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.

Large-Scale Free-Surface Flow Simulations Using FEM

2005 ◽  
Author(s):  
Shahrouz Aliabadi ◽  
Marvin Watts ◽  
Andrew Johnson
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Water Waves ◽  
Stokes Equations ◽  
Surface Flow ◽  
Rigid Body Dynamics ◽  
Element Formulation ◽  
Computational Domain ◽  
Governing Equations ◽  
Floating Objects

A parallel finite element fluid-structure interaction free-surface solver is developed for numerical simulation of water waves interacting with floating objects. In our approach, the governing equations are the Navier-Stokes equations written for two incompressible fluids. An interface function with two distinct values serves as a marker identifying the location of the interface. The numerical method is based on writing stabilized finite element formulations in an arbitrary Lagrangian-Eulerian frame. This allows us to handle the motion of the floating objects by moving the computational nodes. In the mesh-moving schemes, we assume that the computational domain is made of elastic materials. The linear elasticity equations are solved to obtain the displacements. In order to update the position of the floating object, the nonlinear rigid body dynamics equations are coupled with the governing equations of fluids and are solved simultaneously. The mooring forces are modeled using nonlinear cables and linear spring models. The finite element formulation is implemented on Cray X1.

scholarly journals BUBBLE BURSTING AT A FREE SURFACE IN A CLOSED DOMAIN

2016 ◽  
Vol 42 ◽  
pp. 1660160
Author(s):  
NIAN-NIAN LIU ◽  
SHUAI ZHANG ◽  
SHI-PING WANG
Keyword(s):  
Wave Propagation ◽  
Free Surface ◽  
Laplace Equation ◽  
Water Waves ◽  
Water Wave ◽  
Velocity Potential ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Closed Domain ◽  
Bubble Motion

When a charge explodes underwater near a free surface, a bubble would be generated and the surface pushed up very high. Experiments have shown that the motion of the spike lags a lot behind the bubble motion. Many studies only focus on the nonlinear interaction between the bubble and free surface while the water waves afterward is mainly studied based on the linear theory. The nonlinear motion of the water wave after the bubble pulsation is seldom studied. In this study, we concerns the interaction between underwater explosion generated bubble and a free surface and its bursting at a free surface in a closed domain. Suppose that the fluid outside the bubble is incompressible, non-viscous and irrotational and the velocity potential satisfies the Laplace equation. Boundary integral method is used to solve the Laplace equation for the velocity potential. The bubble content is described by an adiabatic law. The whole process of the bubble motion and subsequently the water wave propagation will be simulated in this paper. Particular attention will be focused on the phenomenon of water wave propagation in a closed domain.

Finite Element Analysis of the Distributed Vibration Absorbers for Structural Noise Control

2005 ◽  
Author(s):  
Ashwini Gautam ◽  
Chris Fuller ◽  
James Carneal
Keyword(s):  
Finite Element ◽  
Numerical Model ◽  
Base Plate ◽  
Element Model ◽  
Fe Model ◽  
Vibration Absorbers ◽  
Element Analysis ◽  
Poroelastic Media ◽  
Hexahedral Elements ◽  
Component Models

This work presents an extensive analysis of the properties of distributed vibration absorbers (DVAs) and their effectiveness in controlling the sound radiation from the base structure. The DVA acts as a distributed mass absorber consisting of a thin metal sheet covering a layer of acoustic foam (porous media) that behaves like a distributed spring-mass-damper system. To assess the effectiveness of these DVAs in controlling the vibration of the base structures (plate) a detailed finite elements model has been developed for the DVA and base plate structure. The foam was modeled as a poroelastic media using 8 node hexahedral elements. The structural (plate) domain was modeled using 16 degree of freedom plate elements. Each of the finite element models have been validated by comparing the numerical results with the available analytical and experimental results. These component models were combined to model the DVA. Preliminary experiments conducted on the DVAs have shown an excellent agreement between the results obtained from the numerical model of the DVA and from the experiments. The component models and the DVA model were then combined into a larger FE model comprised of a base plate with the DVA treatment on its surface. The results from the simulation of this numerical model have shown that there has been a significant reduction in the vibration levels of the base plate due to DVA treatment on it. It has been shown from this work that the inclusion of the DVAs on the base plate reduces their vibration response and therefore the radiated noise. Moreover, the detailed development of the finite element model for the foam has provided us with the capability to analyze the physics behind the behavior of the distributed vibration absorbers (DVAs) and to develop more optimized designs for the same.

