Search results for: nonlocal boundary condition

Authors: M. Abdelmalek

Abstract:

In this work, we study the hypersurfaces of constant weighted mean curvature embedded in weighted manifolds. We give a condition about these hypersurfaces to be minimal. This condition is given by the ellipticity of the weighted Newton transformations. We especially prove that two compact hypersurfaces of constant weighted mean curvature embedded in space forms and with the intersection in at least a point of the boundary must be transverse. The method is based on the calculus of the matrix of the second fundamental form in a boundary point and then the matrix associated with the Newton transformations. By equality, we find the weighted elementary symmetric function on the boundary of the hypersurface. We give in the end some examples and applications. Especially in Euclidean space, we use the above result to prove the Alexandrov spherical caps conjecture for the weighted case.

Keywords: weighted mean curvature, weighted manifolds, ellipticity, Newton transformations

Procedia PDF Downloads 93

Authors: Asghar Ebrahimi, Elyas Lakzian

Abstract:

For the analysis of flow inside micro geometries, classical CFD methods can not accurately predict the behavior of flow. Alternatively, the gas flow through micro geometries can be investigated precisely using the direct simulation Monte Carlo (DSMC) method. In the present paper, a pressure boundary condition is utilized to simulate a gaseous flow inside a micro channel using the DSMC method. Accuracy of simulation is guaranteed by choosing proper cell dimension and number of particle per cell analysis. Also, results of simulation are compared with the results of reliable references. Good agreement with results certifies the correctness of new boundary condition implemented on the micro channel.

Keywords: pressure boundary condition, DSMC, micro channel, cell dimension, particle per cell

Procedia PDF Downloads 478

Authors: Omar S. Qaftan, T. T. Sabbagh

Abstract:

This paper studies the free-field response by adopting a flexible membrane container as soil boundary for experimental shaking table tests. The influence of the soil container boundary on the soil behaviour and the dynamic soil properties under seismic effect were examined. A flexible container with 1/50 scale factor was adopted in the experimental tests, including construction, instrumentation, and determination of the results of dynamic tests on a shaking table. Horizontal face displacements and accelerations were analysed to determine the influence of the container boundary on the performance of the soil. The outputs results show that the flexible boundary container allows more displacement and larger accelerations. The soil in a rigid wall container cannot deform as similar as the soil in the real field does. Therefore, the response of flexible container tested is believed to be more reliable for soil boundary than that in the rigid container.

Keywords: soil, seismic, earthquake, interaction

Procedia PDF Downloads 298

Authors: M. Eskandarighadi, C. R. McGann

Abstract:

It is observed from past experiences of earthquakes that local site conditions can significantly affect the strong ground motion characteristics experience at the site. One-dimensional seismic site response analysis is the most common approach for investigating site response. This approach assumes that soil is homogeneous and infinitely extended in the horizontal direction. Therefore, tying side boundaries together is one way to model this behavior, as the wave passage is assumed to be only vertical. However, 1D analysis cannot capture the 2D nature of wave propagation, soil heterogeneity, and 2D soil profile with features such as inclined layer boundaries. In contrast, 2D seismic site response modeling can consider all of the mentioned factors to better understand local site effects on strong ground motions. 2D wave propagation and considering that the soil profile on the two sides of the model may not be identical clarifies the importance of a boundary condition on each side that can minimize the unwanted reflections from the edges of the model and input appropriate loading conditions. Ideally, the model size should be sufficiently large to minimize the wave reflection, however, due to computational limitations, increasing the model size is impractical in some cases. Another approach is to employ free-field boundary conditions that take into account the free-field motion that would exist far from the model domain and apply this to the sides of the model. This research focuses on implementing free-field boundary conditions in OpenSees for 2D site response analysisComparisons are made between 1D models and 2D models with various boundary conditions, and details and limitations of the developed free-field boundary modeling approach are discussed.

