scholarly journals EXTENDED BOUSSINESQ EQUATIONS FOR WAVES IN TWO POROUS LAYERS

2018 ◽  
pp. 92
Author(s):  
Changhoon Lee ◽  
Van Nghi Vu ◽  
Tae-Hwa Jung ◽  
Thanh Thu Huynh
Keyword(s):  
Experimental Data ◽  
Porous Layer ◽  
Analytical Solutions ◽  
Water Waves ◽  
Royal Society ◽  
Boussinesq Equations ◽  
Water Layer ◽  
Boussinesq Model ◽  
Porous Layers ◽  
Good Agreement

In this study we continue the work of Vu et al. (2018) [Coastal Eng. 139, 85-97] to develop an extended Boussinesq model that predicts the propagation of water waves in two porous layers. The first and second layer can be a water layer or a porous layer. The inertial and drag resistances are considered in the developed model. After being successfully validated against the analytical solutions, the model is used to simulate waves propagating over a submerged triangular porous bar. The numerical results show good agreement with the physical experimental data of Hsiao et al. (1998) [Proc. Royal Society of London A 458, 1291-1322].

scholarly journals Interaction of Water Waves and a Submerged Parabolic Obstacle in the Presence of a Following Uniform/Shear Current Using RANS Model

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yen-Lung Chen ◽  
Jing-Bo Hung ◽  
Shih-Lun Hsu ◽  
Shih-Chun Hsiao ◽  
Yuan-Chieh Wu
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Numerical Model ◽  
Analytical Solutions ◽  
Water Waves ◽  
Surface Deformation ◽  
Navier Stokes ◽  
Regular Waves ◽  
Uniform Shear ◽  
Shear Current

This paper simulates regular waves propagating over a submerged parabolic obstacle in the presence of a uniform/shear current using a two-dimensional numerical model, named COBRAS (Cornell Breaking and Structure). The numerical model solves the Reynolds-Averaged Navier-Stokes (RANS) equations and the free surface deformation is tracked using the volume of fluid method (VOF). The capability of the numerical model to simulate regular waves with a uniform or shear current over a constant water depth is first validated with available analytical solutions and experimental data. Comparisons among the experimental data, analytical solutions, and present numerical results show good agreements. Then, regular waves propagating over a submerged parabolic obstacle with a following current are investigated. Detailed discussions including those on the velocity and vorticity fields and the relation between free surface and vorticity are given.

Hydrodynamics of the Flow Around a Circular Cylinder Sheathed by a Porous Layer

2004 ◽  
Author(s):  
M. P. Sobera ◽  
C. R. Kleijn ◽  
P. Brasser ◽  
H. E. A. van den Akker
Keyword(s):  
Experimental Data ◽  
Circular Cylinder ◽  
Porous Layer ◽  
Vortex Shedding ◽  
Small Distance ◽  
Grid Refinement ◽  
Solid Cylinder ◽  
Local Grid Refinement ◽  
Local Grid ◽  
Good Agreement

A detailed study of the turbulent flow at Re = 3900 around a circular cylinder, sheathed at some small distance by a porous layer, has been performed by means of Direct Numerical Simulation with a commercial unstructured finite volume based Computational Fluid Dynamics solver. First, to benchmark the performance of this code and the validity of the applied local grid refinement, simulations of the flow around a bare circular cylinder at the same Re were performed. Results were compared to that of an academic CFD solver and to numerical and experimental data from literature and good agreement was found. Subsequently, a detailed study of the flow around a porous layer sheathed cylinder at the same Re, was performed. The flow in the space between the outer porous and the inner solid cylinder was found to be laminar and periodic, with a frequency locked to that of the vortex shedding in the wake behind the cylinder. A good agreement was found to experimental data from literature.

scholarly journals Effects of aquifer geometry on seawater intrusion in annulus segment island aquifers

2021 ◽  
Author(s):  
Zhaoyang Luo ◽  
Jun Kong ◽  
Chengji Shen ◽  
Pei Xin ◽  
Chunhui Lu ◽  
...  
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Seawater Intrusion ◽  
Analytical Solutions ◽  
Boussinesq Equations ◽  
Flow Boundary ◽  
Aquifer Geometry

Abstract. Seawater intrusion in island aquifers is considered analytically, specifically for annulus segment aquifers (ASAs), i.e., aquifers that (in plan) have the shape of an annulus segment. Based on the Ghijben-Herzberg and hillslope-storage Boussinesq equations, analytical solutions are derived for steady-state seawater intrusion for ASAs, with a focus on the freshwater-seawater interface and its corresponding watertable elevation. These analytical solutions, after comparing their predictions with experimental data, are employed to investigate the effects of aquifer geometry on seawater intrusion in island aquifers. Three different geometries of ASA are compared: convergent (smaller side facing the lagoon), rectangular and divergent (larger side facing the sea). The results show that the predictions from the analytical solutions are in well agreement with the experimental data for both recharge events. In addition, seawater intrusion is most extensive in divergent aquifers, and conversely for convergent aquifers. Accordingly, the watertable elevation is lowest in divergent aquifers and highest in convergent aquifers. Moreover, the effects of aquifer geometry on the freshwater-seawater interface and watertable elevation vary with aquifer width and distance to the no-flow boundary. Both a larger aquifer width and distance to the no-flow boundary weaken the effects of aquifer geometry and hence lead to a smaller deviation of seawater intrusion between the three geometries.