scholarly journals An alternative approach to study irrotational periodic gravity water waves

2021 ◽  
Vol 72 (4) ◽  
Author(s):  
Biswajit Basu ◽  
Calin I. Martin
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Water Wave ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Stagnation Points ◽  
Alternative Approach ◽  
New Formulation ◽  
Bounded Below ◽  
Surface Dynamic

AbstractWe are concerned here with an analysis of the nonlinear irrotational gravity water wave problem with a free surface over a water flow bounded below by a flat bed. We employ a new formulation involving an expression (called flow force) which contains pressure terms, thus having the potential to handle intricate surface dynamic boundary conditions. The proposed formulation neither requires the graph assumption of the free surface nor does require the absence of stagnation points. By way of this alternative approach we prove the existence of a local curve of solutions to the water wave problem with fixed flow force and more relaxed assumptions.

Numerical Simulation of Nonlinear Water Wave Propagation Over Rippled Bed

2007 ◽  
Author(s):  
Gerasimos A. Kolokythas ◽  
Athanassios A. Dimas
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Water Waves ◽  
Stokes Equations ◽  
Surface Flow ◽  
Surface Boundary ◽  
Computational Domain ◽  
Time Step ◽  
Outflow Boundary ◽  
Rippled Bed

In the present study, numerical simulations of the free-surface flow, developing by the propagation of nonlinear water waves over a rippled bottom, are performed assuming that the corresponding flow is two-dimensional, incompressible and viscous. The simulations are based on the numerical solution of the Navier-Stokes equations subject to the fully-nonlinear free-surface boundary conditions and the suitable bottom, inflow and outflow boundary conditions. The equations are properly transformed so that the computational domain becomes time-independent. For the spatial discretization, a hybrid scheme with finite-differences and Chebyshev polynomials is applied, while a fractional time-step scheme is used for the temporal discretization. A wave absorption zone is placed at the outflow region in order to efficiently minimize reflection of waves by the outflow boundary. The numerical model is validated by comparison to the analytical solution for the laminar, oscillatory, current flow which develops a uniform boundary layer over a horizontal bottom. For the propagation of finite-amplitude waves over a rigid rippled bed, the case with wavelength to water depth ratio λ/d0 = 6 and wave height to wavelength ratio H0/λ = 0.05 is considered. The ripples have parabolic shape, while their dimensions — length and height — are chosen accordingly to fit laboratory and field data. Results indicate that the wall shear stress over the ripples and the form drag forces on the ripples increase with increasing ripple height, while the corresponding friction force is insensitive to this increase. Therefore, the percentage of friction in the total drag force decreases with increasing ripple height.

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.

Numerical simulations of nonlinear axisymmetric flows with a free surface

1987 ◽  
Vol 178 ◽  
pp. 195-219 ◽  
Author(s):  
Douglas G. Dommermuth ◽  
Dick K. P. Yue
Keyword(s):  
Free Surface ◽  
Numerical Simulations ◽  
Three Dimensional ◽  
Vertical Cylinder ◽  
Free Surface Flows ◽  
Boundary Integral ◽  
The Body ◽  
Special Treatment ◽  
Computational Domain ◽  
Vortex Sheets

A numerical method is developed for nonlinear three-dimensional but axisymmetric free-surface problems using a mixed Eulerian-Lagrangian scheme under the assumption of potential flow. Taking advantage of axisymmetry, Rankine ring sources are used in a Green's theorem boundary-integral formulation to solve the field equation; and the free surface is then updated in time following Lagrangian points. A special treatment of the free surface and body intersection points is generalized to this case which avoids the difficulties associated with the singularity there. To allow for long-time simulations, the nonlinear computational domain is matched to a transient linear wavefield outside. When the matching boundary is placed at a suitable distance (depending on wave amplitude), numerical simulations can, in principle, be continued indefinitely in time. Based on a simple stability argument, a regriding algorithm similar to that of Fink & Soh (1974) for vortex sheets is generalized to free-surface flows, which removes the instabilities experienced by earlier investigators and eliminates the need for artificial smoothing. The resulting scheme is very robust and stable.For illustration, three computational examples are presented: (i) the growth and collapse of a vapour cavity near the free surface; (ii) the heaving of a floating vertical cylinder starting from rest; and (iii) the heaving of an inverted vertical cone. For the cavity problem, there is excellent agreement with available experiments. For the wave-body interaction calculations, we are able to obtain and analyse steady-state (limit-cycle) results for the force and flow field in the vicinity of the body.