Keywords: boundary condition, free-field, opensees, site response analysis, wave propagation

Procedia PDF Downloads 161

Authors: Dhaladhuli Pranavi, Amirtham Rajagopal

Abstract:

There are various failure modes in ceramic matrix composites; notable ones are fiber breakage, matrix cracking and fiber matrix debonding. Crack nucleation and propagation in microstructure of such composites requires an understanding of interaction of crack with the multiple inclusion heterogeneous system and interfaces. In order to assess structural integrity, the material parameters especially of the interface that governs the crack growth should be determined. In the present work, a nonlocal phase field approach is proposed to model the crack interface interaction in such composites. Nonlocal approaches help in understanding the complex mechanisms of delamination growth and mitigation and operates at a material length scale. The performance of the proposed formulation is illustrated through representative numerical examples. The model proposed is implemented in the framework of the finite element method. Several parametric studies on interface crack interaction are conducted. The proposed model is easy and simple to implement and works very well in modeling fracture in composite systems.

Keywords: composite, interface, nonlocal, phase field

Procedia PDF Downloads 142

Authors: Mohammad Reza Shahnazari, Reza Kazemi, Ali Saberi

Abstract:

Most of the engineering problems are in nonlinear forms. Nonlinear boundary layer problems defined in infinite intervals contain specific complexities, especially in boundary layer condition conformance. As an example of these nonlinear complex problems, the well-known Blasius equation can be mentioned, which itself is one of the classic boundary layer problems. No analytical solution has been proposed yet for the Blasius equation due to its complexity. In this paper, an analytical method, namely the Kourosh method, based on the singularity perturbation method and the Liao homotopy analysis is utilized to solve the Blasius problem. In this method, an inner solution is developed in the [0,1] interval to expedite the solution convergence. The magnitude of the f ˝(0), as an essential quantity for determining the physical parameters, is directly calculated from the solution of the boundary condition problem. The advantages of this solution are that it does not need any numerical solution, it has a closed form and that its validation is shown in the entire [0,∞] interval. Furthermore, all of the desirable parameters could be extracted through a series of simple analytical operations from the final solution. This solution also satisfies the continuity conditions, which is one of the main contributions of this paper in comparison with most of the other proposed analytical solutions available in the literature. Comparison with numerical solutions reveals that the proposed method is highly accurate and convenient for application.

Keywords: Blasius equation, boundary layer, Kourosh method, analytical solution

Procedia PDF Downloads 394

Authors: Ch. Ramreddy, P. Naveen, D. Srinivasacharya

Abstract:

The objective of the present study is to investigate the effect of nonlinear temperature and concentration on the mixed convective flow of micropolar fluid over an inclined flat plate in a non-Darcy porous medium in the presence of convective boundary condition. In order to analyze all the essential features, the transformed nonlinear conservation equations are worked out numerically by spectral method. By insisting the comparison between vertical, horizontal and inclined plates, the physical quantities of the flow and its characteristics are exhibited graphically and quantitatively with various parameters. An increase in the coupling number and inclination of angle tend to decrease the skin friction, mass transfer rate and the reverse change is there in wall couple stress and heat transfer rate. The nominal effect on the wall couple stress and skin friction is encountered whereas the significant effect on the local heat and mass transfer rates are found for high enough values of Biot number.

Keywords: convective boundary condition, micropolar fluid, non-darcy porous medium, non-linear convection, spectral method

Procedia PDF Downloads 279

Authors: Te Wen Tu, Sen Yung Lee

Abstract:

An alternative approach is proposed to develop the analytic solution for one dimensional heat conduction with one mixed type boundary condition and general time-dependent heat transfer coefficient. In this study, the physic meaning of the solution procedure is revealed. It is shown that the shifting function takes the physic meaning of the reciprocal of Biot function in the initial time. Numerical results show the accuracy of this study. Comparing with those given in the existing literature, the difference is less than 0.3%.