SYMBOLIC COMPUTATION OF BÄCKLUND TRANSFORMATION AND EXACT SOLUTIONS TO THE VARIANT BOUSSINESQ MODEL FOR WATER WAVES

1999 ◽  
Vol 10 (06) ◽  
pp. 983-987
Author(s):  
BO TIAN
Keyword(s):  
Exact Solutions ◽  
Symbolic Computation ◽  
Analytical Solutions ◽  
Water Waves ◽  
Bäcklund Transformation ◽  
Explicit Solutions ◽  
Backlund Transformation ◽  
Boussinesq Model ◽  
Exact Analytical Solutions ◽  
Symbolic Computations

In this paper, we show how computerized symbolic computations can be used to find an auto-Bäcklund transformation and a family of exact analytical solutions to the variant Boussinesq model for water waves. Sample explicit solutions are presented, which are respectively solitonic and rational.

Laser Induced Temperature Rise In Semiconductors : Analytical Solutions, Application to the Transient

1983 ◽  
Vol 13 ◽  
Author(s):  
Alain Maruani ◽  
Y.I. Nissim ◽  
F. Bonnouvrier ◽  
D. Paquet
Keyword(s):  
Experimental Data ◽  
Analytical Solutions ◽  
Temperature Rise ◽  
Laser Heating ◽  
Integral Transforms ◽  
Surface Absorption ◽  
Cw Laser ◽  
Analytical Results ◽  
Good Agreement

ABSTRACTIt is shown how the systematic use of the method of integral transforms greatly simplifies the calculation of the temperature rises in laser irradiated media. In general, this method leads ultimately either to analytical results or to very simple numerical integrals (e.g. no poles, exponential kernels). We focus here on the analytical results, and discuss some aspects of CW laser heating, for large surface absorption, including radial dependance, depth dependance and transient nonlinearities. The new results derived in this treatment are in good agreement with experimental data from other studies.

Numerical Simulations of Hydraulic Jumps in Water Sloshing and Water Impacting

2001 ◽  
Vol 124 (1) ◽  
pp. 215-226 ◽  
Author(s):  
Tzung-hang Lee ◽  
Zhengquan Zhou ◽  
Yusong Cao
Keyword(s):  
Experimental Data ◽  
Numerical Simulations ◽  
Shallow Water ◽  
Numerical Investigation ◽  
Analytical Solutions ◽  
Water Reservoir ◽  
Hydraulic Jumps ◽  
Dam Breaking ◽  
Water Problems ◽  
Good Agreement

A numerical investigation on Glimm’s method as applied to water sloshing and impacting is carried out. Emphasis is given to the handling and predicting hydraulic jumps. The effects of the spatial and temporal discretizations are examined. Three shallow water problems, 1) dam-breaking problem, 2) water sloshing in a rolling tank, and 3) impact of breaking of a water reservoir, are studied. It is shown numerically that Glimm’s method is stable and converged solutions can be obtained. The characteristics of the hydraulic jumps are well captured by the numerical calculations. The numerical results are in good agreement with either analytical solutions or experimental data.

scholarly journals Effects of aquifer geometry on seawater intrusion in annulus segment island aquifers

2021 ◽  
Vol 25 (12) ◽  
pp. 6591-6602
Author(s):  
Zhaoyang Luo ◽  
Jun Kong ◽  
Chengji Shen ◽  
Pei Xin ◽  
Chunhui Lu ◽  
...  
Keyword(s):  
Experimental Data ◽  
Sensitivity Analysis ◽  
Steady State ◽  
Seawater Intrusion ◽  
Analytical Solutions ◽  
Boussinesq Equations ◽  
Flow Boundary ◽  
Circle Center ◽  
Aquifer Geometry ◽  
Opposite Tendency

Abstract. Seawater intrusion in island aquifers was considered analytically, specifically for annulus segment aquifers (ASAs), i.e., aquifers that (in plan) have the shape of an annulus segment. Based on the Ghijben–Herzberg and hillslope-storage Boussinesq equations, analytical solutions were derived for steady-state seawater intrusion in ASAs, with a focus on the freshwater–seawater interface and its corresponding watertable elevation. Predictions of the analytical solutions compared well with experimental data, and so they were employed to investigate the effects of aquifer geometry on seawater intrusion in island aquifers. Three different ASA geometries were compared: convergent (smaller side is facing the lagoon, larger side is the internal no-flow boundary and flow converges towards the lagoon), rectangular and divergent (smaller side is the internal no-flow boundary, larger side is facing the sea and flow diverges towards the sea). Depending on the aquifer geometry, seawater intrusion was found to vary greatly, such that the assumption of a rectangular aquifer to model an ASA can lead to poor estimates of seawater intrusion. Other factors being equal, compared with rectangular aquifers, seawater intrusion is more extensive, and watertable elevation is lower in divergent aquifers, with the opposite tendency in convergent aquifers. Sensitivity analysis further indicated that the effects of aquifer geometry on seawater intrusion and watertable elevation vary with aquifer width and distance from the circle center to the inner arc (the lagoon boundary for convergent aquifers or the internal no-flow boundary for divergent aquifers). A larger aquifer width and distance from the circle center to the inner arc weaken the effects of aquifer geometry, and hence differences in predictions for the three geometries become less pronounced.

