Numerical solutions to wave interaction with rubblemound breakwaters

1990 ◽  
Vol 17 (2) ◽  
pp. 252-261 ◽  
Author(s):  
Kevin R. Hall
Keyword(s):  
Numerical Modelling ◽  
Numerical Solution ◽  
Numerical Solutions ◽  
Scale Effects ◽  
Numerical Models ◽  
Internal Flow ◽  
Wave Interaction ◽  
Theoretical Development ◽  
Porous Media Flow ◽  
Complex Flow

The interaction of a wave with a rubblemound breakwater results in a complex flow field which is both nonlinear and turbulent, particularly within a region close to the surface of the structure. Numerical models describing internal flow in a rubblemound breakwater are becoming increasingly important, particularly as the influence of scale effects on internal flow in physical hydraulic models are becoming understood as important. A number of numerical models to predict the internal breakwater flow kinematics have been produced in the past two decades. This paper provides a review of the state-of-the-art of numerical modelling of wave interaction with rubblemound breakwaters. Details of the theoretical development and the resulting numerical solution techniques are presented. Methods for incorporating secondary effects such as two-phase (air–water) flow, inertia, and unbalanced boundary conditions are discussed. Limitations of the models resulting from the validity of the assumptions made in order to effect a numerical solution are discussed. Key words: breakwaters, internal flow, porous media flow, numerical modelling, rubblemound breakwaters.

scholarly journals Numerical Modeling of Tsunami Waves Interaction with Porous and Impermeable Vertical Barriers

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Manuel del Jesus ◽  
Javier L. Lara ◽  
Inigo J. Losada
Keyword(s):  
Stokes Equations ◽  
Tsunami Wave ◽  
Numerical Models ◽  
Wave Interaction ◽  
Wave Pattern ◽  
Navier Stokes ◽  
Economic Losses ◽  
Wave Flow ◽  
Complex Flow ◽  
Tsunami Waves

Tsunami wave interaction with coastal regions is responsible for very important human and economic losses. In order to properly design coastal defenses against these natural catastrophes, new numerical models need to be developed that complement existing laboratory measurements and field data. The use of numerical models based on the Navier-Stokes equations appears as a reasonable approach due to their ability to evaluate complex flow patterns around coastal structures without the inherent limitations of the classical depth-averaged models. In the present study, a Navier-Stokes-based model, IH-3VOF, is applied to study the interaction of tsunami waves with porous and impermeable structures. IH-3VOF is able to simulate wave flow within the porous structures by means of the volume-averaged Reynolds-averaged Navier-Stokes (VARANS) equations. The equations solved by the model and their numerical implementation are presented here. A numerical analysis of the interaction of a tsunami wave with both an impermeable and porous vertical breakwater is carried out. The wave-induced three-dimensional wave pattern is analysed from the simulations. The role paid by the porous media is also investigated. Finally, flow around the breakwater is analyzed identifying different flow behaviors in the vicinity of the breakwater and in the far field of the structure.

scholarly journals CRITICAL REVIEW OF MODERN NUMERICAL MODELLING OF SNOW ACCUMULATION ON ROOFS WITH ARBITRARY GEOMETRY

2021 ◽  
Vol 17 (4) ◽  
pp. 40-59
Author(s):  
Alexander Belostotsky ◽  
Nikita Britikov ◽  
Oleg Goryachevsky
Keyword(s):  
Numerical Methods ◽  
Numerical Modelling ◽  
Mathematical Models ◽  
Scale Effects ◽  
Numerical Models ◽  
Complex Problem ◽  
Snow Accumulation ◽  
Wind Tunnels ◽  
Arbitrary Geometry ◽  
Snow Transport

