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.

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.

Validation of Open-Source SPH Code DualSPHysics for Numerical Simulations of Water Entry and Exit of a Rigid Body

2017 ◽  
Author(s):  
Sergei K. Buruchenko ◽  
Ricardo B. Canelas
Keyword(s):  
Free Surface ◽  
Rigid Body ◽  
Stokes Equations ◽  
Offshore Structures ◽  
Water Entry ◽  
Surface Flow ◽  
Rigid Body Dynamics ◽  
Structural Safety ◽  
Entry And Exit ◽  
Momentum Exchange

Water entry and exit of a body is an important topic in naval hydrodynamics as these phenomena play relevant roles both for offshore structures and vessels. Water entry and exit events are intrinsically transient and represent intense topological changes in the system, with large amounts of momentum exchange between phases. At its onset, they can be characterized by highly localized, both in space and time, loads on the vessel, influencing both the local structural safety of the structure and the global loads acting on it. The DualSPHysics code is proposed as a numerical tool for the simulation of fluid and floating object interaction. The numerical model is based on a Smoothed Particle Hydrodynamics discretization of the Navier-Stokes equations and Newton’s equations for rigid body dynamics. This paper examines the water impact, fluid motions, and movement of objects in the conventional case studies of object entry and exit from still water. A two dimensional body drop analysis was carried out demonstrating acceptable agreement of the movement of the object with published experimental and numerical results. The velocity field of the fluid is also captured and analyzed. Simulations for water entry and exit of a buoyant and neutral density cylinder compares well with previous experimental, numerical, and empirical studies in penetration, free surface evolution and object kinematics. These results provide a good foundation to evaluate the accuracy and stability of the DualSPHysics implementation for modeling the interaction between free surface flow and free moving floating objects.

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.

A Fractional Two-Step Finite Element Formulation for Unsteady Free Surface Flow Using ALE Method

2004 ◽  
Vol 261-263 ◽  
pp. 573-578
Author(s):  
Q. Li ◽  
H.Z. Liu ◽  
Zhuo Zhuang ◽  
S. Yamaguchi ◽  
Masao Toyoda
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Free Surface Flow ◽  
Linear Interpolation ◽  
Surface Flow ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Step Method ◽  
Fractional Step Method ◽  
Ale Method

A numerical algorithm using equal-order linear finite element and fractional two-step method is presented in this paper, which is used for analysis of incompressible viscous fluid flow with free surface problems. In order to avoid severe mesh distortions, ALE method is used for dealing with the free surface sloshing. For numerical integration, the fractional step method is employed, which is useful because the same linear interpolation functions for both velocity and pressure could be carried out in the finite element formulation. The present algorithm has been applied to some examples and proved to be accurate and more efficient.

Free-Surface Flow Simulations With Interactively Moving Bodies

2017 ◽  
Author(s):  
Arthur E. P. Veldman ◽  
Henk Seubers ◽  
Peter van der Plas ◽  
Joop Helder
Keyword(s):  
Free Surface ◽  
Free Fall ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Numerical Solution Method ◽  
Flow Simulations ◽  
Floating Object ◽  
Offshore Industry ◽  
Floating Objects ◽  
Moving Bodies

The simulation of free-surface flow around moored or floating objects faces a series of challenges, concerning the flow modelling and the numerical solution method. One of the challenges is the simulation of objects whose dynamics is determined by a two-way interaction with the incoming waves. The ‘traditional’ way of numerically coupling the flow dynamics with the dynamics of a floating object becomes unstable (or requires severe underrelaxation) when the added mass is larger than the mass of the object. To deal with this two-way interaction, a more simultaneous type of numerical coupling is being developed. The paper will focus on this issue. To demonstrate the quasi-simultaneous method, a number of simulation results for engineering applications from the offshore industry will be presented, such as the motion of a moored TLP platform in extreme waves, and a free-fall life boat dropping into wavy water.

Nonlinear Sloshing in Fixed and Vertically Excited Containers

2002 ◽  
Author(s):  
Jannette B. Frandsen ◽  
Alistair G. L. Borthwick
Keyword(s):  
Perturbation Theory ◽  
Free Surface ◽  
Small Perturbation ◽  
Numerical Solutions ◽  
Vertical Direction ◽  
Nonlinear Effects ◽  
Breaking Waves ◽  
Surface Flow ◽  
Nonlinear Behaviour ◽  
Computational Domain

