A series solution and numerical technique for wave diffraction by a three-dimensional canyon

Wave Motion ◽  
2004 ◽  
Vol 39 (2) ◽  
pp. 129-142 ◽  
Author(s):  
Wen-I Liao ◽  
Tsung-Jen Teng ◽  
Chau-Shioung Yeh
Keyword(s):  
Wave Diffraction ◽  
Series Solution ◽  
Numerical Technique ◽  
Three Dimensional

Preliminary results of numerical simulation of submarine landslide-generated waves

2021 ◽  
Author(s):  
Ramtin Sabeti ◽  
Mohammad Heidarzadeh
Keyword(s):  
Numerical Simulation ◽  
Numerical Modelling ◽  
Numerical Solutions ◽  
Numerical Technique ◽  
Source Region ◽  
Three Dimensional ◽  
Terminal Velocity ◽  
Sensitivity Analyses ◽  
Physical Experiments ◽  
Set Up

<p>Landslide-generated waves have been major threats to coastal areas and have led to destruction and casualties. Their importance is undisputed, most recently demonstrated by the 2018 Anak Krakatau tsunami, causing several hundred fatalities. The accurate prediction of the maximum initial amplitude of landslide waves (<em>η<sub>max</sub></em>) around the source region is a vital hazard indicator for coastal impact assessment. Laboratory experiments, analytical solutions and numerical modelling are three major methods to investigate the (<em>η<sub>max</sub></em>). However, the numerical modelling approach provides a more flexible and cost- and time-efficient tool. This research presents a numerical simulation of tsunamis due to rigid landslides with consideration of submerged conditions. In particular, this simulation focuses on studying the effect of landslide parameters on <em>η<sub>max</sub>.</em> Results of simulations are compared with our conducted physical experiments at the Brunel University London (UK) to validate the numerical model.</p><p>We employ the fully three-dimensional computational fluid dynamics package, FLOW-3D Hydro for modelling the landslide-generated waves. This software benefit from the Volume of Fluid Method (VOF) as the numerical technique for tracking and locating the free surface. The geometry of the simulation is set up according to the wave tank of physical experiments (i.e. 0.26 m wide, 0.50 m deep and 4.0 m). In order to calibrate the simulation model based on the laboratory measurements, the friction coefficient between solid block and incline is changed to 0.41; likewise, the terminal velocity of the landslide is set to 0.87 m/s. Good agreement between the numerical solutions and the experimental results is found. Sensitivity analyses of landslide parameters (e.g. slide volume, water depth, etc.) on <em>η<sub>max </sub></em>are performed. Dimensionless parameters are employed to study the sensitivity of the initial landslide waves to various landslide parameters.</p>

Three-Dimensional Study of Fatigue Crack Growth in a Rotating Disc

2013 ◽  
Vol 3 (2) ◽  
pp. 45-62
Author(s):  
Eskandari Hadi ◽  
Nami Mohammad Rahim
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Crack Front ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Crack Orientation ◽  
Rotating Disc ◽  
Mesh Density ◽  
Three Dimensional Finite Element

The problem of fatigue-crack-growth in a rotating disc at different crack orientation angles is studied by using an automated numerical technique, which calculates the stress intensity factors on the crack front through the three-dimensional finite element method. Paris law is used to develop the fatigue shape of initially semi-elliptical surface crack. Because of needs for the higher mesh density and accuracy near the crack, the sub-modeling technique is used in the analysis. The distribution of SIF’s along the crack front at each step of growth is studied and the effect of crack orientation on the rate of crack-growth is investigated. The calculated SIF’s are reasonable and could be used to predict the probable crack growth rates in fracture mechanics analysis and can help engineers to consider in their designing and to prevent any unwanted failure of such components.

Numerical Simulation Study on the Asymmetric Structures of Oscillatory Flow Field in a Baffled Tube Reactor

2004 ◽  
Author(s):  
Yong-Wen Wu ◽  
Jia Wu
Keyword(s):  
Numerical Simulation ◽  
Turbulent Flows ◽  
Oscillatory Flow ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Structured Grid ◽  
Tube Reactor ◽  
Oscillating Boundary ◽  
The Asymmetry ◽  
Laminar And Turbulent Flows