The calculation of snow loads on roofs of buildings and structures with arbitrary geometry is a complex problem, solving which requires simulating snow accumulation with acceptable engineering accuracy. Experiments in wind tunnels, although widely used in recent years, do not allow to reproduce the real full-scale effects of all snow transport subprocesses, since it is impossible to satisfy all the similarity conditions. This situation, coupled with the continuous improvement of mathematical models, numerical methods, computer technologies and related software, makes the development and future implementation of numerical modelling in real construction practice and regulatory documents inevitable. This paper reviews currently existing mathematical models and numerical methods used to calculate the forms of snow deposits. And, although the lack of significant progress in the field of modelling snow accumulation still remains one of the major problems in CFD, use of existing models, supported by field observations and experimental data, allows to reproduce reasonably accurate snow distributions. The importance of the “symbiosis” between classical experimental methods and modern numerical models is specifically emphasized in the paper, as well as the fact that only the joint use of approaches can comprehensively describe modelling of snow accumulation and snow transport and provide better solutions to a wider range of problems.

Study of Available Turbulence and Cavitation Models to Reproduce Flow Patterns in Confined Flows

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
M. Coussirat ◽  
F. Moll ◽  
F. Cappa ◽  
A. Fontanals
Keyword(s):  
Numerical Models ◽  
Internal Flow ◽  
Numerical Results ◽  
Flow State ◽  
Quantitative Criterion ◽  
Complex Flow ◽  
Two Phase ◽  
Computational Costs ◽  
Extensive Analysis ◽  
Confined Flows

Cavitating flow in nozzles is a complex flow which implies a highly turbulent two-phase one. An accurate simulation which improves some numerical results found in the literature was achieved by means of an extensive analysis of the capabilities of several numerical models for turbulence and cavitation. The analysis performed involves calibration/optimization tasks based on the physics of this kind of flow. This work aims to provide a quantitative criterion for the judgment of internal flow state, because it was demonstrated that the numerical results obtained with noncalibrated models could be enhanced by means of a careful calibration and thus saving computational costs.

scholarly journals A fractional order epidemic model for the simulation of outbreaks of Ebola

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Weiqiu Pan ◽  
Tianzeng Li ◽  
Safdar Ali
Keyword(s):  
Numerical Solution ◽  
Root Mean Square ◽  
Fractional Order ◽  
Relative Error ◽  
Numerical Solutions ◽  
Real Data ◽  
Mean Square ◽  
Order Model ◽  
The Real ◽  
Fractional Orders

AbstractThe Ebola outbreak in 2014 caused many infections and deaths. Some literature works have proposed some models to study Ebola virus, such as SIR, SIS, SEIR, etc. It is proved that the fractional order model can describe epidemic dynamics better than the integer order model. In this paper, we propose a fractional order Ebola system and analyze the nonnegative solution, the basic reproduction number $R_{0}$ R 0 , and the stabilities of equilibrium points for the system firstly. In many studies, the numerical solutions of some models cannot fit very well with the real data. Thus, to show the dynamics of the Ebola epidemic, the Gorenflo–Mainardi–Moretti–Paradisi scheme (GMMP) is taken to get the numerical solution of the SEIR fractional order Ebola system and the modified grid approximation method (MGAM) is used to acquire the parameters of the SEIR fractional order Ebola system. We consider that the GMMP method may lead to absurd numerical solutions, so its stability and convergence are given. Then, the new fractional orders, parameters, and the root-mean-square relative error $g(U^{*})=0.4146$ g ( U ∗ ) = 0.4146 are obtained. With the new fractional orders and parameters, the numerical solution of the SEIR fractional order Ebola system is closer to the real data than those models in other literature works. Meanwhile, we find that most of the fractional order Ebola systems have the same order. Hence, the fractional order Ebola system with different orders using the Caputo derivatives is also studied. We also adopt the MGAM algorithm to obtain the new orders, parameters, and the root-mean-square relative error which is $g(U^{*})=0.2744$ g ( U ∗ ) = 0.2744 . With the new parameters and orders, the fractional order Ebola systems with different orders fit very well with the real data.

