scholarly journals On the accuracy and applicability of a new implicit Taylor method and the high-order spectral method on steady nonlinear waves

2020 ◽  
Vol 476 (2243) ◽  
pp. 20200436
Author(s):  
Mathias Klahn ◽  
Per A. Madsen ◽  
David R. Fuhrman
Keyword(s):  
Free Surface ◽  
Water Depth ◽  
Vertical Velocity ◽  
Nonlinear Waves ◽  
Two Dimensional ◽  
Wave Steepness ◽  
Regular Waves ◽  
Truncation Order ◽  
High Order Spectral Method ◽  
Achievable Accuracy

This paper presents an investigation and discussion of the accuracy and applicability of an implicit Taylor (IT) method versus the classical higher-order spectral (HOS) method when used to simulate two-dimensional regular waves. This comparison is relevant, because the HOS method is in fact an explicit perturbation solution of the IT formulation. First, we consider the Dirichlet–Neumann problem of determining the vertical velocity at the free surface given the surface elevation and the surface potential. For this problem, we conclude that the IT method is significantly more accurate than the HOS method when using the same truncation order, M , and spatial resolution, N , and is capable of dealing with steeper waves than the HOS method. Second, we focus on the problem of integrating the two methods in time. In this connection, it turns out that the IT method is less robust than the HOS method for similar truncation orders. We conclude that the IT method should be restricted to M  = 4, while the HOS method can be used with M  ≤ 8. We systematically compare these two options and finally establish the best achievable accuracy of the two methods as a function of the wave steepness and the water depth.

Explicit Approximations for Calculating Potential Flow About a Body

1983 ◽  
Vol 27 (01) ◽  
pp. 1-12
Author(s):  
F. Noblesse ◽  
G. Triantafyllou
Keyword(s):  
Free Surface ◽  
Potential Flow ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Wave Resistance ◽  
Two Dimensional ◽  
Regular Waves ◽  
Practical Applications ◽  
Flow Problems ◽  
Unbounded Fluid

Several explicit approximations for calculating nonlifting potential flow about a body in an unbounded fluid are studied. These approximations are shown to be exact in the particular cases of flows due to translations of ellipsoids, and they are compared with the exact potential for two-dimensional flows about ogives in translatory motions. Two approximations, given by formulas (31) and (32) in the conclusion, appear to be of particular interest for practical applications, and they can be extended to free-surface flow problems, for example, ship wave resistance, and radiation and diffraction of regular waves by a body.

An Approach to Calculate the Probability of Wave Impact on an FPSO Bow

2006 ◽  
Vol 129 (2) ◽  
pp. 73-80 ◽  
Author(s):  
C. Guedes Soares ◽  
R. Pascoal ◽  
E. M. Antão ◽  
A. J. Voogt ◽  
B. Buchner
Keyword(s):  
Free Surface ◽  
Vertical Velocity ◽  
Second Order ◽  
Surface Velocity ◽  
Experimental Program ◽  
Ship Motions ◽  
Wave Steepness ◽  
Wave Impact ◽  
Local Wave ◽  
The Impact

This work aims at characterizing the probability of wave impact and determining the position of impact on an FPSO (floating production storage and offloading platform) bow geometry. In order to determine the instants when impact occurs, an experimental program was performed on a specific bow shape. The bow was instrumented with pressure transducers and the test program, also making use of video recordings, was designed such that it was possible to determine the correlation between undisturbed wave shape and the impact pressure time traces. It has been found that the wave impact at the bow is highly correlated with the local wave steepness, which for very high waves has at least second-order effects. A comparison between the probability distributions of local wave steepness of the experimental undisturbed wave time trace and numerical simulations of second-order wave theory is provided and it confirmed that the latter is very adequate for calculations. The experimental results were further used to determine how the probability of impact varies with free surface vertical velocity. It was found that the significant wave height of the sea state itself does not have significant influence on the result and a regression model was derived for the bow type in the experiments. The proposed model for determining the probability of having an impact is based on combining distributions, adjusted a priori to the numerically generated second-order free surface vertical velocity, and the experimental probability of impact of a known certain seastate and free surface velocity. The analytical description makes it fast and easy to expand to other cases of interest and some example calculations are shown to demonstrate the relative ease of the procedure proposed. The position of the impact is determined by the nonlinear wave crests and the ship motions. The ship motions can be determined based on a linear response to the nonlinear waves considered.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

scholarly journals New exact relations for steady irrotational two-dimensional gravity and capillary surface waves

2017 ◽  
Vol 376 (2111) ◽  
pp. 20170220 ◽  
Author(s):  
Didier Clamond
Keyword(s):  
Free Surface ◽  
Gravity Waves ◽  
Water Waves ◽  
Two Dimensional ◽  
Physical Plane ◽  
Theme Issue ◽  
Nonlinear Water Waves ◽  
Dimensional Gravity ◽  
Irrotational Motion ◽  
Exact Relations

Steady two-dimensional surface capillary–gravity waves in irrotational motion are considered on constant depth. By exploiting the holomorphic properties in the physical plane and introducing some transformations of the boundary conditions at the free surface, new exact relations and equations for the free surface only are derived. In particular, a physical plane counterpart of the Babenko equation is obtained. This article is part of the theme issue ‘Nonlinear water waves’.

Simulation of the Gap Resonance Between Two Rectangular Barges in Regular Waves by a Free Surface Viscous Flow Solver

2013 ◽  
Author(s):  
B. Elie ◽  
G. Reliquet ◽  
P.-E. Guillerm ◽  
O. Thilleul ◽  
P. Ferrant ◽  
...  
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Viscous Flow ◽  
Stokes Equations ◽  
Resonance Phenomenon ◽  
Navier Stokes ◽  
Regular Waves ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Gap Resonance

This paper compares numerical and experimental results in the study of the resonance phenomenon which appears between two side-by-side fixed barges for different sea-states. Simulations were performed using SWENSE (Spectral Wave Explicit Navier-Stokes Equations) approach and results are compared with experimental data on two fixed barges with different headings and bilges. Numerical results, obtained using the SWENSE approach, are able to predict both the frequency and the magnitude of the RAO functions.

Sign in / Sign up

Export Citation Format

Share Document