scholarly journals A NUMERICAL SOLUTION OF BOUSSINESQ TYPE WAVE EQUATIONS

1984 ◽  
Vol 1 (19) ◽  
pp. 72 ◽  
Author(s):  
H. Schaper ◽  
W. Sielke
Keyword(s):  
Boundary Conditions ◽  
Numerical Solution ◽  
Shallow Water ◽  
Wave Equations ◽  
Numerical Models ◽  
Practical Interest ◽  
Wave Climate ◽  
Recent Discussion ◽  
Short Waves ◽  
Transfer Capability

Numerical models of short waves in shallow water, which are of particular interest for the calculation of the wave climate in harbours and coastal areas, have been presented by Abbott et al. (1978) and by Hauguel (1980). These models are based on the solution of the Boussinesq or Serre type equations. A recent discussion of the range of application for the equations has been presented by McCowan (1982). Nevertheless, there is some uncertainty as to which terms in the differential equations are of importance, and how they are to be approximated. Therefore, no final judgement can presently be made on the accuracy and credibility of the solutions. Research on such models is still in progress and is of high theoretical and practical interest. Some of the aspects of current research relate to the handling of nonlinear terms, the non-reflecting boundary conditions and the transfer capability of the models for spectral input. This paper will reflect on these points.

scholarly journals Wave Climate at Shallow Waters along the Abu Dhabi Coast

Water ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 985 ◽  
Author(s):  
Waleed Hamza ◽  
Letizia Lusito ◽  
Francesco Ligorio ◽  
Giuseppe Tomasicchio ◽  
Felice D’Alessandro
Keyword(s):  
Shallow Water ◽  
Numerical Models ◽  
Grid Point ◽  
Arabian Gulf ◽  
Acoustic Doppler Current Profiler ◽  
Wave Climate ◽  
Abu Dhabi ◽  
Water Conditions ◽  
Key Factor ◽  
Offshore Wave

High-resolution, reliable global atmospheric and oceanic numerical models can represent a key factor in designing a coastal intervention. At the present, two main centers have the capabilities to produce them: the National Oceanic and Atmospheric Administration (NOAA) in the U.S.A. and the European Centre for Medium-Range Weather Forecasts (ECMWF). The NOAA and ECMWF wave models are developed, in particular, for different water regions: deep, intermediate, and shallow water regions using different types of spatial and temporal grids. Recently, in the Arabian Gulf (also named Persian Gulf), the Abu Dhabi Municipality (ADM) installed an ADCP (Acoustic Doppler Current Profiler) to observe the atmospheric and oceanographic conditions (water level, significant wave height, peak wave period, water temperature, and wind speed and direction) at 6 m water depth, in the vicinity of the shoreline of the Saadiyat beach. Courtesy of Abu Dhabi Municipality, this observations dataset is available; the recorded data span the period from June 2015 to January 2018 (included), with a time resolution of 10 min and 30 min for the atmospheric and oceanographic variables, respectively. At the ADCP deployment location (ADMins), the wave climate has been determined using wave propagation of the NOAA offshore wave dataset by means of the Simulating WAves Nearshore (SWAN) numerical model, the NOAA and ECMWF wave datasets at the closest grid point in shallow water conditions, and the SPM ’84 hindcasting method with the NOAA wind dataset used as input. It is shown that the best agreement with the observed wave climate is obtained using the SPM ’84 hindcasting method for the shallow water conditions.

scholarly journals IRREGULAR WAVE TRANSFORMATION IN A BOUSSINESO WAVE MODEL

1986 ◽  
Vol 1 (20) ◽  
pp. 205
Author(s):  
H.H. Pruser ◽  
H. Schaper ◽  
W. Zielke
Keyword(s):  
Water Waves ◽  
Wave Equations ◽  
Numerical Models ◽  
Wave Model ◽  
Wave Climate ◽  
Irregular Waves ◽  
Wave Transformation ◽  
Diffraction Reflection ◽  
Irregular Wave ◽  
Wave Models

Numerical wave models for shallow water waves are of particular importance for the calculation of the wave climate in harbours and coastal areas. Especially nonlinear time domain models, which are based on the Boussinesq-Wave- Equations, may be helpful in the future for simulating the interaction of currents with refraction, diffraction, reflection and for simulating shoaling..-of irregular waves in natural areas; a potential which has not yet been fully developed. During the last ten years numerical models, based on these equations, have been published; such as ABBOTT et. al. , HAUGUEL and SCHAPER / ZIELKE . Research on this topic is currently being carried on. Some efforts have been made to verify the capability of the models to describe the various physical phenomena. However, up to now, verification has been limited to regular waves. The aim of this paper therefore is, to consider questions concerning irregular, nonlinear waves.

On the numerical solution of a class of partial differential equations

1958 ◽  
Vol 54 (2) ◽  
pp. 214-218 ◽  
Author(s):  
A. S. Douglas
Keyword(s):  
Wave Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Ground State ◽  
Wave Equations ◽  
Ground State Solution ◽  
Electronic Computing ◽  
Image Position

ABSTRACTFor a suitable choice of E*, the solution as t becomes large of the equationwhere Y is given independent of t over the space boundaries, tends to the ground state solution of the wave equationwith the same boundary conditions on P as on Y. As a preliminary to using this relation to solve wave equations in more than one variable, the solution of the equationhas been studied. Methods of numerical solution are discussed, and the convergence of these is examined. Some practical experiments using an electronic computing machine are described.

Modelling solid transport in building drainage systems

1996 ◽  
Vol 33 (9) ◽  
pp. 9-16 ◽  
Author(s):  
John A. Swaffield ◽  
John A. McDougall
Keyword(s):  
Decision Making ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Water Conservation ◽  
Transient Flow ◽  
Drainage System ◽  
System Model ◽  
Flow Depth ◽  
Flow Conditions ◽  
Solid Transport

The transient flow conditions within a building drainage system may be simulated by the numerical solution of the defining equations of momentum and continuity, coupled to a knowledge of the boundary conditions representing either appliances discharging to the network or particular network terminations. While the fundamental mathematics has long been available, it is the availability of fast, affordable and accessible computing that has allowed the development of the simulations presented in this paper. A drainage system model for unsteady partially filled pipeflow will be presented in this paper. The model is capable of predicting flow depth and rate, and solid velocity, throughout a complex network. The ability of such models to assist in the decision making and design processes will be shown, particularly in such areas as appliance design and water conservation.

Axisymmetric flow near the critical point on the moving boundary

2010 ◽  
Vol 7 ◽  
pp. 182-190
Author(s):  
I.Sh. Nasibullayev ◽  
E.Sh. Nasibullaeva
Keyword(s):  
Fluid Flow ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Axial Velocity ◽  
Moving Boundary ◽  
Axisymmetric Flow ◽  
Boundary Motion ◽  
Newton Raphson ◽  
Raphson Method

In this paper the investigation of the axisymmetric flow of a liquid with a boundary perpendicular to the flow is considered. Analytical equations are derived for the radial and axial velocity and pressure components of fluid flow in a pipe of finite length with a movable right boundary, and boundary conditions on the moving boundary are also defined. A numerical solution of the problem on a finite-difference grid by the iterative Newton-Raphson method for various velocities of the boundary motion is obtained.

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