Staggered Grids

The cornerstone of mimetic finite differentiation (FD) is that discrete gradients and divergences, in combination with a novel boundary flux operator satisfies an approximation to the Gauss–Divergence theorem. In this paper, we propose a spatially staggered second-order discretization of the acoustic wave equation that fully exploits all these mimetic operators on the implementation of free surface and absorbing boundary conditions. Explicit time integration is carried out by using the standard three-level central FD stencil. Applications of this new method to simple 2-D seismic scenarios are also presented and discussed.

A three-dimensional multidirectional nonlinear numerical wave tank (NWT) based on the Navier-Stokes equations and the Finite Volume Method (FVM) is developed by using the two-phase hydrodynamic flow solver naoe-FOAM-SJTU based on the open source toolbox OpenFOAM. The free surface is capturing with the Volume Of Fluids (VOF). The directional wave including Stokes wave, solitary wave and nonlinear wave are simulated and verified. The multi-directional waves are also simulated with particular wave spectral such as JONSWAP and wave directional spreading function. The obtained numerical results show the capability of the solver to generate different type of multidirectional nonlinear waves accurately. Meanwhile, it implies that the presented NWT can easily extend to model the wave-structures interactions, which will be great help to the offshore structures design.

A possible approach for modeling two-dimensional convection-diffusion problems in a cell-centered scheme with an unstructured triangular grid is the use of the Circumcenter, that is the center of the circumference that passes through the vertices of the triangular volume. This point is used to calculate all variables involved in the numerical simulation, and a Finite Volume Method was use to discretize the equations of an Incompressible Viscous Flow. This work analyzes classical problems of bidimensional flow, such as the inlet region of a Poiseuille flow, lid-driven cavity, backward-facing step and free convection with Boussinesq approximation. The application of the method has been shown to be a simple and flexible scheme and the results fit the analytical, experimental or numeric data presented in the literature.

A new analysis of the momentum interpolation method is presented in this paper. A modified method using quadratic interpolating polynomials for the calculation of the cell-face velocities is projected. The performance of the proposed method is examined and its application to lid-driven cavity problem is tested. The numerical results are compared with standard reported benchmark solutions for a different flow conditions. The numerical results show clearly the advantage of the new approach over the original momentum interpolation method, in terms of numerical accuracy, rate of convergence, and computational efficiency.

We consider the application of computer algebra for the derivation of the formula for the preservation of the cosymmetry property through discretization of partial differential equations. The finite difference approximations of differential operators for both regular and staggered grids are derived and applied to the planar filtration-convection problem.

We consider the application of computer algebra for the derivation of the formula for the preservation of the cosymmetry property through discretization of partial differential equations. The finite difference approximations of differential operators for both regular and staggered grids are derived and applied to the planar filtration-convection problem.

Mass exchange through gas-liquid interfaces, whose liquid side has a turbulent nature, are still difficult to quantify due to the unclosed set of turbulence equations, which are also nonlinear. This paper describes an efficient method to overcome this difficulty, by substituting the statistical variables of the original equations by statistical relationships furnished by the Random Square Waves (RSW) tool. Oscillatory records are simplified using random square waves (ideal and binary), which allow a theoretical statistical treatment of the signals. This tool was applied to the concentration boundary layer at the gas-liquid interface. Normalized mass fluxes and mean concentration profiles were obtained using Taylor-series-based solutions, which allow for consideration of transient situations through the successive calculation of the higher order coefficients (derivatives). Comparisons with experimental data available in open literature are presented as a first evaluation of the Taylor series, showing promising results. This method is a viable tool, and this study shows novel conclusions that reproduce general tendencies observed in one-dimensional mass transfer phenomena in boundary layers.

The cornerstone of mimetic finite differentiation (FD) is that discrete gradients and divergences, in combination with a novel boundary flux operator satisfies an approximation to the Gauss–Divergence theorem. In this paper, we propose a spatially staggered second-order discretization of the acoustic wave equation that fully exploits all these mimetic operators on the implementation of free surface and absorbing boundary conditions. Explicit time integration is carried out by using the standard three-level central FD stencil. Applications of this new method to simple 2-D seismic scenarios are also presented and discussed.

