An Efficient Numerical Model of Hyperbolic Mild-Slope Equation

2007 ◽  
Author(s):  
Zhiyao Song ◽  
Honggui Zhang ◽  
Jun Kong ◽  
Ruijie Li ◽  
Wei Zhang
Keyword(s):  
Wave Propagation ◽  
Numerical Model ◽  
Water Waves ◽  
Computational Time ◽  
Transient Wave ◽  
Flat Bottom ◽  
The Real ◽  
Wave Elevation ◽  
Mild Slope Equation ◽  
Effective Wave

Introduction of an effective wave elevation function, the simplest time-dependent hyperbolic mild-slope equation has been presented and an effective numerical model for the water wave propagation has been established combined with different boundary conditions in this paper. Through computing the effective wave elevation and transforming into the real transient wave motion, then related wave heights are computed. Because the truncation errors of the presented model only induced by the dissipation terms, but those of Lin’s model (2004) contributed by the convection terms, dissipation terms and source terms, the error analysis shows that calculation stability of this model is enhanced obviously compared with Lin’s one. The tests show that this model succeeds to the merit in Lin’s one and the computer program simpler, computational time shorter because of calculation stability enhanced efficiently and computer memory decreased obviously. The presented model has the capability of simulating exactly the location of transient wave front by the speed of wave propagation in the first test, which is important for the real-time prediction of the arrival time of water waves generated in the deep sea. The model is validated against experimental data for combined wave refraction and diffraction over submerged circular shoal on a flat bottom in the second test. Good agreements are gained. The model can be applied to the theory research and engineering applications about the wave propagation in the coastal waters.

Numerical Study on Coastal Wave and Near-Shore Current Interaction

2014 ◽  
Author(s):  
Jun Tang ◽  
Yongming Shen ◽  
Yigang Lv
Keyword(s):  
Wave Propagation ◽  
Numerical Model ◽  
Water Wave ◽  
Wave Radiation ◽  
Radiation Stress ◽  
Propagation Angle ◽  
Mild Slope Equation ◽  
Near Shore ◽  
Wave Induced ◽  
Wave Radiation Stress

Coastal waves and near-shore currents have been investigated by many researchers. This paper developed a two-dimensional numerical model of near-shore waves and currents to study breaking wave induced current. In the model, near-shore water wave was simulated by a parabolic mild slope equation incorporating current effect and wave energy dissipation due to breaking, and current was simulated by a nonlinear shallow water equation incorporating wave exerted radiation stress. Wave radiation stress was calculated based on complex wave amplitude in the parabolic mild slope equation, and this result in an effective method for calculating wave radiation stress using an intrinsic wave propagation angle that differs from the ones of using explicit wave propagation angle. Wave and current interactions were considered by cycling the wave and current equation to a steady state. The model was used to study waves and wave-induced longshore currents at the Obaköy coastal water which is located at the Mediterranean coast of Turkey. The numerical results for water wave induced longshore current were validated by measured data to demonstrate the efficiency of the numerical model, and water waves and longshore currents were analyzed based on the numerical results.

A pseudospectral approach for scattering of water waves

1994 ◽  
Vol 445 (1925) ◽  
pp. 619-636 ◽  
Keyword(s):  
Wave Field ◽  
Water Waves ◽  
Parabolic Model ◽  
Beach Profile ◽  
Flat Bottom ◽  
Propagation Models ◽  
Wave Refraction ◽  
Collocation Points ◽  
Mild Slope Equation ◽  
Backward Wave

Wave propagation models for scattering of water waves are developed based on the mild-slope equation. The pseudospectral Fourier approach is used to reduce the mild-slope equation to a set of ordinary differential equations for the mod­ified potential, ϕ√CC g , at collocation points in the alongshore direction. The wave field is then decoupled into a series of wave modes including all forward and backward propagating modes. Ignoring the backward wave field as a first approximation, a wide-angle parabolic model is derived. When the backward wave field is important, both forward and backward wave fields are obtained by construct­ing the Bremmer series solution. A small-angle parabolic model is also developed for comparison. Numerical results are presented for wave refraction over an equi­librium beach profile and wave focusing over a submerged circular shoal on a flat bottom. The importance of the backward scattering is illustrated by the latter example.