Nonlinear diffusive surface waves in porous media

1997 ◽  
Vol 347 ◽  
pp. 119-139 ◽  
Author(s):  
PHILIP L.-F. LIU ◽  
JIANGANG WEN
Keyword(s):  
Experimental Data ◽  
Porous Medium ◽  
Surface Wave ◽  
Water Waves ◽  
General Equation ◽  
Numerical Solutions ◽  
Boussinesq Equations ◽  
Surface Wave Propagation ◽  
Damping Rate ◽  
Order Of Magnitude

A fully nonlinear, diffusive, and weakly dispersive wave equation is derived for describing gravity surface wave propagation in a shallow porous medium. Darcy's flow is assumed in a homogeneous and isotropic porous medium. In deriving the general equation, the depth of the porous medium is assumed to be small in comparison with the horizontal length scale, i.e. O(μ2) =O(h0/L)2[Lt ]1. The order of magnitude of accuracy of the general equation is O(μ4). Simplified governing equations are also obtained for the situation where the magnitude of the free-surface fluctuations is also small, O(ε)=O(a/h0)[Lt ]1, and is of the same order of magnitude as O(μ2). The resulting equation is of O(μ4, ε2) and is equivalent to the Boussinesq equations for water waves. Because of the dissipative nature of the porous medium flow, the damping rate of the surface wave is of the same order magnitude as the wavenumber. The tide-induced groundwater fluctuations are investigated by using the newly derived equation. Perturbation solutions as well as numerical solutions are obtained. These solutions compare very well with experimental data. The interactions between a solitary wave and a rectangular porous breakwater are then examined by solving the Boussinesq equations and the newly derived equations together. Numerical solutions for transmitted waves for different porous breakwaters are obtained and compared with experimental data. Excellent agreement is observed.

Energy Levels and Electromagnetic Transition of 90-94mo Nuclei Using Ibm-1

2020 ◽  
pp. 149-152
Keyword(s):  
Experimental Data ◽  
Transition Probability ◽  
Energy Levels ◽  
Dynamical Symmetry ◽  
Interacting Boson Model ◽  
Excitation Energies ◽  
Electromagnetic Transition ◽  
Boson Model ◽  
Energy States ◽  
Good Agreement

The energy states for the J , b , ɤ bands and electromagnetic transitions B (E2) values for even – even molybdenum 90 – 94 Mo nuclei are calculated in the present work of "the interacting boson model (IBM-1)" . The parameters of the equation of IBM-1 Hamiltonian are determined which yield the best excellent suit the experimental energy states . The positive parity of energy states are obtained by using IBS1. for program for even 90 – 94 Mo isotopes with bosons number 5 , 4 and 5 respectively. The" reduced transition probability B(E2)" of these neuclei are calculated and compared with the experimental data . The ratio of the excitation energies of the 41+ to 21+ states ( R4/2) are also calculated . The calculated and experimental (R4/2) values showed that the 90 – 94 Mo nuclei have the vibrational dynamical symmetry U(5). Good agreement was found from comparison between the calculated energy states and electric quadruple probabilities B(E2) transition of the 90–94Mo isotopes with the experimental data .

On the Exact Soliton Solutions of Some Nonlinear PDE by Tan-Cot Method

2018 ◽  
Vol 5 (1) ◽  
pp. 31-36
Author(s):  
Md Monirul Islam ◽  
Muztuba Ahbab ◽  
Md Robiul Islam ◽  
Md Humayun Kabir
Keyword(s):  
Solitary Wave ◽  
Acoustic Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Rectangular Channel ◽  
Soliton Solutions ◽  
Boussinesq Equations ◽  
Travelling Wave ◽  
Ion Acoustic Waves ◽  
Analytical System

For many solitary wave applications, various approximate models have been proposed. Certainly, the most famous solitary wave equations are the K-dV, BBM and Boussinesq equations. The K-dV equation was originally derived to describe shallow water waves in a rectangular channel. Surprisingly, the equation also models ion-acoustic waves and magneto-hydrodynamic waves in plasmas, waves in elastic rods, equatorial planetary waves, acoustic waves on a crystal lattice, and more. If we describe all of the above situation, we must be needed a solution function of their governing equations. The Tan-cot method is applied to obtain exact travelling wave solutions to the generalized Korteweg-de Vries (gK-dV) equation and generalized Benjamin-Bona- Mahony (BBM) equation which are important equations to evaluate wide variety of physical applications. In this paper we described the soliton behavior of gK-dV and BBM equations by analytical system especially using Tan-cot method and shown in graphically. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 5(1), Dec 2018 P 31-36

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