Keywords: analytic solution, heat transfer coefficient, shifting function method, time-dependent boundary condition

Procedia PDF Downloads 433

Authors: Dongxu Chen, Yipeng Li

Abstract:

This paper presents an information geometry NonlocalMeans(NLM) algorithm for Poisson denoising. NLM estimates a noise-free pixel as a weighted average of image pixels, where each pixel is weighted according to the similarity between image patches in Euclidean space. In this work, every pixel is a Poisson distribution locally estimated by Maximum Likelihood (ML), all distributions consist of a statistical manifold. A NLM denoising algorithm is conducted on the statistical manifold where Fisher information matrix can be used for computing distribution geodesics referenced as the similarity between patches. This approach was demonstrated to be competitive with related state-of-the-art methods.

Keywords: image denoising, Poisson noise, information geometry, nonlocal-means

Procedia PDF Downloads 285

Authors: T. A. Biala

Abstract:

This paper deals with the numerical integration of the general second order multipoint boundary value problems. This has been achieved by the development of a continuous linear multistep method (LMM). The continuous LMM is used to construct a main discrete method to be used with some initial and final methods (also obtained from the continuous LMM) so that they form a discrete analogue of the continuous second order boundary value problems. These methods are used as boundary value methods and adapted to cope with the integration of the general second order multipoint boundary value problems. The convergence, the use and the region of absolute stability of the methods are discussed. Several numerical examples are implemented to elucidate our solution process.

Keywords: linear multistep methods, boundary value methods, second order multipoint boundary value problems, convergence

Procedia PDF Downloads 377

Authors: Pradeepa Teegala, Ramreddy Chetteti

Abstract:

This work emphasizes the effects of heat generation/absorption and Joule heating on chemically reacting micropolar fluid flow over a truncated cone with convective boundary condition. For this complex fluid flow problem, the similarity solution does not exist and hence using non-similarity transformations, the governing fluid flow equations along with related boundary conditions are transformed into a set of non-dimensional partial differential equations. Several authors have applied the spectral quasi-linearization method to solve the ordinary differential equations, but here the resulting nonlinear partial differential equations are solved for non-similarity solution by using a recently developed method called the spectral quasi-linearization method (SQLM). Comparison with previously published work on special cases of the problem is performed and found to be in excellent agreement. The influence of pertinent parameters namely Biot number, Joule heating, heat generation/absorption, chemical reaction, micropolar and magnetic field on physical quantities of the flow are displayed through graphs and the salient features are explored in detail. Further, the results are analyzed by comparing with two special cases, namely, vertical plate and full cone wherever possible.

Keywords: chemical reaction, convective boundary condition, joule heating, micropolar fluid, spectral quasilinearization method

Procedia PDF Downloads 348

Authors: Reda Mankbadi

Abstract:

The current work explores the use of Synthetic Jet Actuators (SJAs) for control of the acoustic radiation of a low-speed transitioning airfoil in a uniform stream. In the adopted numerical procedure, the actuator is modeled without its resonator cavity through imposing a simple fluctuating-velocity boundary condition at the bottom of the actuator's orifice. The orifice cavity, with the properly defined boundary condition, is then embedded into the airfoil surface. High-accuracy viscous simulations are then conducted to study the effects of the actuation on sound radiated by the airfoil. Results show that SJA can considerably suppress the radiated sound of the airfoil in uniform incoming stream.

Keywords: simulations, aeroacoustics, wind turbine noise, synthetic jet actuators (SJAs)

Procedia PDF Downloads 355

Authors: Shamsul Chowdhury

Abstract:

