Numerical Simulation of Motions of Two-Dimensional Floating Bodies

1993 ◽  
Vol 37 (04) ◽  
pp. 307-330
Author(s):  
D. Sen
Keyword(s):  
Wave Train ◽  
Boundary Integral ◽  
Nonlinear Phenomena ◽  
Computational Domain ◽  
Two Dimensional ◽  
Floating Bodies ◽  
Basic Algorithm ◽  
Numerical Predictions ◽  
Nonlinear Free Surface ◽  
Surface Constraints

A potential-flow numerical model is described for time-simulation of motions of two-dimensional floating bodies subjected to an oncoming wave train. The model is fully nonlinear in that no assumptions of smallness either in wave steepness or in body motions are made. The basic algorithm is based on a boundary integral formulation and time-stepping of the nonlinear free-surface constraints in an Eulerian frame of reference. Simple techniques are devised to overcome numerical instability problems that are encountered in the proposed method. The simulation time can be extended over several periods of steady-state oscillations depending on the size of the computational domain. Several illustrative results simulating large heave and roll motions as well as drifting of a rectangular body are presented and discussed. The numerical predictions are also evaluated against model tests which include several nonnegligible nonlinear phenomena, and the agreement is encouraging.

scholarly journals Hydroelastic behaviour and analysis of marine structures

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Fuat Kara
Keyword(s):  
Three Dimensional ◽  
Bending Moment ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Forward Speed ◽  
Floating Bodies ◽  
Numerical Predictions ◽  
Wigley Hull ◽  
Elastic Modes ◽  
Surface Green Function

The numerical predictions of the hydroelasticity of floating bodies with and without forward speed are presented using a direct time domain approximation. Boundary-Integral Equation Method (BIEM) with three-dimensional transient free surface Green function and Neumman-Kelvin approximation is used for the solution of the hydrodynamic part and solved as impulsive velocity potential whilst Euler-Bernoulli beam approach is used for the structural analysis with analytically defined modeshapes. The hydrodynamic and structural parts are then fully coupled through modal analysis for the solution of the hydroelastic problem. A stiff structure is then studied assuming that contributions of rigid body modes are much bigger than elastic modes. A rectangular barge with zero speed and Wigley hull form with forward speed are used for the numerical analyses and the comparisons of the present ITU-WAVE numerical results for response amplitude operator, bending moment, shear force etc. show satisfactory agreement with existing experimental results.

Numerical Modelling of Wave Resonance in a Narrow Gap Between Two Floating Bodies in Close Proximity Using a Hybrid Model

2019 ◽  
Author(s):  
S. Yan ◽  
Q. W. Ma ◽  
Junxian Wang ◽  
Jinghua Wang
Keyword(s):  
Hybrid Model ◽  
Computational Domain ◽  
Narrow Gap ◽  
Viscous Effects ◽  
Floating Bodies ◽  
Nonlinear Potential Theory ◽  
Numerical Predictions ◽  
Wave Resonance ◽  
Close Proximity ◽  
Incident Waves

Abstract This paper presents a numerical investigation on the wave resonance in a narrow gap between two floating bodies in close proximity using a hybrid model, qaleFOAM, which combines a two-phase Navier-Stokes model (NS) and the fully nonlinear potential theory (FNPT) using a spatially hierarchical approach. The former governs the computational domain near the floating bodies and the gap, where the viscous effects are significant, and is solved by using OpenFOAM/InterDyMFoam. The latter covers the rest of the domain and solved by using the Quasi Lagrangian Eulerian Finite Element Method (QALE-FEM). The model is validated by comparing its numerical predictions with experimental data in the cases with linear incident waves. Systematic investigations using incident waves with different steepness are then followed to explore the nonlinear effects on the wave resonance.

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 Fractional order elliptic problems with inhomogeneous Dirichlet boundary conditions

2020 ◽  
Vol 23 (2) ◽  
pp. 378-389
Author(s):  
Ferenc Izsák ◽  
Gábor Maros
Keyword(s):  
Fractional Order ◽  
Boundary Data ◽  
Dirichlet Boundary ◽  
Elliptic Problems ◽  
Integral Form ◽  
Uniqueness Result ◽  
Boundary Integral ◽  
Dirichlet Boundary Conditions ◽  
Two Dimensional ◽  
Potential Operators

AbstractFractional-order elliptic problems are investigated in case of inhomogeneous Dirichlet boundary data. The boundary integral form is proposed as a suitable mathematical model. The corresponding theory is completed by sharpening the mapping properties of the corresponding potential operators. The existence-uniqueness result is stated also for two-dimensional domains. Finally, a mild condition is provided to ensure the existence of the classical solution of the boundary integral equation.

scholarly journals The Numerical Analysis of the Flow on the Smooth and Nonsmooth Boundaries by IBEM/DBIEM

