scholarly journals Suppression of Irregular Frequency Effect in Hydrodynamic Problems and Free-Surface Singularity Treatment

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Yujie Liu ◽  
Jeffrey M. Falzarano
Keyword(s):  
Free Surface ◽  
Green Function ◽  
Natural Gas ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Liquefied Natural Gas ◽  
Frequency Effect ◽  
Irregular Frequency ◽  
The Matrix ◽  
Offshore Industry

Multibody operations are routinely performed in offshore activities, for example, the floating liquefied natural gas (FLNG) and liquefied natural gas carrier (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, it 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 multibody 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.

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 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 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.

Calculation of the Magnetization of Permanent Magnets, Based on the Method for Solving the Inverse Problem Using Parallel Calculations

2021 ◽  
Vol 64 (1) ◽  
pp. 13-21
Author(s):  
Petr Denisov ◽  
◽  
Anna Balaban ◽  
Keyword(s):  
Inverse Problem ◽  
Permanent Magnets ◽  
Parallel Implementation ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Tikhonov Regularization Method ◽  
Field Pattern ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
The Matrix

The article proposes the modification of a technique for assessing the magnetization of permanent magnets from the known field pattern. The identification method is based on solving an ill-conditioned system of linear algebraic equations by the Tikhonov regularization method. The method of boundary integral equations based on scalar potentials is used to compile the matrix of coefficients. The article presents the algorithm that uses parallel computations when performing the most time-consuming operations to reduce the time for solving the inverse problem. In order to check the proposed method, a program was developed that allows to simulate the measurement process: to calculate the direct problem and find the magnetic induction at the points of the air gap, then introduce the error into the "measurement results" and solve the inverse problem. The results of nu-merical experiments that allow us to evaluate the advantages of parallel implementation using the capabilities of modern multi-core processors are presented.

Risk and Reliability Analyses for Innovative LNG Offshore Floating Units

2013 ◽  
Author(s):  
Olivier Benyessaad ◽  
Diane Ruf
Keyword(s):  
Natural Gas ◽  
Hazard Assessment ◽  
Liquefied Natural Gas ◽  
Energy Resources ◽  
Reliability Engineering ◽  
Qualitative And Quantitative ◽  
The World ◽  
Different Types ◽  
Offshore Industry

The development of the Liquefied Natural Gas (LNG) offshore industry is viewed as a major improvement in the exploitation of the world’s energy resources. Most energy analysts agree that significant increases in Natural Gas (NG) demand is expected in the next decades due to relatively low prices and an important gas quantity worldwide. In order to develop the use of this resource, many innovative offshore floating installations have been developed and are currently deployed all over the world. However, hazards linked to LNG and due to hydrocarbon releases are not always so well understood or controlled. Thus, in order to quantify and understand these risks associated to LNG treatment or containment as well as their consequences, a number of different types of risk and reliability engineering techniques can be used at different stages of the project. The following will present specific analyses that have been performed on innovative LNG Offshore floating units to provide a qualitative and quantitative hazard assessment by predicting the consequences and the frequencies of these hazards, while improving the reliability of the installation and its availability. The paper will first introduce the LNG offshore industry outlining the different installations possibilities and the associated hazards. Then, based on recent projects, it will detail the risk-based methodology applied to ensure the safety and the profitability of such innovative installations when no rules are able to frame fully the development of these projects. Finally, after having pointed out the ins and outs of risk studies, a case study using most of the methods presented previously will be developed.

New Higher Order Numeric Quadratures for Regular or Singular Functions on an Interval: Applications for the Helmholtz Integral Equation

1999 ◽  
Author(s):  
Philippe Helluy ◽  
Sylvain Maire ◽  
Patrice Ravel
Keyword(s):  
Integral Equation ◽  
Green Function ◽  
Integral Equations ◽  
Integration Method ◽  
Boundary Integral Equations ◽  
Higher Order ◽  
Boundary Integral ◽  
Numerical Resolution ◽  
Singular Functions ◽  
The Green Function

Abstract A high order integration method is presented for regular or singular integrands over an integral. This method appears to be very useful to compute the integrals of the green function in the numerical resolution of boundary integral equations.

scholarly journals Wave Propagation Due to an Embedded Seismic Source in a Graded Half-Plane with Relief Peculiarities Part I: Mechanical Model and Computational Technique

2015 ◽  
Vol 45 (1) ◽  
pp. 87-98
Author(s):  
I.-K. Fontara ◽  
F. Wuttke ◽  
S. Parvanova ◽  
P. Dineva
Keyword(s):  
Free Surface ◽  
Half Plane ◽  
Surface Relief ◽  
Boundary Integral Equations ◽  
Seismic Source ◽  
Seismic Signal ◽  
Companion Paper ◽  
Boundary Integral ◽  
Computational Technique ◽  
Seismic Wave Field

Abstract This work addresses the evaluation of the seismic wave field in a graded half-plane with free-surface and/or sub-surface relief subjected to shear horizontally (SH)-polarized wave, radiating from an embedded seismic source. The considered boundary value problem is transformed into a system of boundary integral equations (BIEs) along the boundaries of the free-surface and of any sub-surface relief, using an analytically derived frequency-dependent Green’s function for a quadratically inhomogeneous in depth half-plane. The numerical solution yields synthetic seismic signals at any point of the half-plane in both frequency and time domain following application of Fast Fourier Transform (FFT). Finally, in the companion paper, the verification and numerical simulation studies demonstrate the accuracy and efficiency of the present computational approach. The proposed BIE tool possesses the potential to reveal the sensitivity of the seismic signal to the type and properties of the seismic source, to the existence and type of the material gradient and to the lateral inhomogeneity, due to the free-surface and/or sub-surface relief peculiarities.

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