Convection-diffusion problems arise frequently in many areas of applied sciences and engineering. In this paper, we solve a convection-diffusion problem by central differencing scheme, upwinding differencing scheme (which are special cases of finite volume scheme) and finite difference scheme at various Peclet numbers. It is observed that when central differencing scheme is applied, the solution changes rapidly at high Peclet number because when velocity is large, the flow term becomes large, and the convection term dominates. Similarly, when velocity is low, the diffusion term dominates and the solution diverges, i.e., mathematically the system does not satisfy the criteria of consistency. On applying upwinding differencing scheme, we conclude that the criteria of consistency is satisfied because in this scheme the flow direction is also considered. To support our study, a test example is taken and comparison of the numerical solutions with the analytical solutions is done.

A high accurate finite volume method based on the use of Moving Least Squares (MLS) approximants is presented for the resolution of the incompressible Navier-Stokes equations on unstructured grids. Moreover, in order to eliminate the decoupling between pressure and velocity, we present a new Momentum Interpolation Method that allows interpolations better than linear on any kind of mesh. The accuracy of the new method is evaluated by a steady and unsteady test cases.

The computation of multiphase flows presenting high density ratios, where the fluids involved are considered immiscible, are of great importance for fundamental physics and industrial applications; such as the study of liquid-gas interfaces, wave motion, simulation of bubbly flows and atomization, injection in diesel engines, chemical processes and others. This work presents and analyzes a collocated and staggered finite-volume mesh discretizations suitable for three-dimensional unstructured meshes, which are able to simulate immiscible multiphase flows with high density ratios. More over, these mesh schemes numerically conserve mass and momentum while minimize errors in the conservation of kinetic energy.

Flow analysis of backward-facing step is claimed to be a necessity when it comes to Computational Fluid Dynamics solver validation. The turbulence development with both separation and reattachment passing through the step has become the practical challenge for solver developers ever since the numerical computation revolution started. In-line with the trend, this work is predestined to further validate the use of Splitting velocity-pressure coupling method with immersed boundary extension for unsteady Navier-Stokes flow solver. The comparison is launched with steady numerical results via established software for commonly used benchmark backward-facing step construction. Flow parameters in both solvers are set equivalent to Reynolds number of 1000. The assessment is carried out when the flow has reached steady flow condition. The streamwise velocity profiles are well-matched where the maximum error is within 4%. The reattachment distance measured from the developed solver is also in good agreement with the reference results with only 1.84% difference recorded. The comparison proves that the solver developed in this work could become a very handy alternative especially when we look at the solver simplicity and the number of nodes it consumes to obtain comparable results.

A high accurate finite volume method based on the use of Moving Least Squares (MLS) approximants is presented for the resolution of the incompressible Navier-Stokes equations on unstructured grids. Moreover, in order to eliminate the decoupling between pressure and velocity, we present a new Momentum Interpolation Method that allows interpolations better than linear on any kind of mesh. The accuracy of the new method is evaluated by a steady and unsteady test cases.

In this paper, a two-dimensional Numerical Wave Tank (NWT) is proposed to calculate the static pressure variation along the lower wall of an experimental wave-flume. The experimental setup was a 4.72m long wave flume with a flap-type wave-maker. The experiments were carried out at various water heights of 100mm, 80mm, and 60mm, with a motor speed of 60 rpm. The numerical simulations were completed using ANSYS™ Fluent, with two sets solutions: 1) the unsteady, three-dimensional Reynolds Averaged Navier-Stokes (URANS) equations coupled with a k-e turbulence model; 2) unsteady 3-D Euler equations. In both computations, the volume of fluid (VOF) method was used to capture the free surface and a grid independence study was completed. The unsteady Euler simulations showed the best agreement to the experimental results. Several cases were run to complete validation and verification of the numerical model, and the CFD results are in good agreement with the experiment. Thus, for small two-di...