The oscillatory flow in a baffled tube reactor provides a significant enhancement of radial transfer of momentum, heat and mass and a good control of axial back mixing at a wide range of net flow rate. But little has been known about reliable details of the three-dimensional structure of flow field in this kind of flow because most published studies in the area were based on the two-dimensional simulation techniques. This paper implemented a three-dimensional numerical simulation study on the asymmetry of flow pattern in the baffled tube reactor which was observed experimentally. A systematic study by numerical simulation was carried out which covered a range of oscillatory Reynolds number (Reo) from 100 to 5,000 and employed models respectively for laminar and turbulent flows. It was found in the simulation that under symmetric boundary conditions the transition from axially symmetric flow to asymmetric one depended on the numerical technique employed in simulation. With a structured grid frame the transition occurred at Reo much greater than that with an unstructured grid frame, for both laminar and turbulent flows. It is not rational that the onset of the transition changes with the accuracy of numerical technique. Based on the simulation results, it was postulated that the asymmetry appeared in simulations with symmetric boundary conditions might result from the accumulation of calculation errors but the asymmetry observed in experiments might result from the slight asymmetry of geometry which exists inevitably in any experiment apparatus. To explore the influence of the slight asymmetry of geometry, the effect of the eccentricity of baffles and the declination of oscillating boundary were studied by use of the finite volume method with a structured grid and adaptive time steps. The simulation result showed that both the eccentricity of baffles and the declination of oscillating boundary have obvious influence on the asymmetry of flow patterns for laminar and turbulent flow. More details were discussed in the paper.

scholarly journals Real-Time Computer Simulation of Three Dimensional Elastostatics Using the Finite Point Method

2011 ◽  
Vol 110-116 ◽  
pp. 2740-2745
Author(s):  
Kirana Kumara P. ◽  
Ashitava Ghosal
Keyword(s):  
Real Time ◽  
Graphics Processing Unit ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Point Method ◽  
Processing Unit ◽  
Finite Point ◽  
Deformable Solids ◽  
Finite Point Method ◽  
Linear Elastostatics

Real-time simulation of deformable solids is essential for some applications such as biological organ simulations for surgical simulators. In this work, deformable solids are approximated to be linear elastic, and an easy and straight forward numerical technique, the Finite Point Method (FPM), is used to model three dimensional linear elastostatics. Graphics Processing Unit (GPU) is used to accelerate computations. Results show that the Finite Point Method, together with GPU, can compute three dimensional linear elastostatic responses of solids at rates suitable for real-time graphics, for solids represented by reasonable number of points.

Inhomogeneous thermal conduction equations

1978 ◽  
Vol 56 (7) ◽  
pp. 928-935
Author(s):  
C. S. Lai
Keyword(s):  
Differential Equations ◽  
Thermal Conduction ◽  
Series Solution ◽  
Nonlinear Differential Equations ◽  
Three Dimensional ◽  
Incompressible Fluids ◽  
Self Similar Solution ◽  
Self Similar ◽  
A New Technique ◽  
The One

The method of self-similar solution of partial differential equations is applied to the one-, two-, and three-dimensional inhomogeneous thermal conduction equations with the thermometric conductivities χ ~ rmWn. Analytical solutions are obtained for the case that the total amount of heat is conserved. For the case that the temperature is maintained constant at r = 0, a new technique of the series solution about the point of intercept is proposed to solve the resultant nonlinear differential equations. The solutions obtained are useful in studying the thermal conduction characteristics of some incompressible fluids.

Dynamic Stability Analysis of a Flexible Rotor Filled With Liquid Based on Three-Dimensional Flow

2018 ◽  
Vol 141 (5) ◽  
Author(s):  
Guangding Wang ◽  
Huiqun Yuan
Keyword(s):  
Dynamic Stability ◽  
Numerical Technique ◽  
Fluid Dynamic ◽  
Dynamic Pressure ◽  
Three Dimensional ◽  
Frequency Equation ◽  
Fourier Series Expansion ◽  
Flexible Rotor ◽  
Three Dimensional Flow ◽  
Dimensional Flow

This paper deals with the dynamic stability of a flexible liquid-filled rotor. On the basis of three-dimensional flow, the fluid perturbation motion is analyzed and the fluid–structure interaction equation is established, combining with continuity equation, the expression of fluid force exerted on rotor is derived in terms of Fourier series expansion. Considering the complex nonlinear relationship between fluid dynamic pressure and the rotor deformation function, they are expanded in terms of the eigenfunction of a dry rotor. The whirling frequency equation of a flexible rotor partially filled with liquid is obtained based on the rotor static equilibrium equation. Finally, the numerical technique is used to analyze the dynamic stability of the rotor system, and the influences of system parameters on unstable region are discussed.

Rigorous accounting diffraction on non-plane gratings irradiated by non-planar waves

2021 ◽  
Author(s):  
Leonid I. Goray
Keyword(s):  
Plane Wave ◽  
Wave Diffraction ◽  
Plane Waves ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Transverse Magnetic ◽  
Incident Field ◽  
Boundary Integral ◽  
Cylindrical Waves ◽  
Plane Wave Diffraction