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Gang Xu ◽  
Guangwei Zhao ◽  
Jing Chen ◽  
Shuqi Wang ◽  
Weichao Shi
Keyword(s):  
Boundary Value ◽  
Three Dimensional ◽  
Boundary Surface ◽  
Tangential Velocity ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Surface Shape ◽  
Normal Vector ◽  
Computational Domain ◽  
Nonsmooth Boundary

The value of the tangential velocity on the Boundary Value Problem (BVP) is inaccurate when comparing the results with analytical solutions by Indirect Boundary Element Method (IBEM), especially at the intersection region where the normal vector is changing rapidly (named nonsmooth boundary). In this study, the singularity of the BVP, which is directly arranged in the center of the surface of the fluid computing domain, is moved outside the computational domain by using the Desingularized Boundary Integral Equation Method (DBIEM). In order to analyze the accuracy of the IBEM/DBIEM and validate the above-mentioned problem, three-dimensional uniform flow over a sphere has been presented. The convergent study of the presented model has been investigated, including desingularized distance in the DBIEM. Then, the numerical results were compared with the analytical solution. It was found that the accuracy of velocity distribution in the flow field has been greatly improved at the intersection region, which has suddenly changed the boundary surface shape of the fluid domain. The conclusions can guide the study on the flow over nonsmooth boundaries by using boundary value method.

scholarly journals Existence and uniqueness in the theory of bending of elastic plates

1986 ◽  
Vol 29 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Christian Constanda
Keyword(s):  
Existence And Uniqueness ◽  
Integral Equation Method ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Equilibrium Equations ◽  
Dimensional Theory ◽  
Neumann Problems ◽  
Image Position

Kirchhoff's kinematic hypothesis that leads to an approximate two-dimensional theory of bending of elastic plates consists in assuming that the displacements have the form [1]In general, the Dirichlet and Neumann problems for the equilibrium equations obtained on the basis of (1.1) cannot be solved by the boundary integral equation method both inside and outside a bounded domain because the corresponding matrix of fundamental solutions does not vanish at infinity [2]. However, as we show in this paper, the method is still applicable if the asymptotic behaviour of the solution is suitably restricted.

Nonlinear Vibrations in a 2-Dimensional Protein Cluster Model with Linear Bonds

2000 ◽  
Vol 214 (1) ◽  
Author(s):  
E.G. Shidlovskaya ◽  
L. Schimansky-Geier ◽  
Yu.M. Romanovsky
Keyword(s):  
Active Site ◽  
Internal Resonance ◽  
Cluster Model ◽  
Active Sites ◽  
Nonlinear Vibrations ◽  
Nonlinear Phenomena ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Two Dimensional Model

A two dimensional model for the substrate inside a pocket of an active site of an enzyme is presented and investigated as a vibrational system. The parameters of the system are evaluated for α-chymotrypsin. In the case of internal resonance it is analytically and numerically shown that the energy concentrated on a certain degree of freedom might be several times larger than in the non-resonant case. Additionally, the system is driven by harmonic excitations and again energy due to nonlinear phenomena is redistributed inhomogeneously. These results may be of importance for the determination of the rates of catalytic events of substrates bound in pockets of active sites.

Methods to Accelerate Ray Tracing in the Monte Carlo Method for Surface-to-Surface Radiation Transport

2006 ◽  
Vol 128 (9) ◽  
pp. 945-952 ◽  
Author(s):  
Sandip Mazumder
Keyword(s):  
Monte Carlo ◽  
Ray Tracing ◽  
Radiation Transport ◽  
Three Dimensional ◽  
Intersection Point ◽  
Surface Radiation ◽  
Computational Domain ◽  
Two Dimensional ◽  
Spatial Partitioning ◽  
The Monte Carlo Method

Two different algorithms to accelerate ray tracing in surface-to-surface radiation Monte Carlo calculations are investigated. The first algorithm is the well-known binary spatial partitioning (BSP) algorithm, which recursively bisects the computational domain into a set of hierarchically linked boxes that are then made use of to narrow down the number of ray-surface intersection calculations. The second algorithm is the volume-by-volume advancement (VVA) algorithm. This algorithm is new and employs the volumetric mesh to advance the ray through the computational domain until a legitimate intersection point is found. The algorithms are tested for two classical problems, namely an open box, and a box in a box, in both two-dimensional (2D) and three-dimensional (3D) geometries with various mesh sizes. Both algorithms are found to result in orders of magnitude gains in computational efficiency over direct calculations that do not employ any acceleration strategy. For three-dimensional geometries, the VVA algorithm is found to be clearly superior to BSP, particularly for cases with obstructions within the computational domain. For two-dimensional geometries, the VVA algorithm is found to be superior to the BSP algorithm only when obstructions are present and are densely packed.

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