The objective of this paper is to present the detailed analysis of the turbulent wave boundary layer produced by progressive finite-amplitude waves theory. Most of the works have done for the mass transport in the turbulent boundary layer assuming the eddy viscosity is not time varying, where the sediment movement is induced by the mean velocity. Near the ocean bottom, the waves produce a thin turbulent boundary layer, where the flow is highly rotational, and shear stress associated with the fluid motion cannot be neglected. The magnitude and the predominant direction of the sediment transport near the bottom are known to be closely related to the flow in the wave induced boundary layer. The magnitude of water particle velocity at the Crest phase differs from the one of the Trough phases due to the non-linearity of the waves, which plays an important role to determine the sediment movement. The non-linearity of the waves become predominant in the surf zone area, where the sediment movement occurs vigorously. Therefore, in order to describe the flow near the bottom and relationship between the flow and the movement of the sediment, the analysis was done using the non-linear boundary layer equation and the finite amplitude wave theory was applied to represent the velocity fields in the turbulent wave boundary layer. At first, the calculation was done for turbulent wave boundary layer by two-dimensional model where throughout the calculation is non-linear. But Stokes second order wave profile is adopted at the upper boundary. The calculated profile was compared with the experimental data. Finally, the calculation is done based on various modes of the velocity and turbulent energy. The mean velocity is found to differ from condition of the relative depth and the roughness. It is also found that due to non-linearity, the absolute value for velocity and turbulent energy as well as Reynolds stress are asymmetric. The mean velocity of the laminar boundary layer is always positive but in the turbulent boundary layer plays a very complicated role.

Keywords: wave boundary, mass transport, mean velocity, shear stress

Procedia PDF Downloads 262

Authors: G. Ravi Kiran, G. Radhakrishnamacharya

Abstract:

This paper investigates the effects of slip boundary condition and wall properties on the dispersion of a solute matter in peristaltic flow of an incompressible micropolar fluid through a porous medium. Long wavelength approximation, Taylor's limiting condition and dynamic boundary conditions at the flexible walls are used to obtain the average effective dispersion coefficient in the presence of combined homogeneous and heterogeneous chemical reactions. The effects of various pertinent parameters on the effective dispersion coefficient are discussed. It is observed that peristalsis enhances dispersion. It also increases with micropolar parameter, cross viscosity coefficient, Darcy number, slip parameter and wall parameters. Further, dispersion decreases with homogenous chemical reaction rate and heterogeneous chemical reaction rate.

Keywords: chemical reaction, dispersion, peristalsis, slip condition, wall properties

Procedia PDF Downloads 468

Authors: M. Abir Hossain, M. Shahjada Tarafder

Abstract:

This paper deals with the analysis of potential flow past two-dimensional body by discretizing the body into panels where the Laplace equation was applied to each panel. The Laplace equation was solved at each panel by applying the boundary conditions. The boundary condition was applied at each panel to mathematically formulate the problem and then convert the problem into a computer-solvable problem. Kutta condition was applied at both the leading and trailing edges to see whether the condition is satisfied or not. Another approach that is applied for the analysis is Vortex Lattice Method (VLM). A vortex ring is considered at each control point. Using the Biot-Savart Law the strength at each control point is calculated and hence the pressure differentials are measured. For the comparison of the analytic result with the experimental result, different NACA section hydrofoil is used. The analytic result of NACA 0012 and NACA 0015 are compared with the experimental result of Abbott and Doenhoff and found significant conformity with the achieved result.

Keywords: Kutta condition, Law of Biot-Savart, pressure differentials, potential flow, vortex lattice method

Procedia PDF Downloads 190

Authors: S. Kida

Abstract:

We consider the flow of an incompressible viscous fluid in a precessing sphere whose spin and precession axes are orthogonal to each other. The flow is characterized by two non-dimensional parameters, the Reynolds number Re and the Poincare number Po. For which values of (Re, Po) will the flow approach a steady state from an arbitrary initial condition? To answer it we are searching the instability boundary of the steady states in the whole (Re, Po) plane. Here, we focus the rapidly rotating and weakly precessing limit, i.e., Re >> 1 and Po << 1. The steady flow was obtained by the asymptotic expansion for small ε=Po Re¹/² << 1. The flow exhibits nearly a solid-body rotation in the whole sphere except for a thin boundary layer which develops over the sphere surface. The thickness of this boundary layer is of O(δ), where δ=Re⁻¹/², except where two circular critical bands of thickness of O(δ⁴/⁵) and of width of O(δ²/⁵) which are located away from the spin axis by about 60°. We perform the linear stability analysis of the steady flow. We assume that the disturbances are localized in the critical bands and make an expansion analysis in terms of ε to derive the eigenvalue problem for the growth rate of the disturbance, which is solved numerically. As the solution, we obtain an asymptote of the stability boundary as Po=28.36Re⁻⁰.⁸. This agrees excellently with the corresponding laboratory experiments and numerical simulations. One of the most popular instability mechanisms so far is the parametric instability, which turns out, however, not to give the correct stability boundary. The present instability is different from the parametric instability.