Энергосберегающие технологии и оборудование Приведені результати експериментальних та числових досліджень теплообміну шахових пакетів плоскоовальних труб. Вивчено вплив режимних і геометричних факторів на інтенсивність теплообміну пакетів плоскоовальних труб. Встановлено, що при фіксованій геометрії труб (d 2 /d 1 =const) варіювання крокових характеристик пакетів в межах S 1 /d 1 =2...3,5 та S 2 /d 1 =2,4...5,3 змінює інтенсивність теплообміну на (8...12) %, а варіювання d 2 /d 1 від 2 до 5,0 при фіксованих крокових характеристиках на (10...25) % Ключові слова: пакети труб, профіль, плоскоовальна, потік, інтенсивність теплообміну, числові, обтікання Приведены результаты экспериментальных и численных исследований теплообмена шахматных пакетов плоскоовальных труб. Изучено влияние режимных и геометрических факторов на интенсивность теплообмена пакетов плоскоовальных труб. Установлено, что при фиксированной геометрии труб (d 2 /d 1 =const) варьирование шаговых характеристик пакетов в пределах S 1 /d 1 =2...3,5 и S 2 /d 1 =2,4...5,3 изменяет интенсивность теплообмена на (8...12) %, а варьирование d 2 /d 1 от 2 до 5,0 при фиксированных шаговых характеристиках на (10...25

In this paper, a two-dimensional Numerical Wave Tank (NWT) is proposed to calculate the static pressure variation along the lower wall of an experimental wave-flume. The experimental setup was a 4.72m long wave flume with a flap-type wave-maker. The experiments were carried out at various water heights of 100mm, 80mm, and 60mm, with a motor speed of 60 rpm. The numerical simulations were completed using ANSYS™ Fluent, with two sets solutions: 1) the unsteady, three-dimensional Reynolds Averaged Navier-Stokes (URANS) equations coupled with a k-e turbulence model; 2) unsteady 3-D Euler equations. In both computations, the volume of fluid (VOF) method was used to capture the free surface and a grid independence study was completed. The unsteady Euler simulations showed the best agreement to the experimental results. Several cases were run to complete validation and verification of the numerical model, and the CFD results are in good agreement with the experiment. Thus, for small two-di...

A high accurate finite volume method based on the use of Moving Least Squares (MLS) approximants is presented for the resolution of the incompressible Navier-Stokes equations on unstructured grids. Moreover, in order to eliminate the decoupling between pressure and velocity, we present a new Momentum Interpolation Method that allows interpolations better than linear on any kind of mesh. The accuracy of the new method is evaluated by a steady and unsteady test cases.

Convection-diffusion problems arise frequently in many areas of applied sciences and engineering. In this paper, we solve a convection-diffusion problem by central differencing scheme, upwinding differencing scheme (which are special cases of finite volume scheme) and finite difference scheme at various Peclet numbers. It is observed that when central differencing scheme is applied, the solution changes rapidly at high Peclet number because when velocity is large, the flow term becomes large, and the convection term dominates. Similarly, when velocity is low, the diffusion term dominates and the solution diverges, i.e., mathematically the system does not satisfy the criteria of consistency. On applying upwinding differencing scheme, we conclude that the criteria of consistency is satisfied because in this scheme the flow direction is also considered. To support our study, a test example is taken and comparison of the numerical solutions with the analytical solutions is done.

This research aimed to investigate: (i) whether there was a statistically significant difference of the ability in writing descriptive texts between the students who were taught through Gallery Walk technique and those who were treated with the conventional method, and (ii) how the students’ responses concerning the implementation of Gallery Walk technique. The research was conducted to 30 students in class X MIPA 1 and 30 students in class X MIPA 2. Pre-Test Post-Test Control Group design was used in this research. The data were obtained through the writing test and questionnaires. The result showed that there was a statistically significant difference of the students’ writing ability between students who were taught through gallery walk technique and those who were treated with the conventional method. The students’ responses of Gallery Walk technique in teaching writing were positive. This suggests that Gallery Walk technique facilitates the students to improve their writing abil...

