scholarly journals Momentum Conservative Scheme for Simulating Wave Runup and Underwater Landslide

2019 ◽  
Vol 4 (1) ◽  
pp. 29
Author(s):  
Didit Adytia
Keyword(s):  
Water Waves ◽  
Harmonic Wave ◽  
Equation Model ◽  
Boundary Integral ◽  
Staggered Grid ◽  
Wave Runup ◽  
Tsunami Waves ◽  
Conservative Scheme ◽  
Underwater Landslide ◽  
Grid Scheme

This paper focuses on the numerical modelling and simulation of tsunami waves triggered by an underwater landslide. The equation of motion for water waves is represented by the Nonlinear Shallow Water Equations (NSWE). Meanwhile, the motion of underwater landslide is modeled by incorporating a term for bottom motion into the NSWE. The model is solved numerically by using a finite volume method with a momentum conservative staggered grid scheme that is proposed by Stelling & Duinmeijer 2003 [12].  Here, we modify the scheme for the implementation of bottom motion. The accuracy of the implementation for representing wave runup and rundown is shown by performing the runup of harmonic wave as proposed by Carrier & Greenspan 1958 [2], and also solitary wave runup of Synolakis, 1986 [14], for both breaking and non-breaking cases. For the underwater landslide, result of the simulation is compared with simulation using the Boundary Integral Equation Model (BIEM) that is performed by Lynett and Liu, 2002 [9].

Numerical Simulation of Wave Runup and Overtopping for Short and Long Waves Using Staggered Grid Variational Boussinesq

2020 ◽  
Vol 14 (05) ◽  
pp. 2040005
Author(s):  
Didit Adytia ◽  
Sri Redjeki Pudjaprasetya
Keyword(s):  
Experimental Data ◽  
Numerical Simulation ◽  
Water Waves ◽  
Wave Model ◽  
Long Waves ◽  
Wave Number ◽  
Staggered Grid ◽  
Type Model ◽  
Wave Runup ◽  
Conservative Scheme

In designing a numerical tool for simulating a wide variety of water waves, i.e. short to long waves, an accurate and robust wave model and numerical implementation are needed. Dispersion and nonlinearity are the two most important physical aspects that should be modeled accurately. To be applicable to simulate many coastal engineering applications, the numerical scheme should be capable of simulating wave runup and overtopping. In this paper, we extend the capability of a Boussinesq-type model called Variational Boussinesq (VB) model for simulating the runup and overtopping of water waves. To that end, the vertical layer of the fluid is modeled continuously by a linear combination of three functions. If two of these three functions have been incorporated in the previous numerical approximation called the SVB model, this paper discusses the improvement of SVB model by incorporating all the three functions. This approach improve the dispersive property of the SVB model due to its ability to simulate short waves up to kd = 20, compared to the previous model which was only up to kd = 7, where k denotes wave number and d water depth. Furthermore, the model is implemented numerically by using the staggered conservative scheme. In the new implementation, the model is switched to the non-dispersive Shallow Water Equations (SWE) when dealing with a dry area for runup and overtopping phenomena. The new implementation is tested against analytical solutions of soliton propagation and standing wave phenomenon; moreover, it is also tested against experimental data from hydrodynamic laboratories for simulating solitary wave breaking above a sloping bottom, composite beach, and in a structure for simulating overtopping phenomenon. The implementation is also tested against experimental data for simulating irregular wave propagation and runup above a fringing reef. The results of numerical simulation agree quite well with experimental data.

scholarly journals Simulasi Numerik Persamaan Gelombang Air Dangkal untuk Kasus Bendungan Bobol

2021 ◽  
Vol 5 (1) ◽  
pp. 31-38
Author(s):  
Raditya Panji Umbara
Keyword(s):  
Water Waves ◽  
Complex Geometry ◽  
Shallow Water Equation ◽  
Two Dimensions ◽  
Dam Break ◽  
Staggered Grid ◽  
Material Loss ◽  
Grid Scheme ◽  
The Stability ◽  
Volume Method

