scholarly journals THREE-DIMENSIONAL NUMERICAL ANALYSIS ON DEFORMATION OF RUN-UP TSUNAMI AND TSUNAMI FORCE ACTING ON SQUARE STRUCTURES

2011 ◽  
Vol 1 (32) ◽  
pp. 14 ◽  
Author(s):  
Tomoaki Nakamura ◽  
Norimi Mizutani ◽  
Koji Fujima
Keyword(s):  
Three Dimensional ◽  
Interaction Model ◽  
Navier Stokes ◽  
Interface Tracking ◽  
Time Step ◽  
Porous Flow ◽  
Inundation Depth ◽  
Coupling Procedure ◽  
Run Up ◽  
Tsunami Run Up

A three-dimensional two-way coupled fluid-sediment interaction model (FSM) is applied to investigate run-up tsunami deformation and tsunami force acting on square structures on land. The FSM consists of a generalized Navier-Stokes solver (GNS) for multi-phase flow including porous flow, a volume of fluid module (VFM) for air-water interface tracking, and a sediment transport module (STM) for fluid-sediment interface tracking. In the FSM, a two-way coupling procedure is implemented at each time step to connect the GNS with the VFM and the STM. The predictive capability of the FSM is demonstrated through comparison between numerical results and experimental data in terms of water surface elevation, inundation depth, and tsunami force. The process of tsunami run-up in the presence of square structures is investigated in terms of vortex structures. The result shows that the FSM is a useful tool providing detailed information in discussing run-up tsunami deformation and tsunami force.

A Nonlinear Three-Dimensional Coupled Fluid-Sediment Interaction Model for Large Seabed Deformation

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Tomoaki Nakamura ◽  
Solomon C. Yim
Keyword(s):  
Sediment Transport ◽  
Three Dimensional ◽  
Interaction Model ◽  
Navier Stokes ◽  
Coupling Scheme ◽  
Model Parameters ◽  
Interface Tracking ◽  
Beach Profile ◽  
Time Step ◽  
Profile Change

A nonlinear three-dimensional two-way coupled fluid-sediment interaction model is developed in this study. The model is composed of a generalized Navier–Stokes solver (GNS) with a volume of fluid module for air-water interface tracking and a sediment transport module (STM) for fluid-sediment interface tracking. The GNS model is based on the finite difference method with a turbulent stress model of large-eddy simulation to compute incompressible viscous multiphase flows. The STM is used to compute nonlinear sediment bed profile change due to bed-load sediment transport. A two-way coupling scheme connecting GNS with STM is implemented at each time step to ensure the fluid-sediment interaction. For validation, the fluid-sediment interaction model is applied to predict cross-shore profile change of a sloping beach due to breaking solitary waves, and the resulting predictions are examined and compared with the measured data from a set of hydraulic tests. It is found that the fluid-sediment interaction model predicts reasonably well the sediment transport and the resulting beach profile change. The sensitivity of model parameters involving the sediment transport to the beach profile change is analyzed. Finally, the fluid-sediment interaction model is applied to predict local scour in front of a quay wall due to a jet flow to demonstrate its applicability to general three-dimensional problems.

Numerical integration of the three-dimensional Navier-Stokes equations for incompressible flow

1969 ◽  
Vol 37 (4) ◽  
pp. 727-750 ◽  
Author(s):  
Gareth P. Williams
Keyword(s):  
Poisson Equation ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Wave Flow ◽  
Trigonometric Interpolation ◽  
Time Step ◽  
Navier Stokes Equations ◽  
The Poisson Equation

A method of numerically integrating the Navier-Stokes equations for certain three-dimensional incompressible flows is described. The technique is presented through application to the particular problem of describing thermal convection in a rotating annulus. The equations, in cylindrical polar co-ordinate form, are integrated with respect to time by a marching process, together with the solving of a Poisson equation for the pressure. A suitable form of the finite difference equations gives a computationally-stable long-term integration with reasonably faithful representation of the spatial and temporal characteristics of the flow.Trigonometric interpolation techniques provide accurate (discretely exact) solutions to the Poisson equation. By using an auxiliary algorithm for rapid evaluation of trigonometric transforms, the proportion of computation needed to solve the Poisson equation can be reduced to less than 25% of the total time needed to’ advance one time step. Computing on a UNIVAC 1108 machine, the flow can be advanced one time-step in 2 sec for a 14 × 14 × 14 grid upward to 96 sec for a 60 × 34 × 34 grid.As an example of the method, some features of a solution for steady wave flow in annulus convection are presented. The resemblance of this flow to the classical Eady wave is noted.