Flows of variable viscosity fluids have many industrial applications in fluid mechanics and in engineering such as pump flows for highly viscous fluids. Carrying out a literature survey, it was found that in most cases the fluid viscosity is mainly temperature dependent. Numerical investigation of such flows involves the solution of the Navier-Stokes equations with an extra difficulty arising from the fact that the viscosity is not constant over the flow field. This article presents an analytical solution to the Navier-Stokes equations for the case of laminar flows in rotating systems with variable viscosity fluids. The equations are written in a cylindrical relative frame of reference rotating with a constant angular velocity. In the following, appropriate reference quantities are chosen to provide the non-dimensional form of the partial differential equations. The proposed solution that satisfies the continuity, the momentum and the energy equation, is expressed in terms of the Bessel function of the first kind and of exponential functions. Carrying out algebraic manipulations, it is proven that the proposed solution satisfies all the governing equations. Plots of the velocity, pressure and temperature distributions show the influence of the radius and of the axial coordinate to the flow field.

Flow analysis of backward-facing step is claimed to be a necessity when it comes to Computational Fluid Dynamics solver validation. The turbulence development with both separation and reattachment passing through the step has become the practical challenge for solver developers ever since the numerical computation revolution started. In-line with the trend, this work is predestined to further validate the use of Splitting velocity-pressure coupling method with immersed boundary extension for unsteady Navier-Stokes flow solver. The comparison is launched with steady numerical results via established software for commonly used benchmark backward-facing step construction. Flow parameters in both solvers are set equivalent to Reynolds number of 1000. The assessment is carried out when the flow has reached steady flow condition. The streamwise velocity profiles are well-matched where the maximum error is within 4%. The reattachment distance measured from the developed solver is also in good agreement with the reference results with only 1.84% difference recorded. The comparison proves that the solver developed in this work could become a very handy alternative especially when we look at the solver simplicity and the number of nodes it consumes to obtain comparable results.

In disasters, whether natural or man-made, establishing a wireless network to recover the damaged or destroyed cellular network infrastructure is very important to save lives. Network throughput and power consumption are critical factors when designing such a wireless network. It is essential to ensure that the network can connect all people with the optimum ability to handle information traffic while utilizing less energy. The conventional clustering (CC) technology with D2D communication has enhanced the efficiency and power consumption of a wireless network. In disaster circumstances, however, using CC continues to be a challenge in ensuring that all user devices (UEs) can join the cluster. In this respect, this paper presents an approach termed Cluster Formation and Cluster Head Selection (CFACHS) to ensure that all UEs in the area affected have joined a cluster. CFACHS also targets enhancing the wireless network performance in terms of its throughput and power consumption. CFACHS partitions each cluster into two groups named Main Cluster (MC) with its Main Cluster Head (MCH) and a Sub-Cluster (SC) with its Sub-Cluster Head (SCH). In order to route the information, an algorithm named MCHs multi-hop routing path has been developed and implemented. Extensive simulation experiments were conducted using MATLAB to compare the performance of CFACHS with CFACHS without-SC and CC in terms of the network’s capacity and power consumption. The results reveal that CFACHS was advantageous in minimizing network power consumption, increasing power efficiency by 27.97% and 25.54% sequentially. Also, CFACHS enhanced network capacity by 7.8125% and 11.875%, respectively.

The finite-difference discretizations for the planar problem of natural convection of incompressible fluid in a porous medium which preserve the cosymmetry property and discrete symmetries are presented. The equations in stream function and temperature are computed using staggered and non-staggered schemes in uniform and nonuniform rectangular grids.

This researchaimed to improve the Student’s ability in writing descriptive text through Language Experience Approach (LEA). This research was designed by using Classroom Action Research (CAR) which was done in two cycles. Incollecting the data, observation paper and test were usedas the research instruments. Based on the data analysis,showed that the result of the observation paper of researcher’s activities in meeting I was 68,75 % while meeting II was 81,25% and cycle II in the first meeting was 87,5% while in the second meeting was 93,75%. While the result of students’ observation paper of students activities in cycle I in meeting I was 78,9% while in second meeting was 79,1% and cycle II in the meeting I was 83,2% while in the meeting II was 87,6%. The students’ test result in cycle Iwas 59,5%while in cycle II was 75,46%.Based on the research findings, in implementing Language Experience Approach (LEA) in teaching writing more interesting, effective and efissien in learning Engl...