Abstract The modified boundary integral equation method (MIM) is considered a rigorous theoretical application for the diffraction of cylindrical waves by arbitrary profiled plane gratings, as well as for the diffraction of plane/non-planar waves by concave/convex gratings. This study investigates two-dimensional (2D) diffraction problems of the filiform source electromagnetic field scattered by a plane lamellar grating and of plane waves scattered by a similar cylindrical-shaped grating. Unlike the problem of plane wave diffraction by a plane grating, the field of a localised source does not satisfy the quasi-periodicity requirement. Fourier transform is used to reduce the solution of the problem of localised source diffraction by the grating in the whole region to the solution of the problem of diffraction inside one Floquet channel. By considering the periodicity of the geometry structure, the problem of Floquet terms for the image can be formulated so that it enables the application of the MIM developed for plane wave diffraction problems. Accounting of the local structure of an incident field enables both the prediction of the corresponding efficiencies and the specification of the bounds within which the approximation of the incident field with plane waves is correct. For 2D diffraction problems of the high-conductive plane grating irradiated by cylindrical waves and the cylindrical high-conductive grating irradiated by plane waves, decompositions in sets of plane waves/sections are investigated. The application of such decomposition, including the dependence on the number of plane waves/sections and radii of the grating and wave front shape, was demonstrated for lamellar, sinusoidal and saw-tooth grating examples in the 0th & –1st orders as well as in the transverse electric and transverse magnetic polarisations. The primary effects of plane wave/section partitions of non-planar wave fronts and curved grating shapes on the exact solutions for 2D and three-dimensional (conical) diffraction problems are discussed.

scholarly journals A Fourier Series Solution for Transient Three‐Dimensional Thermohaline Convection in Porous Enclosures

2020 ◽  
Vol 56 (11) ◽  
Author(s):  
Sara Tabrizinejadas ◽  
Marwan Fahs ◽  
Behzad Ataie‐Ashtiani ◽  
Craig T. Simmons ◽  
Raphaël Chiara Roupert ◽  
...  
Keyword(s):  
Fourier Series ◽  
Series Solution ◽  
Three Dimensional ◽  
Thermohaline Convection

Impact Simulation of Liquid-Filled Containers Including Fluid-Structure Interaction—Part 1: Theory

1993 ◽  
Vol 115 (1) ◽  
pp. 68-72 ◽  
Author(s):  
R. G. Sauve´ ◽  
G. D. Morandin ◽  
E. Nadeau
Keyword(s):  
Fluid Model ◽  
Numerical Technique ◽  
Liquid Radioactive Waste ◽  
Three Dimensional ◽  
Volumetric Strain ◽  
Computer Code ◽  
Compressible Medium ◽  
Hydrodynamic Effect ◽  
Inviscid Fluid ◽  
Element Discretization

In a number of applications, the hydrodynamic effect of a fluid must be included in the structural evaluation of liquid-filled vessels undergoing transient loading. Prime examples are liquid radioactive waste transportation packages. These packages must demonstrate the ability to withstand severe accidental impact scenarios. A hydrodynamic model of the fluid is developed using a finite element discretization of the momentum equations for a three-dimensional continuum. An inviscid fluid model with an isotropic stress state is considered. A barotropic equation of state, relating volumetric strain to pressure, is used to characterize the fluid behavior. The formulation considers the continuum as a compressible medium only, so that no tension fields are permitted. The numerical technique is incorporated into the existing general-purpose three-dimensional structural computer code H3DMAP. Part 1 of the paper describes the theory and implementation along with comparisons with classical theory. Part 2 describes the experimental validation of the theoretical approach. Excellent correlation between predicted and experimental results is obtained.

Investigation of Numerical Evaluation Improvement for Three-Dimensional Infinite Cylindrical Heat Conduction Problems

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Te Pi ◽  
Kevin Cole ◽  
Qingjun Zhao ◽  
Wei Zhao
Keyword(s):  
Thermal Properties ◽  
Heat Conduction ◽  
Numerical Evaluation ◽  
Series Solution ◽  
Three Dimensional ◽  
Well Test ◽  
Computer Evaluation ◽  
Evaluation Time ◽  
Finite Body ◽  
Cylindrical Geometries

Abstract To estimate the thermal properties from transient data, a model is needed to produce numerical values with sufficient precision. Iterative regression or other estimation procedures must be applied to evaluate the model again and again. From this perspective, infinite or semi-infinite heat conduction problems are a challenge. Since the analytical solution usually contains improper integrals that need to be computed numerically, computer-evaluation speed is a serious issue. To improve the computation speed with precision maintained, an analytical method has been applied to three-dimensional (3D) cylindrical geometries. In this method, the numerical evaluation time is improved by replacing the integral-containing solution by a suitable finite body series solution. The precision of the series solution may be controlled to a high level and the required computer time may be minimized by a suitable choice of the extent of the finite body. The practical applications for 3D geometries include the line-source method for obtaining thermal properties, the estimation of thermal properties by the laser-flash method, and the estimation of aquifer properties or petroleum-field properties from well-test measurements. This paper is an extension of earlier works on one-dimensional (1D) and two-dimensional (2D) cylindrical geometries. In this paper, the computer-evaluation time for the finite geometry 3D solutions is shown to be hundreds of times faster than the infinite or semi-infinite solution with the precision maintained.

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