scholarly journals Three-Dimensional Simulation of Fluid–Structure Interaction Problems Using Monolithic Semi-Implicit Algorithm

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 94 ◽  
Author(s):  
Cornel Marius Murea
Keyword(s):  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Arbitrary Lagrangian Eulerian ◽  
Time Step ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Dimensional Simulation ◽  
Updated Lagrangian

A monolithic semi-implicit method is presented for three-dimensional simulation of fluid–structure interaction problems. The updated Lagrangian framework is used for the structure modeled by linear elasticity equation and, for the fluid governed by the Navier–Stokes equations, we employ the Arbitrary Lagrangian Eulerian method. We use a global mesh for the fluid–structure domain where the fluid–structure interface is an interior boundary. The continuity of velocity at the interface is automatically satisfied by using globally continuous finite element for the velocity in the fluid–structure mesh. The method is fast because we solve only a linear system at each time step. Three-dimensional numerical tests are presented.

Numerical Solution of Incompressible Unsteady Flows in Turbomachinery

2000 ◽  
Vol 123 (3) ◽  
pp. 680-685 ◽  
Author(s):  
L. He ◽  
K. Sato
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Time Stepping ◽  
Incompressible Viscous Flow ◽  
Dual Time Stepping

A three-dimensional incompressible viscous flow solver of the thin-layer Navier-Stokes equations was developed for the unsteady turbomachinery flow computations. The solution algorithm for the unsteady flows combines the dual time stepping technique with the artificial compressibility approach for solving the incompressible unsteady flow governing equations. For time accurate calculations, subiterations are introduced by marching the equations in the pseudo-time to fully recover the incompressible continuity equation at each real time step, accelerated with a multi-grid technique. Computations of test cases show satisfactory agreements with corresponding theoretical and experimental results, demonstrating the validity and applicability of the present method to unsteady incompressible turbomachinery flows.

Strongly Coupled Fluid-Structure Interactions via a New Navier-Stokes Method for Prediction of Vortex-Induced Vibrations

2005 ◽  
Author(s):  
Yannis Kallinderis ◽  
Hyung Taek Ahn
Keyword(s):  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Design Tool ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Vortex Induced Vibrations ◽  
Offshore Industry

Numerical prediction of vortex-induced vibrations requires employment of the unsteady Navier-Stokes equations. Current Navier-Stokes solvers are quite expensive for three-dimensional flow-structure applications. Acceptance of Computational Fluid Dynamics as a design tool for the offshore industry requires improvements to current CFD methods in order to address the following important issues: (i) stability and computation cost of the numerical simulation process, (ii) restriction on the size of the allowable time-step due to the coupling of the flow and structure solution processes, (iii) excessive number of computational elements for 3-D applications, and (iv) accuracy and computational cost of turbulence models used for high Reynolds number flow. The above four problems are addressed via a new numerical method which employs strong coupling between the flow and the structure solutions. Special coupling is also employed between the Reynolds-averaged Navier-Stokes equations and the Spalart-Allmaras turbulence model. An element-type independent spatial discretization scheme is also presented which can handle general hybrid meshes consisting of hexahedra, prisms, pyramids, and tetrahedral.