In this paper, we consider some elastodynamics problems in 2D unbounded domains, with soft scattering conditions at the boundary, and their solution by the Boundary Element Method (BEM). The displacement identifying the elastic wave propagation is represented by both direct and indirect boundary integral formulations, which depend on the traction or on the jump of the traction at the boundary of the propagation domain, respectively. We study the characteristic singularities of the single layer and the double layer integral operators, which are involved in the considered energetic weak forms. Some algorithmic considerations about the parallel implementation of the energetic BEM and the quadrature techniques applied to overcome the issues due to the weak and the strong singularities of the integration kernels are proposed. Numerical simulations follow, showing a comparison between the external displacements obtained by the indirect and the direct formulations.

The cornerstone of mimetic finite differentiation (FD) is that discrete gradients and divergences, in combination with a novel boundary flux operator satisfies an approximation to the Gauss–Divergence theorem. In this paper, we propose a spatially staggered second-order discretization of the acoustic wave equation that fully exploits all these mimetic operators on the implementation of free surface and absorbing boundary conditions. Explicit time integration is carried out by using the standard three-level central FD stencil. Applications of this new method to simple 2-D seismic scenarios are also presented and discussed.

The computation of multiphase flows presenting high density ratios, where the fluids involved are considered immiscible, are of great importance for fundamental physics and industrial applications; such as the study of liquid-gas interfaces, wave motion, simulation of bubbly flows and atomization, injection in diesel engines, chemical processes and others. This work presents and analyzes a collocated and staggered finite-volume mesh discretizations suitable for three-dimensional unstructured meshes, which are able to simulate immiscible multiphase flows with high density ratios. More over, these mesh schemes numerically conserve mass and momentum while minimize errors in the conservation of kinetic energy.

In  this paper, modified volume of fluid method
based on flux correct transport (FCT) and Youngs’ VOF
(YV) method using new advection method are presented.
These methods are from simple line interface construction
and piecewise linear interface construction methods. The
developed model in this study is based on the Navier–Stokes
equations (NSE) which describe the laminar flow of an
incompressible viscous fluid. To model turbulence, the coupled Navier–Stokes and standard k−ε model as the Reynolds
average NSE are used. These equations are discretized using
finite difference method on the Cartesian staggered grids and
solved using simplified marker and cell method. The free surface is displaced using the volume of fluid method based on
FCT and Youngs’ algorithms. In these methods, for staggered
grids, fluxes to neighboring cells are estimated based on cell
face velocities. It means that fluid particles in the cell have
the same velocity of the cell faces. However, in practice,
these particles have a variable velocity between velocities
of two adjacent cell faces. In the modified models of this
research, the velocity in mass center of fluid cell is estimated
and used to calculate fluxes from cell faces. The performance
of the modified scheme has been evaluated using a number of
alternative schemes taking into account translation, rotation;
shear test and dam break on dry bed. Finally, Airy waves
are generated by these models. The results showed that the
modified models are more accurate than the original ones.

A two-dimensional (2D) numerical model is developed for the wave simulation and propagation in a wave flume. The fluid flow is assumed to be viscous and incompressible, and the Navier-Stokes and continuity equations are used as the governing equations. The standard k-ε model is used to model the turbulent flow. The Navier-Stokes equations are discretized using the staggered grid finite difference method and solved by the simplified marker and cell (SMAC) method. Waves are generated and propagated using a piston type wave maker. An open boundary condition is used at the end of the numerical flume. Some standard tests, such as the lid-driven cavity, the constant unidirectional velocity field, the shearing flow, and the dam-break on the dry bed, are performed to valid the model. To demonstrate the capability and accuracy of the present method, the results of generated waves are compared with available wave theories. Finally, the clustering technique (CT) is used for the mesh generation, and the best condition is suggested.

This study aimed to adjust the turbulence models to the real behavior of the numerical wave flume (NWF) and the future research that will be carried out on it, according to the turbulence model that best adjusts to each particular case study. The k-ε, k-ω and large-eddy simulation (LES) models, using the volume of fluid (VOF) method, were analyzed and compared respectively. The wavemaker theory was followed to faithfully reproduce the waves, which were measured in an experimental wave flume (EWF) and compared with the theory to validate each turbulence model. Besides, reflection was measured with the Mansard and Funke method, which has shown promising results when studying one of the most critical turbulent behaviors in the wave flume, called the breaking of the waves. The free surface displacement obtained with each turbulence model was compared with the recorded signals located at three points of the experimental wave flume, in the time domain of each run, respectively. Finally, t...