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>

scholarly journals Modelling of mirror mode structures as propagating slow magnetosonic solitons

2009 ◽  
Vol 27 (12) ◽  
pp. 4379-4389 ◽  
Author(s):  
K. Stasiewicz ◽  
C. Z. Cheng
Keyword(s):  
Numerical Modelling ◽  
Excellent Agreement ◽  
Plasma Flow ◽  
Numerical Solutions ◽  
Small Subset ◽  
Instability Condition ◽  
Magnetic Pulsations ◽  
Fluid Theory ◽  
Mirror Mode ◽  
Two Fluid

Abstract. Cluster measurements in the magnetosheath with spacecraft separations of 2000 km indicate that magnetic pulsations interpreted as mirror mode structures are not frozen in plasma flow, but do propagate with speeds of up to ~50 km/s. Properties of these pulsations are shown to be consistent with propagating slow magnetosonic solitons. By using nonlinear two fluid theory we demonstrate that the well known classical mirror instability condition corresponds to a small subset in a continuum of exponentially varying solutions. With the measured plasma moments we have determined parameters of the polybaric pressure model in the region of occurrence of mirror type structures and applied it to numerical modelling of these structures. In individual cases we obtain excellent agreement between observed mirror mode structures and numerical solutions for magnetosonic solitons.

scholarly journals Unconditional Positive Stable Numerical Solution of Partial Integrodifferential Option Pricing Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
M. Fakharany ◽  
R. Company ◽  
L. Jódar
Keyword(s):  
Option Pricing ◽  
Numerical Solution ◽  
Numerical Solutions ◽  
Stable Process ◽  
Integration Formula ◽  
Pricing Models ◽  
Integral Term ◽  
Pricing Problems ◽  
Stability And Consistency ◽  
Partial Integrodifferential Equation

This paper is concerned with the numerical solution of partial integrodifferential equation for option pricing models under a tempered stable process known as CGMY model. A double discretization finite difference scheme is used for the treatment of the unbounded nonlocal integral term. We also introduce in the scheme the Patankar-trick to guarantee unconditional nonnegative numerical solutions. Integration formula of open type is used in order to improve the accuracy of the approximation of the integral part. Stability and consistency are also studied. Illustrative examples are included.

scholarly journals Forecasting the impact of buildings with multi-storey underground parts on the displacement of subsoil using modern numerical tools

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Hanna Michalak ◽  
Paweł Przybysz
Keyword(s):  
Numerical Modelling ◽  
Numerical Models ◽  
Deep Excavation ◽  
Design And Implementation ◽  
Numerical Tools ◽  
Excavation Support ◽  
Area Of Influence ◽  
The Impact ◽  
New Buildings ◽  
Ground Part

Abstract The paper will analyse and review the experience to date in determining the impact range of implementation of deeply founded structures on the displacement of the subsoil in the vicinity. With the background of these experiences, primarily empirical, the present possibilities of using numerical modelling to forecast the displacements of the terrain surface in various stages of works, that is, execution of deep excavation support systems, excavation-deepening phases with successive adding of struts, construction of underground levels and erection of the above-ground part of the building, will be presented. Based on the results of own research, conclusions on the use of 3D numerical models in spatial shaping and designing the structure of underground parts of new buildings erected in dense urban development will be presented. The characterised 3D numerical models were verified, taking into account the actual results of geodetic measurements of the completed buildings. Determining the range and forecasting the displacements of the subsoil are necessary for the design and implementation of investments due to the need to ensure the safety of erection and use of a new building and the buildings located within the area of influence.

scholarly journals THE USE OF ARRAY PROCESSORS FOR NUMERICAL MODELLING OF TIDAL ESTUARY DYNAMICS

1980 ◽  
Vol 1 (17) ◽  
pp. 142
Author(s):  
D. Prandle ◽  
E.R. Funke ◽  
N.L. Crookshank ◽  
R. Renner
Keyword(s):  
Numerical Model ◽  
Numerical Modelling ◽  
Hybrid Model ◽  
Numerical Models ◽  
Computer Time ◽  
Scale Model ◽  
Hybrid Modelling ◽  
Tidal Propagation ◽  
Physical Scale ◽  
Array Processors