A Navier–Stokes Analysis of Airfoils in Oscillating Transonic Cascades for the Prediction of Aerodynamic Damping

1997 ◽  
Vol 119 (1) ◽  
pp. 77-84 ◽  
Author(s):  
R. S. Abhari ◽  
M. Giles
Keyword(s):  
Numerical Study ◽  
Three Dimensional ◽  
Outer Region ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Time Step ◽  
Aerodynamic Damping ◽  
Transonic Compressor ◽  
Standard Configuration ◽  
The Impact

An unsteady, compressible, two-dimensional, thin shear layer Navier–Stokes solver is modified to predict the motion-dependent unsteady flow around oscillating airfoils in a cascade. A quasi-three-dimensional formulations is used to account for the stream-wise variation of streamtube height. The code uses Ni’s Lax–Wendroff algorithm in the outer region, an implicit ADI method in the inner region, conservative coupling at the interface, and the Baldwin–Lomax turbulence model. The computational mesh consists of an O-grid around each blade plus an unstructured outer grid of quadrilateral or triangular cells. The unstructured computational grid was adapted to the flow to better resolve shocks and wakes. Motion of each airfoil was simulated at each time step by stretching and compressing the mesh within the O-grid. This imposed motion consists of harmonic solid body translation in two directions and rotation, combined with the correct interblade phase angles. The validity of the code is illustrated by comparing its predictions to a number of test cases, including an axially oscillating flat plate in laminar flow, the Aeroelasticity of Turbomachines Symposium Fourth Standard Configuration (a transonic turbine cascade), and the Seventh Standard Configuration (a transonic compressor cascade). The overall comparison between the predictions and the test data is reasonably good. A numerical study on a generic transonic compressor rotor was performed in which the impact of varying the amplitude of the airfoil oscillation on the normalized predicted magnitude and phase of the unsteady pressure around the airfoil was studied. It was observed that for this transonic compressor, the nondimensional aerodynamic damping was influenced by the amplitude of the oscillation.

Prediction of VIV Response of a Flexible Pipe by Coupling a Viscous Flow Solver and a Beam Finite Element Solver

2009 ◽  
Author(s):  
Juan P. Pontaza ◽  
Raghu G. Menon
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Flexible Pipe ◽  
Time Step ◽  
Flow Solver ◽  
Instantaneous Flow ◽  
Numerical Predictions ◽  
Instantaneous Flow Field ◽  
Euler Bernoulli Beam

The paper describes a fluid-structure interaction (FSI) modeling approach to predict the VIV response of a flexible pipe by coupling a three-dimensional viscous incompressible Navier-Stokes solver with a beam finite element solver – in time domain. The flexible pipe is modeled as an Euler-Bernoulli beam subject to instantaneous flow-induced forces and solved using C1 conforming finite element basis functions in space and an unconditionally stable Newmark-type discretization scheme in time. At each time step the instantaneous incremental displacement is fed back to the fluid flow solver, where the position of the pipe is updated to compute the resulting instantaneous flow field and associated flow-induced forces. Numerical predictions from the FSI model are compared to experimental measurements of a flexible pipe subject to uniform free-stream currents.

Three-Dimensional Navier–Stokes Computation of Turbomachinery Flows Using an Explicit Numerical Procedure and a Coupled k–ε Turbulence Model

1992 ◽  
Vol 114 (3) ◽  
pp. 627-642 ◽  
Author(s):  
R. F. Kunz ◽  
B. Lakshminarayana
Keyword(s):  
Reynolds Number ◽  
Turbulence Model ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Secondary Flows ◽  
Quality Data ◽  
Navier Stokes ◽  
Evaluation Procedure ◽  
Pressure Probe ◽  
Time Step

An explicit, three-dimensional, coupled Navier–Stokes/k–ε technique has been developed and successfully applied to complex internal flow calculations. Several features of the procedure, which enable convergent and accurate calculation of high Reynolds number two-dimensional cascade flows, have been extended to three dimensions, including a low Reynolds number compressible form of the k–ε turbulence model, local time-step specification based on hyperbolic and parabolic stability requirements, and eigenvalue and local velocity scaling of artificial dissipation operators. A flux evaluation procedure, which eliminates the finite difference metric singularity at leading and trailing edges on H- and C-grids, is presented. The code is used to predict the pressure distribution, primary velocity, and secondary flows in an incompressible, turbulent curved duct flow for which CFD validation quality data are available. Also, a subsonic compressor rotor passage, for which detailed laser, rotating hot-wire, and five-hole pressure probe measurements have been made is computed. Detailed comparisons between predicted and measured core flow and near-wall velocity profiles, wake profiles, and spanwise mixing effects downstream of the rotor passage are presented for this case. It is found that the technique provides accurate and convergent engineering simulation of these complex turbulent flows.

