Nonlinear Water Waves in the Presence of Submerged Elliptic Cylinder

2004 ◽  
Author(s):  
Nikolai I. Makarenko
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Boundary Integral Equations ◽  
Fluid Velocity ◽  
Elliptic Cylinder ◽  
Small Time ◽  
Boundary Integral ◽  
Nonlinear Water Waves ◽  
Wave Elevation ◽  
Boundary Equations

The fully nonlinear problem on unsteady two-dimensional water waves generated by elliptic cylinder, that is horizontally submerged beneath a free surface, is considered. An analytical boundary integral equations method using a version of Milne-Thomson transformation is developed. Boundary equations (the BEq system) determine immediately exact wave elevation and fluid velocity at free surface. Small-time solution expansion is obtained in the case of accelerated cylinder starting from rest.

scholarly journals Non-linear water waves generated by impulsive motion of submerged obstacles

2014 ◽  
Vol 14 (4) ◽  
pp. 751-756 ◽  
Author(s):  
N. I. Makarenko ◽  
V. K. Kostikov
Keyword(s):  
Water Waves ◽  
Linear Problem ◽  
Elliptic Cylinder ◽  
Small Time ◽  
Impulsive Motion ◽  
Wave Elevation ◽  
Fluid Velocities ◽  
Non Linear ◽  
Model Equations ◽  
Moving Obstacle

Abstract. A fully non-linear problem on unsteady water waves generated by an impulsively moving obstacle is studied analytically. Our method involves reduction of the Euler equations to the integral-differential system for the wave elevation together with normal and tangential fluid velocities at a free surface. Exact model equations are derived in explicit form in a case where an isolated obstacle is presented by a totally submerged elliptic cylinder. A small-time asymptotic solution is constructed for a cylinder which starts with constant acceleration from rest. It is demonstrated that the leading-order solution terms describe several wave regimes such as the formation of non-stationary splash jets by vertical rising or vertical submersion of the obstacle; the generation of diverging waves is also observed.

scholarly journals Non-linear water waves generated by impulsive motion of submerged obstacle

2013 ◽  
Vol 1 (6) ◽  
pp. 7647-7665
Author(s):  
N. I. Makarenko ◽  
V. K. Kostikov
Keyword(s):  
Water Waves ◽  
Elliptic Cylinder ◽  
Small Time ◽  
Leading Order ◽  
Constant Acceleration ◽  
Impulsive Motion ◽  
Wave Elevation ◽  
Fluid Velocities ◽  
Model Equations ◽  
Moving Obstacle

Abstract. Fully nonlinear problem on unsteady water waves generated by impulsively moving obstacle is studied analytically. Our method involves the reduction of Euler equations to the integral-differential system for the wave elevation together with normal and tangential fluid velocities at the free surface. Exact model equations are derived in explicit form in the case when the isolated obstacle is presented by totally submerged elliptic cylinder. Small-time asymptotic solution is constructed for the cylinder which starts with constant acceleration from rest. It is demonstrated that the leading-order solution terms describe several wave regimes such as the formation of non-stationary splash jets by vertical rising or vertical submersion of the obstacle, as well as the generation of diverging waves is observed.

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’.

A B-Spline Based BEM for Unsteady Free-Surface Flows

1999 ◽  
Vol 43 (01) ◽  
pp. 13-24
Author(s):  
M. Landrini ◽  
G. Grytøyr ◽  
O. M. Faltinsen
Keyword(s):  
Free Surface ◽  
Evolution Equations ◽  
Boundary Integral Equations ◽  
Fluid Dynamic ◽  
Domain Boundary ◽  
Free Surface Flows ◽  
Boundary Integral ◽  
Surface Flows ◽  
B Spline ◽  
Nonlinear Free Surface

Fully nonlinear free-surface flows are numerically studied in the framework of the potential theory. The problem is formulated in terms of boundary integral equations which are solved by means of an arbitrary high-order boundary element method based on B-Spline representation of both the geometry and the fluid dynamic variables along the domain boundary. The solution is stepped forward in time either by following Lagrangian points attached to the free surface or by a less conventional scheme in which evolution equations for the B-Spline coefficients are integrated in time. Numerical examples for inner and outer free-surface flows are shown. The accuracy of the numerical solution is assessed either by checking mass and energy conservation or by comparing with reference solutions. Good results are generally obtained. Extended use of the developed algorithm to more applied problems in the context of naval hydrodynamics is now under development.

Nonlinear free-surface flow due to an impulsively started submerged point sink

1998 ◽  
Vol 364 ◽  
pp. 325-347 ◽  
Author(s):  
MING XUE ◽  
DICK K. P. YUE
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Numerical Study ◽  
Free Surface Flow ◽  
Small Time ◽  
Surface Flow ◽  
Boundary Integral ◽  
Critical Regime ◽  
Gravitational Acceleration ◽  
Nonlinear Free Surface