Technological failure and natural disasters that caused the dam-break resulted in huge losses, both material loss and loss of life. The mathematical model for the dam-break can use the shallow water equation. In this paper, modeling the dam-break in two dimensions is solved by using the finite volume method with a stagerred-grid scheme. The staggered-grid scheme produces more accurate and robust when compared to the Lax-Friedrics scheme. The stability of the water waves on the part of the damaged dam wall is also well preserved using a staggered-grid scheme. Modeling a dam-break with real bathymetric data will be a challenge for further research, because it involves a more complex geometry.

scholarly journals Bound Coherent Structures Propagating on the Free Surface of Deep Water

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 115
Author(s):  
Dmitry Kachulin ◽  
Sergey Dremov ◽  
Alexander Dyachenko
Keyword(s):  
Free Surface ◽  
Deep Water ◽  
Coherent Structures ◽  
Water Waves ◽  
Nonlinear Models ◽  
Ideal Incompressible Fluid ◽  
Equation Model ◽  
System Of Nonlinear Equations ◽  
Potential Flows ◽  
Deep Water Waves

This article presents a study of bound periodically oscillating coherent structures arising on the free surface of deep water. Such structures resemble the well known bi-soliton solution of the nonlinear Schrödinger equation. The research was carried out in the super-compact Dyachenko-Zakharov equation model for unidirectional deep water waves and the full system of nonlinear equations for potential flows of an ideal incompressible fluid written in conformal variables. The special numerical algorithm that includes a damping procedure of radiation and velocity adjusting was used for obtaining such bound structures. The results showed that in both nonlinear models for deep water waves after the damping is turned off, a periodically oscillating bound structure remains on the fluid surface and propagates stably over hundreds of thousands of characteristic wave periods without losing energy.

On the modulation of water waves on shear flows

1976 ◽  
Vol 347 (1651) ◽  
pp. 537-546 ◽  
Keyword(s):  
Water Waves ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Vries Equation ◽  
Harmonic Wave ◽  
Short Wave ◽  
Long Wave ◽  
Stokes Waves ◽  
The Stability ◽  
Wave Limit

The method of multiple scales is used to examine the slow modulation of a harmonic wave moving over the surface of a two dimensional channel. The flow is assumed inviscid and incompressible, but the basic flow takes the form of an arbitrary shear. The appropriate nonlinear Schrödinger equation is derived with coefficients that depend, in a complicated way, on the shear. It is shown that this equation agrees with previous work for the case of no shear; it also agrees in the long wave limit with the appropriate short wave limit of the Korteweg-de Vries equation, the shear being arbitrary. Finally, it is remarked that the stability of Stokes waves over any shear can be examined by using the results derived here.

Efficient asymptotics of solutions to the Cauchy problem with localized initial data for linear systems of differential and pseudodifferential equations

2021 ◽  
Vol 76 (5) ◽  
pp. 745-819
Author(s):  
S. Yu. Dobrokhotov ◽  
V. E. Nazaikinskii ◽  
A. I. Shafarevich
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Water Waves ◽  
Theory Of Elasticity ◽  
Extensive Literature ◽  
Pseudodifferential Equations ◽  
Tsunami Waves ◽  
The Cauchy Problem ◽  
Linear Differential ◽  
Localized Initial Data

Abstract We say that the initial data in the Cauchy problem are localized if they are given by functions concentrated in a neighbourhood of a submanifold of positive codimension, and the size of this neighbourhood depends on a small parameter and tends to zero together with the parameter. Although the solutions of linear differential and pseudodifferential equations with localized initial data constitute a relatively narrow subclass of the set of all solutions, they are very important from the point of view of physical applications. Such solutions, which arise in many branches of mathematical physics, describe the propagation of perturbations of various natural phenomena (tsunami waves caused by an underwater earthquake, electromagnetic waves emitted by antennas, etc.), and there is extensive literature devoted to such solutions (including the study of their asymptotic behaviour). It is natural to say that an asymptotics is efficient when it makes it possible to examine the problem quickly enough with relatively few computations. The notion of efficiency depends on the available computational tools and has changed significantly with the advent of Wolfram Mathematica, Matlab, and similar computing systems, which provide fundamentally new possibilities for the operational implementation and visualization of mathematical constructions, but which also impose new requirements on the construction of the asymptotics. We give an overview of modern methods for constructing efficient asymptotics in problems with localized initial data. The class of equations and systems under consideration includes the Schrödinger and Dirac equations, the Maxwell equations, the linearized gasdynamic and hydrodynamic equations, the equations of the linear theory of surface water waves, the equations of the theory of elasticity, the acoustic equations, and so on. Bibliography: 109 titles.