Keywords: boundary layer, critical band, instability, precessing sphere

Procedia PDF Downloads 155

Authors: Michael J. Cutler

Abstract:

This paper presents what musical boundary play can look like when beginning music learners work with professional musicians with an emphasis on composition. Music education can be re-imagined through the lenses of boundary objects and boundary play by engaging non-professional musicians in collaborative sound creation, improvisation and composition along with professional musicians. To the author’s best knowledge, no similar study exists on boundary objects and boundary play in music education. The literature reviewed for this paper explores the epistemological perspectives connected to music education and situates musical boundary play as an alternative approach to the more prevalent paradigms of music education in K-12 settings. A qualitative multiple-case study design was chosen to seek an in-depth understanding of the role of boundary objects and musical boundary play. The constant comparative method was utilized in analyzing and interpreting the data resulting in the development of effective, transferable theory. The study gathered relevant data using audio and video recordings of musical boundary play, artifacts, interviews, and observations. Findings from this study offer insight into the development of a more inclusive music education and yield a pedagogical framework for music education based on musical boundary play. Through the facilitation of musical boundary play, it is possible for music learners to experience musical sound creation, improvisation and composition in the same way an instrumentalist or vocalist would without the acquisition of complex component operations required to play a traditional instrument or sing in a proficient manner.

Keywords: boundary play, boundary objects, music education, music pedagogy, musical boundary play

Procedia PDF Downloads 128

Authors: Pradeepa Teegala, Ramreddy Chitteti

Abstract:

This article analyzes the mixed convection flow of chemically reacting micropolar fluid over a truncated cone embedded in non-Darcy porous medium with convective boundary condition. In addition, heat generation/absorption and Joule heating effects are taken into consideration. The similarity solution does not exist for this complex fluid flow problem, and hence non-similarity transformations are used to convert the governing fluid flow equations along with related boundary conditions into a set of nondimensional partial differential equations. Many authors have been applied the spectral quasi-linearization method to solve the ordinary differential equations, but here the resulting nonlinear partial differential equations are solved for non-similarity solution by using a recently developed method called the spectral quasi-linearization method (SQLM). Comparison with previously published work on special cases of the problem is performed and found to be in excellent agreement. The effect of pertinent parameters namely, Biot number, mixed convection parameter, heat generation/absorption, Joule heating, Forchheimer number, chemical reaction, micropolar and magnetic field on physical quantities of the flow are displayed through graphs and the salient features are explored in detail. Further, the results are analyzed by comparing with two special cases, namely, vertical plate and full cone wherever possible.

Keywords: chemical reaction, convective boundary condition, joule heating, micropolar fluid, mixed convection, spectral quasi-linearization method

Procedia PDF Downloads 277

Authors: Xu Runzhang, Yang Yanbing, Niu Yi, Zhang Mingyou, Liu Yu

Abstract:

For a class of semilinear parabolic equations with linear dynamical boundary conditions in a bounded domain, we obtain both global solutions and finite time blow-up solutions when the initial data varies in the phase space H1(Ω). Our main tools are the comparison principle, the potential well method and the concavity method. In particular, we discuss the behavior of the solutions with the initial data at critical and high energy level.