An Integrated Musculoskeletal-Finite-Element Model to Evaluate Effects of Load Carriage on the Tibia During Walking

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
Chun Xu ◽  
Amy Silder ◽  
Ju Zhang ◽  
Julie Hughes ◽  
Ginu Unnikrishnan ◽  
...  
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Injury Risk ◽  
Load Carriage ◽  
Body Motion ◽  
Bone Biomechanics ◽  
External Loading ◽  
Fe Model ◽  
Loading Conditions ◽  
Reaction Forces

Prior studies have assessed the effects of load carriage on the tibia. Here, we expand on these studies and investigate the effects of load carriage on joint reaction forces (JRFs) and the resulting spatiotemporal stress/strain distributions in the tibia. Using full-body motion and ground reaction forces from a female subject, we computed joint and muscle forces during walking for four load carriage conditions. We applied these forces as physiological loading conditions in a finite-element (FE) analysis to compute strain and stress. We derived material properties from computed tomography (CT) images of a sex-, age-, and body mass index-matched subject using a mesh morphing and mapping algorithm, and used them within the FE model. Compared to walking with no load, the knee JRFs were the most sensitive to load carriage, increasing by as much as 26.2% when carrying a 30% of body weight (BW) load (ankle: 16.4% and hip: 19.0%). Moreover, our model revealed disproportionate increases in internal JRFs with increases in load carriage, suggesting a coordinated adjustment in the musculature functions in the lower extremity. FE results reflected the complex effects of spatially varying material properties distribution and muscular engagement on tibial biomechanics during walking. We observed high stresses on the anterior crest and the medial surface of the tibia at pushoff, whereas high cumulative stress during one walking cycle was more prominent in the medioposterior aspect of the tibia. Our findings reinforce the need to include: (1) physiologically accurate loading conditions when modeling healthy subjects undergoing short-term exercise training and (2) the duration of stress exposure when evaluating stress-fracture injury risk. As a fundamental step toward understanding the instantaneous effect of external loading, our study presents a means to assess the relationship between load carriage and bone biomechanics.

Bound Coherent Structures Propagating on the Free Surface of Deep Water

2021 ◽  
Author(s):  
Sergey Dremov ◽  
Dmitry Kachulin ◽  
Alexander Dyachenko
Keyword(s):  
Free Surface ◽  
Incompressible Fluid ◽  
Deep Water ◽  
Coherent Structures ◽  
Water Waves ◽  
Initial Conditions ◽  
Soliton Solutions ◽  
Ideal Incompressible Fluid ◽  
System Of Nonlinear Equations ◽  
Computational Domain

<p><span>               The work presents the results of studying the bound coherent structures propagating on the free surface of ideal incompressible fluid of infinite depth. Examples of such structures are bi-solitons which are exact solutions of the known approximate model for deep water waves — the nonlinear Schrödinger equation (NLSE). Recently, when studying multiple breathers collisions, the occurrence of such objects was found in a more accurate model of the supercompact equation for unidirectional water waves [1]. The aim of this work is obtaining and further studying such structures with different parameters in the supercompact equation and in the full system of nonlinear equations for potential flows of an ideal incompressible fluid written in conformal variables. </span><span>The algorithm used for finding the bound coherent objects was similar to the one described in [2]. As the initial conditions for obtaining such structures in the framework of the above models, the NLSE bi-soliton solutions were used, as well as two single breathers numerically found by the Petviashvili method and placed in a same point of the computational domain. During the evolution calculation the initial structures emitted incoherent waves which were filtered at the boundaries of the domain using the damping procedure. It is shown that after switching off the filtering of radiation, periodically oscillating coherent objects remain on the surface of the liquid, propagate stably during one hundred thousand characteristic wave periods and do not lose energy. The profiles of such structures at different parameters are compared.</span></p><p><span>This work was supported by RSF grant </span><span>19-72-30028</span><span> and </span><span>RFBR grant </span><span>20-31-90093</span><span>.</span></p><p><span>[1] Kachulin D., Dyachenko A., Dremov S. Multiple Soliton Interactions on the Surface of Deep Water //Fluids. – 2020. – Т. 5. – №. 2. – С. 65.</span></p><p><span>[2] Dyachenko A. I., Zakharov V. E. On the formation of freak waves on the surface of deep water //JETP letters. – 2008. – Т. 88. – №. 5. – С. 307.</span></p>

Sign in / Sign up

Export Citation Format

Share Document