This article concerns a solitary wave propagating over a rising bed assuming unsteady, incompressible viscous flow with free surface. The method solves the two dimensional Naiver-Stokes equations for conservation of momentum, continuity equation, and full nonlinear kinematic free-surface equation for Newtonian fluids, as described by the governing equations in a vertical plan. A mapping was developed to trace the deformed free surface by transferring the governing equations from the physical domain to a computational domain. Finally a numerical scheme is developed using finite element modelling technique to predict the flow over a rising bed with using the Arbitrary Lagrangian Eulerian algorithm. The results compare well with other research and results showsare generally favorable.

In this study, the developed procedure of advection in volume of fluid (VOF) method is presented for free surface modeling. The fluid is assumed to be incompressible and viscous and therefore, Navier-Stokes and continuity are considered as governing equations. Applying Youngs’ algorithm in staggered grids, it is assumed that fluid particles in the cell have the same velocity of the cell faces. Therefore, fluxes to neighboring cells are estimated based on cell face velocities. However, these particles can show different velocities between two adjacent cell faces. In developed model, the velocity in mass center of fluid cell is evaluated to calculate fluxes from cell faces. The performance of the model is evaluated using some alternative schemes such as translation, rotation, shear test, and dam break test. These tests showed that the developed procedure improves the results when using coarse grids. Therefore, the Modified Youngs-VOF (MYV) method is suggested as a new VOF algorithm wh...

A two-dimensional (2D) numerical model is developed for the wave simulation and propagation in a wave flume. The fluid flow is assumed to be viscous and incompressible, and the Navier-Stokes and continuity equations are used as the governing equations. The standard k-ε model is used to model the turbulent flow. The Navier-Stokes equations are discretized using the staggered grid finite difference method and solved by the simplified marker and cell (SMAC) method. Waves are generated and propagated using a piston type wave maker. An open boundary condition is used at the end of the numerical flume. Some standard tests, such as the lid-driven cavity, the constant unidirectional velocity field, the shearing flow, and the dam-break on the dry bed, are performed to valid the model. To demonstrate the capability and accuracy of the present method, the results of generated waves are compared with available wave theories. Finally, the clustering technique (CT) is used for the mesh generation, and the best condition is suggested.

This paper describes the capability of a new model, called IH-3VOF to simulate wave-structure interaction problems using a three-dimensional approach. The model is able to deal with physical processes associated with wave interaction with porous structures. The model considers the VARANS equations, a volume-averaged version of the traditional RANS (Reynolds Averaged Navier-Stokes) equations. Turbulence is modeled using a k-ε approach, not only at the clear fluid region (outside the porous media) but also inside the porous media. The model has been validated using laboratory data of free surface time evolution in a fish tank containing a porous dam. Numerical simulations were calibrated by adjusting the porous flow empirical coefficients for two granular material characteristics. Sensitivity analysis of porous parameters has also been performed. The model is proven to reproduce with a high degree of agreement the free surface evolution during the seeping process. Simulations of a threedimensional porous dam breaking problem has been studied, showing the excellent performance of the model in reproducing fluid patterns around a porous structure. The model is powerful tool to examine the near-field flow characteristics around porous structures in three dimensional flow conditions.

This paper describes the capability of a new model, called IH-3VOF to simulate wave-structure interaction problems using a three-dimensional approach. The model is able to deal with physical processes associated with wave interaction with porous structures. The model considers the VARANS equations, a volume-averaged version of the traditional RANS (Reynolds Averaged Navier-Stokes) equations. Turbulence is modeled using a k-ε approach, not only at the clear fluid region (outside the porous media) but also inside the porous media. The model has been validated using laboratory data of free surface time evolution in a fish tank containing a porous dam. Numerical simulations were calibrated by adjusting the porous flow empirical coefficients for two granular material characteristics. Sensitivity analysis of porous parameters has also been performed. The model is proven to reproduce with a high degree of agreement the free surface evolution during the seeping process. Simulations of a threedimensional porous dam breaking problem has been studied, showing the excellent performance of the model in reproducing fluid patterns around a porous structure. The model is powerful tool to examine the near-field flow characteristics around porous structures in three dimensional flow conditions.