MODELING COMPLEX FLOW INDUCED BY WATER WAVES PROPAGATION OVER SUBMERGED SQUARE OBSTACLES

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Mona Abdeltawab Gomaa ◽  
Tamer HMA Kasem ◽  
Andreas Schlenkhoff
Keyword(s):  
Numerical Model ◽  
Wave Energy ◽  
Water Waves ◽  
Initial Conditions ◽  
Computational Time ◽  
Model Parameters ◽  
Shore Protection ◽  
Complex Flow ◽  
Time Step ◽  
Wave Energy Dissipation

Submerged breakwaters are efficient structures used for shore protection. Many design features of these structures are captured upon modeling wave propagation over submerged square obstacles. The presence of separation vortices and large free surface deformations complicates the problem. A multiphase turbulent numerical model is developed using ANSYS commercial package. Careful domain discretization is done employing suitable mesh clustering to capture high gradients. Various numerical model parameters are provided, including grid size and time step. Special attention is directed towards clarifying turbulence initial conditions. Stable simulation results are obtained within acceptable computational time. Numerical results are validated quantitatively using subsurface measurements. Comparison along continuous horizontal and vertical velocity profiles is provided. Temporal and spatial model resolutions are illustrated for three test cases. The effect of wave period and height is well focused. The unsteady vortical structure is visualized. The incident wave energy is calculated and validated against theoretical values. The wave energy dissipation characteristics are briefly explained.

scholarly journals Numerical simulation of acoustic signal propagation in underwater acoustic duct

2021 ◽  
Vol 2 (396) ◽  
pp. 122-133
Author(s):  
F. Legusha ◽  
◽  
Yu. Popov ◽  
Keyword(s):  
Numerical Simulation ◽  
Wave Propagation ◽  
Numerical Model ◽  
Acoustic Signal ◽  
Water Channel ◽  
Vertical Plane ◽  
Signal Propagation ◽  
The Real ◽  
Target Force ◽  
Real Target

Object and purpose of research. The progress in numerical simulation methods significantly widens the capabilities of theoretical analysis in the tasks requiring extensive calculations and input data sets, like sound propagation at sea. This paper discusses the feasibility of a numerical model describing the physics of acoustic signal propagation in a deep-water channel. Materials and methods. Acoustic signal calculation is performed as per the ray-path theory with a numerical model taking into account depth-wise variations of sound velocity and seabed parameters. Main results. It was shown that depending on the vertical distribution of sound speed, the source depth and distance, the acoustic wave propagation direction can change over significant range of angles the in vertical plane. In this regard it is advisable to calculate the real target force of an object of complex geometry not only from heading angle in horizontal plane but also in terms of the possible range of angles in the vertical plane. Conclusion. Model-analyzed angles range of long-range wave propagation may be used for change estimation of object target force characteristics. Practical significance of the study lies in improving the methods of calculation of the real target force of complex shape objects in terms of state-of the art capabilities of simulating the propagation of acoustic signals conditions in the ocean.

scholarly journals Numerical Aspects of Particle-in-Cell Simulations for Plasma-Motion Modeling of Electric Thrusters

Aerospace ◽  
2021 ◽  
Vol 8 (5) ◽  
pp. 138
Author(s):  
Giuseppe Gallo ◽  
Adriano Isoldi ◽  
Dario Del Gatto ◽  
Raffaele Savino ◽  
Amedeo Capozzoli ◽  
...  
Keyword(s):  
Numerical Model ◽  
Computing Time ◽  
Computational Time ◽  
Electric Motors ◽  
Motion Modeling ◽  
Particle In Cell ◽  
Computing Platform ◽  
Hall Effect Thruster ◽  
Set Up ◽  
Pic Code

The present work is focused on a detailed description of an in-house, particle-in-cell code developed by the authors, whose main aim is to perform highly accurate plasma simulations on an off-the-shelf computing platform in a relatively short computational time, despite the large number of macro-particles employed in the computation. A smart strategy to set up the code is proposed, and in particular, the parallel calculation in GPU is explored as a possible solution for the reduction in computing time. An application on a Hall-effect thruster is shown to validate the PIC numerical model and to highlight the strengths of introducing highly accurate schemes for the electric field interpolation and the macroparticle trajectory integration in the time. A further application on a helicon double-layer thruster is presented, in which the particle-in-cell (PIC) code is used as a fast tool to analyze the performance of these specific electric motors.

On the Friction Coefficient in the Numerical Simulation of Tidal Wave Propagation

2010 ◽  
Author(s):  
Z. Y. Song ◽  
C. Cheng ◽  
F. M. Xu ◽  
J. Kong
Keyword(s):  
Numerical Simulation ◽  
Wave Propagation ◽  
Friction Factor ◽  
Tidal Wave ◽  
Computational Time ◽  
Numerical Dissipation ◽  
Courant Number ◽  
Time Step ◽  
Large Time Step ◽  
The Relationship

Based on the analytical solution of one-dimensional simplified equation of damping tidal wave and Heuristic stability analysis, the precision of numerical solution, computational time and the relationship between the numerical dissipation and the friction dissipation are discussed with different numerical schemes in this paper. The results show that (1) when Courant number is less than unity, the explicit solution of tidal wave propagation has higher precision and requires less computational time than the implicit one; (2) large time step is allowed in the implicit scheme in order to reduce the computational time, but the precision of the solution also reduce and the calculation precision should be guaranteed by reducing the friction factor: (3) the friction factor in the implicit solution is related to Courant number, presented as the determined friction factor is smaller than the natural value when Courant number is larger than unity, and their relationship formula is given from the theoretical analysis and the numerical experiments. These results have important application value for the numerical simulation of the tidal wave.

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