The use of array processors for the numerical modelling of estuarine systems is discussed here in the context of "hybrid modelling", however, it is shown that array processors may be used to advantage in independent numerical simulations. Hybrid modelling of tidal estuaries was first introduced by fiolz (1977) and later by Funke and Crookshank (1978). In a hybrid model, tidal propagation in an estuary is simulated by dynamically linking an hydraulic (or physical) scale model of part of the estuary to a numerical model of the remaining part in a manner such that a free interchange of flow occurs at the interface(s). Typically, the elevation of the water surface at the boundary of the scale model is measured and transmitted to the numerical model. In return, the flow computed at the boundary of the numerical model is fed directly into the scale model. This approach enables the extent of the scale model to be limited to the area of immediate interest (or to that area where flow conditions are such that they can be most accurately simulated by a scale model). In addition, since the region simulated by the numerical model can be extended almost indefinitely, the problems of spurious reflections from downstream boundaries can be eliminated. In normal use, numerical models are evaluated on the basis of computing requirements, cost and accuracy. The computer time required to simulate one tide cycle is, in itself, seldom of interest except in so far as it affects the above criteria. However in hybrid modelling this parameter is often paramount since concurrent operation of the numerical and scale models requires that the former must keep pace with the latter. The earlier hybrid model of the St. Lawrence (Funke and Crookshank, 1978) involved a one-dimensional numerical model of the upstream regions of the river. However, future applications are likely to involve extensive two-dimensional numerical simulation.

scholarly journals Use of Jacobians for inverse kinematics of articulated robots : a study on approximate solutions

2020 ◽  
Author(s):  
◽  
Uriel Jacket Tresor Demby's
Keyword(s):  
Numerical Solution ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Fuzzy Inference ◽  
Numerical Approach ◽  
Data Driven ◽  
Approximate Methods ◽  
Inference System ◽  
First Case

In the context of articulated robotic manipulators, the Forward Kinematics (FK) is a highly non-linear function that maps joint configurations of the robot to poses of its endeffector. Furthermore, while in the most useful cases these functions are neither injective (one-to-one) nor surjective (onto), depending on the robot configuration -- i.e. the sequence of prismatic versus revolute joints, and the number of Degrees of Freedom (DoF) -- the associated Inverse Kinematics (IK) problem may be practically or even theoretically impossible to be solved analytically. Therefore, in the past decades, several approximate methods have been developed for many instances of IK problems. The approximate methods can be divided into two distinct categories: data-driven and numerical approaches. In the first case, data-driven approaches have been successfully used for small workspace domains (e.g., task-driven applications), but not fully explored for large ones, i.e. in task-independent applications where a more general IK is required. Similarly, and despite many successful implementations over the years, numerical solutions may fail if an improper matrix inverse is employed (e.g., Moore-Penrose generalized inverse). In this research, we propose a systematic, robust and accurate numerical solution for the IK problem using the Unit-Consistent (UC) and the Mixed (MX) Inverse methods to invert the Jacobians derived from the Denavit-Hartenberg (D-H) representation of the FK for any robot. As we demonstrate, this approach is robust to whether the system is underdetermined (less than 6 DoF) or overdetermined (more than 6 DoF). We compare the proposed numerical solution to data driven solutions using different robots -- with DoF varying from 3 to 7. We conclude that numerical solutions are easier to implement, faster, and more accurate than most data-driven approaches in the literature, specially for large workspaces as in task-independent applications. We particularly compared the proposed numerical approach against two data-driven approaches: Multi-Layer Perceptron (MLP) and Adaptive Neuro-Fuzzy Inference System (ANFIS), while exploring various architectures of these Neural Networks (NN): i.e. number of inputs, number of outputs, depth, and number of nodes in the hidden layers.

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