This paper presents two different numerical methodologies to generate regular gravity waves in a wave tank. We performed numerical simulations of wave generation through the FLUENT ® package, using the Volume of Fluid (VOF) multiphase model to reproduce the wave propagation in the tank. Thus it was possible to analyze two methods for generating regular waves that could be used in future work, especially in the study of devices of energy conversion from ocean waves into electrical energy.

This Brief Report is devoted to the study of the solitary surface wave rotating in the azimuthal direction, arising during water drainage from a cylindrical reservoir, when shallow flow conditions are reached. The linear dependence between the wave speed and its amplitude is shown to be similar to that expected from the classical Korteweg-de Vries equation.

The wave generation due to the presence of a body moving at steady forward speed beneath a free surface has been the subject of extensive research work in marine hydrodynamics. In this study, the free surface effect on the flow around shallowly submerged hydrofoil is numerically computed. Finite Volume Method (FVM) based on Navier-Stokes equations is used for this purpose. The standard NACA 0012 hydrofoil section is used for ease of comparison with available experimental data. The k-ε turbulence model has been ...

Writing is a good way on doing communication. In language learning process, writing is one of the important skill which should be learned by the learners. The using an appropriate technique will be very helpful for the teacher to engage students attention in language learning and also it will improve students knowledge in expressing their idea creatively. KWL (Know, Want, and Learn) is one of the good technique to be applied espeacially in writing Hortatory Exposition Text. The objectives of this research were to find out whether there is an influence of using KWL technique towards students' achievement in writing hortatory exposition and the average score of students' ability in writing hortatory exposition text. In this research, the researcher used experimental method and the sample of this research are 56 students of 2 classes. The samples were taken by using clustering random sampling technique and in collecting the data, the researcher used writing test for the experimental and control groups. T-test formula is used to analyzed the data. The researcher found that the average score of students in experimental group was 71.35 and the average score of students in control group was 63.86. It means that there were difference average score about 7.49 point between those classes. To sum up, the use of KWL technique in teaching writing of hortatory exposition text provides the positive results to increase students' writing achievement.

This study investigated the generation and propagation of water waves in a numerical viscous wave flume. The numerical scheme developed by Huang and collaborators for solving the unsteady two-dimensional Navier-Stokes equations for wavemaking problems was employed to generate different incident waves, including small-and finite-amplitude waves and solitary waves. The accuracy of the numerical results for the wave and velocity profiles was verified by comparison with the analytical solutions. The wave propagation in a numerical wave flume was also investigated. For periodic gravity waves on finite water depth, the results showed that waves with larger Ursell numbers are more stable than those with smaller Ursell numbers. The propagation of solitary waves in the channel is stable. For stable waves, the wave height attenuation caused by the energy dissipation in the wave motion was shown to be consistent with the theoretical results.

The numerical simulation of hydrodynamic wave loading on different types of offshore structures is important to predict forces on and water motion around these structures. This paper presents a numerical study of the effects of two-phase flow on an offshore structure subject to breaking waves.

The present paper models the fundamental problems of fluid flow
using a discretely improved finite difference method on a staggered
computational grid. The developed finite difference formulation is applied to
well-established benchmark problems, namely, the lid-driven cavity flow, the
developing laminar flow in a straight rectangular duct and the backward-facing
step flow. Excellent agreements have been found for all cases. Also, this
approach has successfully handled the pressure of the flow that has been long
considered as one of the main problems in using the finite difference method.

A digital wave tank (DWT) simulation technique has been developed by authors to investigate the interactions of fully nonlinear waves with 3D marine structures. A finite-difference/volume method and a modified marker-and-cell (MAC) algorithm have been used, which are based on the Navier-Stokes (NS) and continuity equations. The fully nonlinear kinematic free-surface condition is implemented by the marker-density function (MDF) technique or the Level-Set (LS) technique developed for one or two fluid layers. In this paper, some applications for various engineering problems with free-surface are introduced and discussed. It includes numerical simulation of marine environments by simulation equipments, fully nonlinear wave motions around offshore structures, nonlinear ship waves, ship motions in waves and marine flow simulation with free-surface. From the presented simulations, it seems that the developed DWT simulation technique can handle various engineering problems with free-surface...