Keywords: high energy level, critical energy level, linear dynamical boundary condition, semilinear parabolic equation

Procedia PDF Downloads 437

Authors: Yifan Dong, Xincheng Pu

Abstract:

Rural settlements originate from the accumulation of residential building elements, and their agglomeration forms the settlement pattern and defines the relationship between the settlement and the inside and outside. The settlement boundary is an important part of the settlement pattern. Compared with the simplification of the urban settlement boundary, the settlement of the country is more complex, fuzzy and uncertain, and then presents a rich and diverse boundary morphological phenomenon. In this paper, China traditional rural settlements plane boundary as the research object, using fractal theory and fractal dimension method, quantitative analysis of planar shape boundary settlement, and expounds the research for the architectural design, ancient architecture protection and renewal and development and the significance of the protection of settlements.

Keywords: rural settlement, border, fractal, quantification

Procedia PDF Downloads 251

Authors: M. Y. Malika, Farzana, Abdul Rehman

Abstract:

The study deals with the steady, 3D MHD boundary layer flow of a non-Newtonian Maxwell fluid flow due to a horizontal surface stretched exponentially in two lateral directions. The temperature at the boundary is assumed to be distributed exponentially and possesses convective boundary conditions. The governing nonlinear system of partial differential equations along with associated boundary conditions is simplified using a suitable transformation and the obtained set of ordinary differential equations is solved through numerical techniques. The effects of important involved parameters associated with fluid flow and heat flux are shown through graphs.

Keywords: boundary layer flow, exponentially stretched surface, Maxwell fluid, numerical solution

Procedia PDF Downloads 591

Authors: Rajeev, N. K. Raigar

Abstract:

In this study, one dimensional phase change problem (a Stefan problem) is considered and a numerical solution of this problem is discussed. First, we use similarity transformation to convert the governing equations into ordinary differential equations with its boundary conditions. The solutions of ordinary differential equation with the associated boundary conditions and interface condition (Stefan condition) are obtained by using a numerical approach based on operational matrix of differentiation of shifted second kind Chebyshev wavelets. The obtained results are compared with existing exact solution which is sufficiently accurate.

Keywords: operational matrix of differentiation, similarity transformation, shifted second kind chebyshev wavelets, stefan problem

Procedia PDF Downloads 404

Authors: Kiran P. Kumar, H. M. Nayana, R. Rakshitha, S. Sushmitha

Abstract:

Aircraft noise is a highly concerned problem in the field of the aviation industry. It is necessary to reduce the noise in order to be environment-friendly. Air-frame noise is caused because of the quick separation of the boundary layer over an aircraft body. So, we have to delay the boundary layer separation of an air-frame and engine nacelle. By following a certain procedure boundary layer separation can be reduced by converting laminar into turbulent and hence early separation can be prevented that leads to the noise reduction. This method has a tendency to reduce the noise of the aircraft hence it can prove efficient and environment-friendly than the present Aircraft.

Keywords: airframe, boundary layer, noise, reduction

Procedia PDF Downloads 484

Authors: K. N. S. Kasi Viswanadham

Abstract:

Coupled system of second order linear and nonlinear boundary value problems occur in various fields of Science and Engineering. In the formulation of the problem, any one of 81 possible types of boundary conditions may occur. These 81 possible boundary conditions are written as a combination of four boundary conditions. To solve a coupled system of boundary value problem with these converted boundary conditions, a collocation method with cubic B-splines as basis functions has been developed. In the collocation method, the mesh points of the space variable domain have been selected as the collocation points. The basis functions have been redefined into a new set of basis functions which in number match with the number of mesh points in the space variable domain. The solution of a non-linear boundary value problem has been obtained as the limit of a sequence of solutions of linear boundary value problems generated by quasilinearization technique. Several linear and nonlinear boundary value problems are presented to test the efficiency of the proposed method and found that numerical results obtained by the present method are in good agreement with the exact solutions available in the literature.

Keywords: collocation method, coupled system, cubic b-splines, mesh points

Procedia PDF Downloads 210

Authors: F. Waffo Tchuimmo, G. S. Kwandio Dongoua, C. U. Yves Mbono Samba, O. Dafounansou, L. Nana

Abstract:

The strength criterion is an important condition of great interest to guarantee the stability of the structural elements. The present work is based on the study of the free vibration of Euler’s Bernoulli column of equal strength in compression while considering its own weight and the axial load in compression and tension subjected to symmetrical boundary conditions. We use the differential quadrature method to investigate the first fifth naturals frequencies parameters of the column according to the different forms of geometrical sections. The results of this work give help in making a judicious choice of type of cross-section and a better boundary condition to guarantee good stability of this type of column in civil constructions.