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.

Cancellation of Non-Harmonic Waves Using a Cycloidal Turbine

2011 ◽  
Author(s):  
John T. Imamura ◽  
Stefan G. Siegel ◽  
Casey Fagley ◽  
Tom McLaughlin
Keyword(s):  
Deep Water ◽  
Water Waves ◽  
Linear Time ◽  
Harmonic Wave ◽  
Point Vortex ◽  
Harmonic Waves ◽  
Incoming Wave ◽  
Response Characteristics ◽  
Depth Water ◽  
Multi Component System

We computationally investigate the ability of a cycloidal turbine to cancel two-dimensional non-harmonic waves in deep water. A cycloidal turbine employs the same geometry as the well established Cycloidal or Voith-Schneider Propeller. It consists of a shaft and one or more hydrofoils that are attached eccentrically to the main shaft and can be independently adjusted in pitch angle as the cycloidal turbine rotates. We simulate the cycloidal turbine interaction with incoming waves by viewing the turbine as a wave generator superimposed with the incoming flow. The generated waves ideally are 180° out of phase and cancel the incoming wave downstream of the turbine. The upstream wave is very small as generation of single-sided waves is a characteristic of the cycloidal turbine as has been shown in prior work. The superposition of the incoming wave and generated wave is investigated in the far-field and we model the hydrofoil as a point vortex. This model has previously been used to successfully terminate regular deep water waves as well as intermediate depth water waves. We explore the ability of this model to cancel non-harmonic waves. Near complete cancellation is possible for a non-harmonic wave with components designed to match those generated by the cycloidal turbine for specified parameters. Cancellation of a specific wave component of a multi-component system is also shown. Also, step changes in the device operating parameters of circulation strength, rotation rate, and submergence depth are explored to give insight to the cycloidal turbine response characteristics and adaptability to changes in incoming waves. Based on these studies a linear, time-invarient (LTI) model is developed which captures the steady state wave frequency response. Such a model can be used for control development in future efforts to efficiently cancel more complex incoming waves.

Gap Resonance of Fixed Floating Multi Caissons

2019 ◽  
Author(s):  
Limin Chen ◽  
Guanghua He ◽  
Harry B. Bingham ◽  
Yanlin Shao
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Offshore Structures ◽  
Wave Number ◽  
Wave Forces ◽  
Wave Runup ◽  
Floating Bodies ◽  
Constrained Interpolation ◽  
Gap Resonance ◽  
Narrow Gaps

Abstract Generally, numerous marine and offshore structures are composed of a number of modules which introduce narrow gaps between the multi-modules arranged side by side. The interaction between water waves and floating structures excites complex wave runup in the gaps and wave forces on the adjacent modules. In this study, free surface oscillations in twin narrow gaps between identical floating rectangular boxes are investigated by establishing a 2D viscous flow numerical wave tank based on a Constrained Interpolation Profile (CIP) method. The Tangent of Hyperbola for INterface Capturing (THINC) method is employed to capture the free surface. The rigid floating bodies are treated by a Virtual Particle Method (VPM). The incident waves are generated by an internal wave maker. For the fixed module cases, the computational results of wave height in narrow gaps are found in good coincidence with the available experimental measurements, especially for the resonant frequencies. The wave forces on the floating bodies are calculated numerically. The characteristic response of wave forces on the leading and rear bodies are consistent with the free surface elevations in the corresponding narrow gaps. With shallow draft, the gap resonance occurs at higher wave number.

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