It is now becoming important to develop our capabilities to simulate coastal ocean flows involved with distinct physical phenomena occurring at a vast range of spatial and temporal scales. This paper presents a hybrid modeling system for such simulation. The system consists of a fully three dimensional (3D) fluid dynamics model and a geophysical fluid dynamics model, which couple with each other in two-way and march in time simultaneously. Particularly, in the hybrid system, the solver for incompressible flow on overset meshes (SIFOM) resolves fully 3D small-scale local flow phenomena, while the unstructured grid finite volume coastal ocean model (FVCOM) captures largescale background flows. The integration of the two models are realized via domain decomposition implemented with an overset grid method. Numerical experiments on performance of the system in resolving flow patterns and solution convergence rate show that the SIFOM-FVCOM system works as intended, and its solutions compare reasonably with data obtained with measurements and other computational approaches. Its unparalleled capabilities to predict multiphysics and multiscale phenomena with highfidelity are demonstrated by three typical applications that are beyond the reach of other currently existing models. It is anticipated that the SIFOM-FVCOM system will serve as a new platform to study many emerging coastal ocean problems. 549 in these examples play pivotal roles in our daily life, environments, resources for energy, etc. For example, the oil spill in the Gulf of Mexico has become the largest environmental disaster in US history, and it will have a profound impact on ecological as well as economic systems . Here and hereafter, the scales refer to observation scales such as characteristic length and time, or, process scales such as those in data analysis.

This research deals with the validation of fluid dynamic models, used for simulating shoaling and breaking solitary waves on slopes, based on experiments performed at the Ecole Supérieure d'Ingénieurs de Marseille's (ESIM) laboratory. A separate paper, also presented at this conference, reports on experiments. In a first part of this work, a fully nonlinear potential flow model based on a Boundary Element Method (BEM) developed at the University of Rhode Island (URI), is used to generate and propagate solitary waves over a slope, up to overturning, in a set-up closely reproducing the laboratory tank geometry and wavemaker system. The BEM model uses a boundary integral equation method for the solution of governing potential flow equations and an explicit Lagrangian time stepping for time integration. In a second part, several Navier-Stokes (NS) models, developed respectively at TREFLE-ENSCPB, IMFT, IRPHE and LSEET are initialized based on the BEM solution and used for modeling breaking solitary waves in a finely discretized region encompassing the top of the slope and the surfzone. The NS models are based on the Volume of Fluid Method (VOF). This paper mostly deals with the first part, which includes calibration and comparison of BEM results with experiments, for the generation of solitary waves in the physical wave tank. Thus, parameters of the physical wave tank were numerically matched, including tank geometry and motion of the wavemaker paddle corresponding to the generation of solitary waves. Use and coupling of the BEM and VOF models for the simulation of solitary wave breaking is discussed in the paper.

This paper is devoted to the numerical simulation of wave breaking. It presents the results of a numerical workshop that was held during the conference LOMA04. The objective is to compare several mathematical models (compressible or incompressible) and associated numerical methods to compute the flow field during a wave breaking over a reef. The methods will also be compared with experiments.

This numerical study has been performed
to predict the flow patterns and characteristics within
permeable pavement. Throughout the design and
planning period for future construction are
increasingly integrating computational fluid
dynamics (CFD) into the process. As a result,
engineers are interested in the reliability of CFD
software to provide accurate flow data for a wide
range of structures. CFD results have generally been
in agreement with physical model experimental data.
A commercially known software, FLOW-3D, is
applied to numerically solve the Navier-stokes
equations for solution domains which are separated
into three regions with overlapping boundaries to
efficiently accommodate the grid resolutions, namely
the honeycomb shaped modular, gravel and
combined honeycomb shaped modular with gravel
fill. The filtration of the fluid within the interstices of
a permeable pavement, is evaluated by integrating the
Reynolds Averaged Navier-Stokes equations (RANS)
inside the voids rather than making use of the
widespread “porous media” approach, such for
example in Hsu et. al. (2002) and Lara et al (2006).