Keywords: free vibration, equal strength, self-weight, tip force, differential quadrature method

Procedia PDF Downloads 137

Authors: Bamikole J. Adeyemi, Prashant Jadhawar, Lateef Akanji

Abstract:

Liquid-liquid interfacial flow is an important process that has applications across many spheres. One such applications are residual oil mobilization, where crude oil and low salinity water are emulsified due to lowered interfacial tension under the condition of low shear rates. The amphiphilic components (asphaltenes and resins) in crude oil are considered to assemble at the interface between the two immiscible liquids. To justify emulsification, drag and snap-off suppression as the main effects of low salinity water, mobilization of residual oil is visualized as thickening and slip of the wetting phase at the brine/crude oil interface which results in the squeezing and drag of the non-wetting phase to the pressure sinks. Meanwhile, defining the boundary conditions for such a system can be very challenging since the interfacial dynamics do not only depend on interfacial tension but also the flow rate. Hence, understanding the flow boundary condition at the brine/crude oil interface is an important step towards defining the influence of low salinity water composition on residual oil mobilization. This work presents a numerical evaluation of three slip boundary conditions that may apply at liquid-liquid interfaces. A mathematical model was developed to describe the evolution of a viscoelastic interfacial thin liquid film. The base model is developed by the asymptotic expansion of the full Navier-Stokes equations for fluid motion due to gradients of surface tension. This model was upscaled to describe the dynamics of the film surface deformation. Subsequently, Jeffrey’s model was integrated into the formulations to account for viscoelastic stress within a long wave approximation of the Navier-Stokes equations. To study the fluid response to a prescribed disturbance, a linear stability analysis (LSA) was performed. The dispersion relation and the corresponding characteristic equation for the growth rate were obtained. Three slip (slip, 1; locking, -1; and no-slip, 0) boundary conditions were examined using the resulted characteristic equation. Also, the dynamics of the evolved interfacial thin liquid film were numerically evaluated by considering the influence of the boundary conditions. The linear stability analysis shows that the boundary conditions of such systems are greatly impacted by the presence of amphiphilic molecules when three different values of interfacial tension were tested. The results for slip and locking conditions are consistent with the fundamental solution representation of the diffusion equation where there is film decay. The interfacial films at both boundary conditions respond to exposure time in a similar manner with increasing growth rate which resulted in the formation of more droplets with time. Contrarily, no-slip boundary condition yielded an unbounded growth and it is not affected by interfacial tension.

Keywords: boundary conditions, liquid-liquid interfaces, low salinity water, residual oil mobilization

Procedia PDF Downloads 130

Authors: Shuang Luo, Er-Xiang Song

Abstract:

Many problems in geotechnical engineering, such as foundation deformation, groundwater seepage, seismic wave propagation and geothermal transfer problems, may involve analysis in the ground which can be seen as extending to infinity. To that end, consideration has to be given regarding how to deal with the unbounded domain to be analyzed by using numerical methods, such as finite element method (FEM), finite difference method (FDM) or finite volume method (FVM). A simple artificial boundary approach derived from the analytical solutions for transient radial seepage problems, is introduced. It should be noted, however, that the analytical solutions used to derive the artificial boundary are particular solutions under certain boundary conditions, such as constant hydraulic head at the origin or constant pumping rate of the well. When dealing with unbounded domains with unsteady boundary conditions, a more sophisticated artificial boundary approach to deal with the infinity of the domain is presented. By applying Laplace transforms and introducing some specially defined auxiliary variables, the global artificial boundary conditions (ABCs) are simplified to local ones so that the computational efficiency is enhanced significantly. The introduced two local ABCs are implemented in a finite element computer program so that various seepage problems can be calculated. The two approaches are first verified by the computation of a one-dimensional radial flow problem, and then tentatively applied to more general two-dimensional cylindrical problems and plane problems. Numerical calculations show that the local ABCs can not only give good results for one-dimensional axisymmetric transient flow, but also applicable for more general problems, such as axisymmetric two-dimensional cylindrical problems, and even more general planar two-dimensional flow problems for well doublet and well groups. An important advantage of the latter local boundary is its applicability for seepage under rapidly changing unsteady boundary conditions, and even the computational results on the truncated boundary are usually quite satisfactory. In this aspect, it is superior over the former local boundary. Simulation of relatively long operational time demonstrates to certain extents the numerical stability of the local boundary. The solutions of the two local ABCs are compared with each other and with those obtained by using large element mesh, which proves the satisfactory performance and obvious superiority over the large mesh model.