Nonlinear effects of standing wave motions in fixed and vertically excited tanks are numerically investigated. The present fully nonlinear model analyses two-dimensional waves in stable and unstable regions of the free-surface flow. Numerical solutions of the governing nonlinear potential flow equations are obtained using a finite-difference time-stepping scheme on adaptively mapped grids. A σ-transformation in the vertical direction that stretches directly between the free-surface and bed boundary is applied to map the moving free surface physical domain onto a fixed computational domain. A horizontal linear mapping is also applied, so that the resulting computational domain is rectangular, and consists of unit square cells. The small-amplitude free-surface predictions in the fixed and vertically excited tanks compare well with 2nd order small perturbation theory. For stable steep waves in the vertically excited tank, the free-surface exhibits nonlinear behaviour. Parametric resonance is evident in the instability zones, as the amplitudes grow exponentially, even for small forcing amplitudes. For steep initial amplitudes the predictions differ considerably from the small perturbation theory solution, demonstrating the importance of nonlinear effects. The present numerical model provides a simple way of simulating steep non-breaking waves. It is computationally quick and accurate, and there is no need for free surface smoothing because of the σ-transformation.

Eulerian FEA With Volume of Solid (VOS) Application in Metal Forming

2010 ◽  
Author(s):  
K. S. Al-Athel ◽  
M. S. Gadala
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Process Improvement ◽  
Metal Forming ◽  
Material Flow ◽  
Solid Mechanics ◽  
Uniform Mesh ◽  
Element Formulation ◽  
Volume Of Fluid Method ◽  
Whole Process

The adaptation of the volume of fluid method (VOF) to solid mechanics (VOS) is presented in this work with the focus on metal forming applications. The method is discussed for a general non-uniform mesh with Eulerian finite element formulation. The implementation of the VOS method in metal forming applications is presented by focusing on topics such as the contact between the tool and the workpiece, tracking of the free surface of the material flow and the connectivity of the free surface during the whole process. Improvement on the connectivity of the free surface and the representation of curves is achieved by considering the mechanics of different metal forming processes. Different applications are simulated and discussed to highlight the capability of the VOS method.

scholarly journals Modeling Free Surface Flows Using Stabilized Finite Element Method

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Deepak Garg ◽  
Antonella Longo ◽  
Paolo Papale
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Computer Code ◽  
Free Surface Flows ◽  
Surface Flows ◽  
Element Method

This work aims to develop a numerical wave tank for viscous and inviscid flows. The Navier-Stokes equations are solved by time-discontinuous stabilized space-time finite element method. The numerical scheme tracks the free surface location using fluid velocity. A segregated algorithm is proposed to iteratively couple the fluid flow and mesh deformation problems. The numerical scheme and the developed computer code are validated over three free surface problems: solitary wave propagation, the collision between two counter moving waves, and wave damping in a viscous fluid. The benchmark tests demonstrate that the numerical approach is effective and an attractive tool for simulating viscous and inviscid free surface flows.

Numerical Investigation of Blade Flutter at or Near Stall in Axial Flow Turbomachines

2001 ◽  
Author(s):  
Wolfgang Höhn
Keyword(s):  
Viscous Flow ◽  
Stokes Equations ◽  
Separated Flow ◽  
Parallel Computer ◽  
Navier Stokes ◽  
Computational Domain ◽  
Compressor Cascade ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Blade Flutter

During the design of the compressor and turbine stages of today’s aeroengines, aerodynamically induced vibrations become increasingly important since higher blade load and better efficiency are desired. In this paper the development of a method based on the unsteady, compressible Navier-Stokes equations in two dimensions is described in order to study the physics of flutter for unsteady viscous flow around cascaded vibrating blades at stall. The governing equations are solved by a finite difference technique in boundary fitted coordinates. The numerical scheme uses the Advection Upstream Splitting Method to discretize the convective terms and central differences discretizing the viscous terms of the fully non-linear Navier-Stokes equations on a moving H-type mesh. The unsteady governing equations are explicitly and implicitly marched in time in a time-accurate way using a four stage Runge-Kutta scheme on a parallel computer or an implicit scheme of the Beam-Warming type on a single processor. Turbulence is modelled using the Baldwin-Lomax turbulence model. The blade flutter phenomenon is simulated by imposing a harmonic motion on the blade, which consists of harmonic body translation in two directions and a rotation, allowing an interblade phase angle between neighboring blades. Non-reflecting boundary conditions are used for the unsteady analysis at inlet and outlet of the computational domain. The computations are performed on multiple blade passages in order to account for nonlinear effects. A subsonic massively stalled unsteady flow case in a compressor cascade is studied. The results, compared with experiments and the predictions of other researchers, show reasonable agreement for inviscid and viscous flow cases for the investigated flow situations with respect to the Steady and unsteady pressure distribution on the blade in separated flow areas as well as the aeroelastic damping. The results show the applicability of the scheme for stalled flow around cascaded blades. As expected the viscous and inviscid computations show different results in regions where viscous effects are important, i.e. in separated flow areas. In particular, different predictions for inviscid and viscous flow for the aerodynamic damping for the investigated flow cases are found.

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