to the experimental measurements of Yamashita (J Soc Nav Arch 141:61–70, 1977). In particular, the comparison of the magnitude of the force harmonics, up to the third order, shows the importance of simulating non-linear interactions, which become important as the ratio of the radius of the cylinder over the wavelength increases. In a second set of applications, we assess the model accuracy in dealing with freely floating bodies. As a first test case, we consider the decaying motion of a freely heaving horizontal circular cylinder released from a non-equilibrium position above the free surface. In this more demanding computations, we verify that total energy fluid-plus-body motion is well conserved, which confirms the accuracy of the fluid-structure interaction algorithm. As a second test case, we consider the free motion of a rectangular barge in waves and compute the first-order response amplitude operators.

An Efficient Three-Dimensional FNPF Numerical Wave Tank for Large-Scale Wave Basin Experiment Simulation

This paper presents a parallel implementation and validation of an accurate and efficient three-dimensional computational model (3D numerical wave tank), based on fully nonlinear potential flow (FNPF) theory, and its extension to incorporate the motion of a laboratory snake piston wavemaker, as well as an absorbing beach, to simulate experiments in a large-scale 3D wave basin. This work is part of a long-term effort to develop a “virtual” computational wave basin to facilitate and complement large-scale physical wave-basin experiments. The code is based on a higher-order boundary-element method combined with a fast multipole algorithm (FMA). Particular efforts were devoted to making the code efficient for large-scale simulations using high-performance computing platforms. The numerical simulation capability can be tailored to serve as an optimization tool at the planning and detailed design stages of large-scale experiments at a specific basin by duplicating its exact physical and algorithmic features. To date, waves that can be generated in the numerical wave tank (NWT) include solitary, cnoidal, and airy waves. In this paper we detail the wave-basin model, mathematical formulation, wave generation, and analyze the performance of the parallelized FNPF-BEM-FMA code as a function of numerical parameters. Experimental or analytical comparisons with NWT results are provided for several cases to assess the accuracy and applicability of the numerical model to practical engineering problems.

Predictive Capability of a 2D FNPF Fluid-Structure Interaction Model

The predictive capability of two-dimensional (2D) fully-nonlinear-potential-flow (FNPF) models of an experimental submerged moored sphere system subjected to waves is examined in this study. The experimental system considered includes both single-degree-of-freedom (SDOF) surge-only and two-degree-of-freedom (2DOF) surge-heave coupled motions, with main sources of nonlinearity from free surface boundary, large geometry, and coupled fluid-structure interaction. The FNPF models that track the nonlinear free-surface boundary exactly hence can accurately model highly nonlinear (nonbreaking) waves. To examine the predictive capability of the approximate 2D models and keep the computational effort manageable, the structural sphere is converted to an equivalent 2D cylinder. Fluid-structure interaction is coupled through an implicit boundary condition enforcing the instantaneous dynamic equilibrium between the fluid and the structure. The numerical models are first calibrated using free-vibration test results and then employed to investigate the wave-excited experimental responses via comparisons of time history and frequency response diagrams. Under monochromatic wave excitations, both SDOF and 2DOF models exhibit complex nonlinear experimental responses including coexistence, harmonics, subharmonics, and superharmonics. It is found that the numerical models can predict the general qualitative nonlinear behavior, harmonic and subharmonic responses as well as bifurcation structure. However, the predictive capability of the models deteriorates for superharmonic resonance possibly due to three-dimensional (3D) effects including diffraction and reflection. To accurately predict the nonlinear behavior of moored sphere motions in the highly sensitive response region, it is recommended that the more computationally intensive 3D numerical models be employed.

Progress on Nonlinear-Wave-Forced Sediment Transport Simulation

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, we report on the use of a numerical wave tank (NWT), based on fully nonlinear potential flow (FNPF) equations, in driving simulations of flow and sediment transport around partially buried obstacles. The suspended sediment transport is modeled in the near-field in a Navier–Stokes (NS) model using an immersed-boundary method and an attached sediment transport simulation module. Turbulence is represented by large eddy simulation (LES). The NWT is based on a higher order boundary element method (BEM), with an explicit second-order time stepping. Hence, only the NWT boundary is discretized. The solution for the velocity potential and its derivatives along the boundary is obtained in the BEM, which subsequently provides a solution at any required internal point within the domain. At initial time, the NS–LES model domain is initialized with the 3-D velocity field provided by the NWT and driven for later time by the pressure gradient field obtained in the NWT. Incident wave fields, as specified in the NWT to drive sediment transport, can be arbitrary. Applications are presented here for single frequency waves, such as produced by a harmonic piston wavemaker in the laboratory, and modulated frequency wave groups. The feasibility of coupling the irrotational flow and NS solutions is demonstrated. </para>

Tsunami Generation by Submarine Mass Failure. I: Modeling, Experimental Validation, and Sensitivity Analyses

Numerical simulations are performed with a two-dimensional (2D) fully nonlinear potential flow (FNPF) model for tsunami generation by two idealized types of submarine mass failure (SMF): underwater slides and slumps. These simulations feature rigid or deforming SMFs with a Gaussian cross section, translating down a plane slope. In each case, the SMF center of mass motion is expressed as a function of geometric, hydrodynamic, and material parameters, following a simple wavemaker formalism, and prescribed as a boundary condition in the FNPF model. Tsunami amplitudes and runup are obtained from computed free surface elevations. Model results are experimentally validated for a rigid 2D slide. Sensitivity studies are performed to estimate the effects of SMF-shape, type, and initial submergence depth—on the generated tsunamis. A strong SMF deformation during motion is shown to significantly enhance tsunami generation, particularly in the far-field. Typical slumps are shown to generate smaller tsunamis than corresponding slides. Both tsunami amplitude and runup are shown to depend strongly on initial SMF submergence depth. For the selected SMF idealized geometry, this dependence is simply expressed by power laws. Other sensitivity analyses are presented in a companion paper, and results from numerical simulations are converted into empirical curve fits predicting characteristic tsunami amplitudes as functions of nondimensional governing parameters. It should be stressed that these empirical formulas are only valid in the vicinity of the tsunami sources and, because of the complexity of the problem, many simplifications were necessary. It is further shown in the companion paper how 2D results can be modified to account for three-dimensional tsunami generation and used for quickly estimating tsunami hazard or for performing simple case studies.

Depth inversion in shallow water based on nonlinear properties of shoaling periodic waves

Two depth inversion algorithms (DIA) applicable to coastal waters are developed, calibrated, and validated based on results of computations of periodic waves shoaling over mild slopes, in a two-dimensional numerical wave tank based on fully nonlinear potential flow (FNPF) theory. In actual field situations, these algorithms would be used to predict the cross-shore depth variation h based on sets of values of wave celerity c and length L, and either wave height H or left–right asymmetry s 2/ s 1, simultaneously measured at a number of locations in the direction of wave propagation, e.g., using video or radar remote sensing techniques. In these DIAs, an empirical relationship, calibrated for a series of computations in the numerical wave tank, is used to express c as a function of relative depth k o h and deep water steepness k o H o. To carry out depth inversion, wave period is first predicted as the mean of observed L/ c values, and H o is then predicted, either based on observed H or s 2/ s 1 values. The celerity relationship is finally inverted to predict depth h. The algorithms are validated by applying them to results of computations for cases with more complex bottom topography and different incident waves than in the original calibration computations. In all cases, root-mean-square (rms)-errors for the depth predictions are found to be less than a few percent, whereas depth predictions based on the linear dispersion relationship—which is still the basis for many state-of-the-art DIAs—have rms-errors 5 to 10 times larger.