The unsteady fully nonlinear free-surface flow due to an impulsively started submerged point sink is studied in the context of incompressible potential flow. For a fixed (initial) submergence h of the point sink in otherwise unbounded fluid, the problem is governed by a single non-dimensional physical parameter, the Froude number, [Fscr ]≡Q/4π(gh5)1/2, where Q is the (constant) volume flux rate and g the gravitational acceleration. We assume axisymmetry and perform a numerical study using a mixed-Eulerian–Lagrangian boundary-integral-equation scheme. We conduct systematic simulations varying the parameter [Fscr ] to obtain a complete quantification of the solution of the problem. Depending on [Fscr ], there are three distinct flow regimes: (i) [Fscr ]<[Fscr ]1≈0.1924 – a ‘sub-critical’ regime marked by a damped wave-like behaviour of the free surface which reaches an asymptotic steady state; (ii) [Fscr ]1<[Fscr ]<[Fscr ]2≈0.1930 – the ‘trans-critical’ regime characterized by a reversal of the downward motion of the free surface above the sink, eventually developing into a sharp upward jet; (iii) [Fscr ]>[Fscr ]2 – a ‘super-critical’ regime marked by the cusp-like collapse of the free surface towards the sink. Mechanisms behind such flow behaviour are discussed and hydrodynamic quantities such as pressure, power and force are obtained in each case. This investigation resolves the question of validity of a steady-state assumption for this problem and also shows that a small-time expansion may be inadequate for predicting the eventual behaviour of the flow.

Suppression of Irregular Frequency in Multi-Body Problem and Free-Surface Singularity Treatment

2016 ◽  
Author(s):  
Yujie Liu ◽  
Jeffrey M. Falzarano
Keyword(s):  
Free Surface ◽  
Green Function ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Frequency Effect ◽  
Irregular Frequency ◽  
The Matrix ◽  
Offshore Industry ◽  
The Green Function ◽  
Multi Body

Multibody operations are routinely performed in offshore activities. One classical example is the FLNG and LNGC side-by-side offloading case. To understand the phenomenon occurring inside the gap is of growing interest to the offshore industry. One important issue is the existence of the irregular frequency effect. The effect can be confused with the physical resonance. Thus it needs to be removed. An extensive survey of the previous approaches to the irregular frequency problem has been undertaken. The matrix formulated in the boundary integral equations will become nearly singular for some frequencies. The existence of numerical round-off errors will make the matrix still solvable by a direct solver, however will result in unreasonably large values in some aspects of the solution, namely the irregular frequency effect. The removal of the irregular effect is important especially for multi-body hydrodynamic analysis in identifying the physical resonances caused by the configuration of floaters. This paper will mainly discuss the lid method on the internal free surface. To reach a higher accuracy, the singularity resulting from the Green function needs special care. Each term in the wave Green function will be evaluated using the corresponding analysis methods. Specifically, an analytical integral method is proposed to treat the log singularity. Finally, results with and without irregular frequency removal will be shown to demonstrate the effectiveness of our proposed method. The validation cases include mini-boxbarge, boxbarge and cylindrical dock, which has apparent irregular frequency effect in their output results.

A New Boundary Equation Solution to the Plate Problem

1989 ◽  
Vol 56 (2) ◽  
pp. 364-374 ◽  
Author(s):  
J. T. Katsikadelis ◽  
A. E. Armena`kas
Keyword(s):  
Boundary Element Method ◽  
Boundary Conditions ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Boundary Equation ◽  
Arbitrary Geometry ◽  
Equation Solution ◽  
The Finite Difference Method ◽  
Boundary Equations

A new boundary equation method is presented for analyzing plates of arbitrary geometry. The plates may have holes and may be subjected to any type of boundary conditions. The boundary value problem for the plate is formulated in terms of two differential and two integral coupled boundary equations which are solved numerically by discretizing the boundary. The differential equations are solved using the finite difference method while the integral equations are solved using the boundary element method. The main advantages of this new method are that the kernels of the boundary integral equations are simple and do not have hyper-singularities. Moreover, the same set of equations is employed for all types of boundary conditions. Furthermore, the use of intrinsic coordinates facilitates the modeling of plates with curvilinear boundaries. The numerical results demonstrate the accuracy and the efficiency of the method.

Finite Element Analysis of Nonlinear Water Wave-Body Interaction: Computational Issues

2012 ◽  
Author(s):  
C. P. Vendhan ◽  
P. Sunny Kumar ◽  
P. Krishnankutty
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Water Waves ◽  
Water Wave ◽  
Large Body ◽  
Boundary Integral ◽  
Body Motion ◽  
Fe Model ◽  
Computational Domain ◽  
Hexahedral Elements

Design of floating structures exposed to water waves often requires nonlinear analysis because of high wave steepness and large body motion. In this context, Mixed Eulerian-Lagrangian (MEL) methods for nonlinear water wave problems based on the potential flow theory have been studied extensively. Here, the Laplace equation with Dirichlet boundary condition on the free surface is solved using the boundary integral method, and a time integration method is used to find the particle displacements and velocity potential on the free surface. Finite element methods based on the MEL formulation have been developed in the 90s. Several researchers have pursued this approach, addressing the various challenges thrown open, such as velocity computation, pressure computation on moving surfaces, remeshing of the computational domain, smoothing and imposition of radiation condition. Apart from these, the implementation of the FE model in particular involves several computational issues such as element property computation, solution of large banded matrix equations, and efficient organization of computer storage, all of which are crucial for the computational tool to become successful. A study of these aspects constitutes the primary focus of the present work. The authors have recently developed a 3-D FE model employing the MEL formulation, which has been applied to predict waves in a flume and basin. The fluid domain is discretized using 20-node hexahedral elements. The free surface equations are solved in the time domain employing the three-point Adams-Bashforth method. Validation of the numerical model and relative computation times for salient steps in the FE model are discussed in the paper.

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