Evaluation of numerical diffusion of the finite volume method when modelling surface waves

2019 ◽  
pp. 106-119
Author(s):  
Елена Сергеевна Тятюшкина ◽  
Андрей Сергеевич Козелков ◽  
Андрей Александрович Куркин ◽  
Вадим Викторович Курулин ◽  
Валентин Робертович Ефремов ◽  
...  
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Calculation Method ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Numerical Diffusion ◽  
Volume Method

Обсуждается применение метода конечных объемов при решении уравнений Навье-Стокса для моделирования поверхностных волн. Сформулирована задача о распространении поверхностных волн, которая используется для оценки численной диффузии в решении уравнений Навье-Стокса. Предлагается методика оценки численной диффузии, выражаемой коэффициентом уменьшения амплитуды волны при прохождении ею одной своей длины (коэффициентом затухания). Дана оценка размеров сетки и шага по времени, выраженных в безразмерных величинах относительно параметров волны, необходимых для обеспечения приемлемого значения коэффициента затухания. Показана степень влияния каждого из сеточных параметров на увеличение коэффициента затухания. The application of numerical simulation methods based on the solution of the full three-dimensional Navier-Stokes equations for modelling of wave propagation on the water surface requires the construction of a grid model containing countable nodes throughout the entire volume of water medium. Insufficient grid resolution leads to insufficient detailing of the fields of velocity and pressure, as well as volume fraction of the liquid, which increases the numerical diffusion of the method and, ultimately, leads to an underestimation of oscillation amplitudes of the medium. A large time step also results in a “blurring” of the solution and significantly reduces its stability, especially when using the schemes which compress the front of the media interface. This paper presents the results of an assessment of acceptable grid sizes and time steps expressed in dimensionless parameters with respect to the wave parameters necessary to ensure accuracy of the solution sufficient for geophysical applications. The estimate is given for the method of calculating three-dimensional multiphase flows with a free surface based on solving the Navier-Stokes equations in a one-velocity approximation based on a completely implicit connection between velocity and pressure using the finite volume method. The finite volume method for the numerical solution of the Navier-Stokes equations is implemented for use on arbitrary unstructured grids. The methodology for estimation of numerical diffusion of the calculation method is proposed. This estimation is expressed as a percentage of the wave amplitude decrease at the distance equal to the one wavelength. In turn the methodology is based on the parameters entered to estimate the acceptable grid sizes and time step for the calculation method. Based on the described methodology, the results of the estimation of the grid resolution in the horizontal and vertical directions, the estimation of the time step, and the evaluation of the influence of the discretization scheme of the convective term are presented.

Tsunami-Induced Overturning of Buildings in Onagawa during the 2011 Tohoku Earthquake

2016 ◽  
Vol 32 (4) ◽  
pp. 1989-2007 ◽  
Author(s):  
Kohji Tokimatsu ◽  
Michitaka Ishida ◽  
Shusaku Inoue
Keyword(s):  
Shallow Water Equation ◽  
Tohoku Earthquake ◽  
Building Performance ◽  
The 2011 Tohoku Earthquake ◽  
Inundation Depth ◽  
Time Histories ◽  
Run Up ◽  
The Time Domain ◽  
Tsunami Run Up ◽  
The Town

A simulation of the tsunami run-up during the 2011 Great Tohoku Earthquake was performed to investigate the mechanisms and differences in overturning failures of buildings in Onagawa, based on a two-dimensional (2-D) shallow water equation with video evidence recorded in the town as reference. The time histories of inundation depth and flow velocity predicted by the analysis enable one to develop a simplified method to estimate the hydrodynamic and buoyant forces acting on a building, as well as its factors of safety against sliding, uplift, and overturning in the time domain. This method was applied to five well-documented cases of buildings that did or did not overturn during the tsunami. Results showed that the proposed method is capable of predicting the differences in building performance qualitatively, including the likelihood, time, and direction of toppling. The results also suggested that the seaward overturning of one building is likely due to its specific topographical location with a hill closely behind that makes the tsunami load significantly less during run-up than during backwash.

Sign in / Sign up

Export Citation Format

Share Document