Keywords: transient seepage, unbounded domain, artificial boundary condition, numerical simulation

Procedia PDF Downloads 295

Authors: Bashiru Abdullahi, Isah Bala Yabo, Ibrahim Yakubu Seini

Abstract:

In this paper, the steady/transient MHD heat transfer within radiative porous channel due to convective boundary conditions is considered. The solution of the steady-state and that of the transient version were conveyed by Perturbation and Finite difference methods respectively. The heat transfer mechanism of the present work ascertains the influence of Biot number〖(B〗_i1), magnetizing parameter (M), radiation parameter(R), temperature difference, suction/injection(S) Grashof number (Gr) and time (t) on velocity (u), temperature(θ), skin friction(τ), and Nusselt number (Nu). The results established were discussed with the help of a line graph. It was found that the velocity, temperature, and skin friction decay with increasing suction/injection and magnetizing parameters while the Nusselt number upsurges with suction/injection at y = 0 and falls at y =1. The steady-state solution was in perfect agreement with the transient version for a significant value of time t. It is interesting to report that the Biot number has a cogent influence consequently, as its values upsurge the result of the present work slant the extended literature.

Keywords: heat transfer, thermal radiation, porous channel, MHD, transient, convective boundary condition

Procedia PDF Downloads 121

Authors: Alexandra Leukauf, Alexander Schirrer, Emir Talic

Abstract:

Numerical computation of wave propagation in a large domain usually requires significant computational effort. Hence, the considered domain must be truncated to a smaller domain of interest. In addition, special boundary conditions, which absorb the outward travelling waves, need to be implemented in order to describe the system domains correctly. In this work, the linear one dimensional wave equation is approximated by utilizing the Fourier Galerkin approach. Furthermore, the artificial boundaries are realized with absorbing boundary conditions. Within this work, a systematic work flow for setting up the wave problem, including the absorbing boundary conditions, is proposed. As a result, a convenient modal system description with an effective absorbing boundary formulation is established. Moreover, the truncated model shows high accuracy compared to the global domain.

Keywords: absorbing boundary conditions, boundary control, Fourier Galerkin approach, modal approach, wave equation

Procedia PDF Downloads 398

Authors: Mohamed Hussein

Abstract:

This paper studies the effect of boundary retaining walls properties on the behavior of the raft foundation. Commercial software program Sap2000 was used in this study. The soil was presented as continuous media (follows the Winkler assumption). Shell elements were employed to model the raft plate. A parametric study has been carried out to examine the effect of boundary retaining walls properties on the behavior of raft plate. These parameters namely, height of the boundary retaining walls, thickness of the boundary retaining walls, flexural rigidity of raft plate, bearing capacity of supporting soil and the earth pressure of boundary soil. The main results which were obtained from this study are positive, negative bending moment, shear stress and deflection in raft plate, where these parameters are considered the main parameters used in design of raft foundation. It was concluded that the boundary retaining walls have a significant effect on the straining actions in raft plate.

Keywords: Sap2000, boundary retaining walls, raft foundations, Winkler model, flexural rigidity

Procedia PDF Downloads 181