Sharif Digital Repository

The characteristic boundary conditions are applied and assessed for the solution of incompressible inviscid flows. The two-dimensional incompressible Euler equations based on the artificial compressibility method are considered and then the characteristic boundary conditions are formulated in the generalized curvilinear coordinates and implemented on both the far-field and wall boundaries. A fourth-order compact finite-difference scheme is used to discretize the resulting system of equations. The solution methodology adopted is more suitable for this assessment because the Euler equations and the high-accurate numerical scheme applied are quite sensitive to the treatment of boundary... 

The preconditioned characteristic boundary conditions based on the artificial compressibility (AC) method are implemented at artificial boundaries for the solution of two- and three-dimensional incompressible viscous flows in the generalized curvilinear coordinates. The compatibility equations and the corresponding characteristic variables (or the Riemann invariants) are mathematically derived and then applied as suitable boundary conditions in a high-order accurate incompressible flow solver. The spatial discretization of the resulting system of equations is carried out by the fourth-order compact finite-difference (FD) scheme. In the preconditioning applied here, the value of AC parameter... 

Based on the first-order shear deformation plate theory, two approaches within the extended Kantorovich method (EKM) are presented for a bending analysis of functionally graded annular sector plates with arbitrary boundary conditions subjected to both uniform and non-uniform loadings. In the first approach, EKM is applied to the functional of the problem, while in the second one EKM is applied to the weighted integral form of the governing differential equations of the problem as presented by Kerr. In both approaches, the system of ordinary differential equations with variable coefficients in r direction and the set of ordinary differential equations with constant coefficients in θ direction... 

Carbon nanoscroll (CNS) is a graphene sheet rolled into a spiral structure with great potential for different applications in nanotechnology. In this paper, an equivalent open shell model is presented to study the vibration behavior of a CNS with arbitrary boundary conditions. The equivalent parameters used for modeling the carbon nanotubes are implemented to simulate the CNS. The interactions between the layers of CNS due to van der Waals forces are included in the model. The uniformly distributed translational and torsional springs along the boundaries are considered to achieve a unified solution for different boundary conditions. To study the vibration characteristics of CNS, total energy... 

We numerically solve the Navier-Stokes equations to study the rarefied gas flow in short micro- and nanoscale channels. The inlet boundary conditions play a critical role in the structure of flow in short channels. Contrary to the classical inlet boundary conditions, which apply uniform velocity and temperature profiles right at the real channel inlet, we apply the same inlet boundary conditions, but at a fictitious position far upstream of the real channel inlet. A constant wall temperature incorporated with suitable temperature jump is applied at the channel walls. Our solutions for both the classical and extended inlet boundary conditions are compared with the results of other available... 

In this paper, cavity flow is simulated numerically. Forced convection in different Reynolds numbers between 100 and 5000 is simulated. Different and complex thermal boundary conditions are applied and various parameters are calculated numerically. Up and down walls are in constant temperature and left and right walls are thermal insulation in the first thermal boundary condition. The Left and the down walls are in constant temperature and the temperature of the up and the right walls changes linearly in the second thermal boundary condition. For the third thermal boundary condition, the left and the down walls are in constant temperature and the temperature of the up and the right walls... 

In this paper, cavity flow is simulated numerically. Forced convection in different Reynolds numbers between 100 and 5000 is simulated. Different and complex thermal boundary conditions are applied and various parameters are calculated numerically. Up and down walls are in constant temperature and left and right walls are thermal insulation in the first thermal boundary condition. The Left and the down walls are in constant temperature and the temperature of the up and the right walls changes linearly in the second thermal boundary condition. For the third thermal boundary condition, the left and the down walls are in constant temperature and the temperature of the up and the right walls... 

Molecular structural mechanics is implemented to model vibrational behavior of defect free single-layered graphene sheets (SLGSs) at constant temperature. To mimic these two-dimensional layers, zigzag and armchair models with cantilever and bridge boundary conditions are adopted. Fundamental frequencies of these nano structures are calculated, and it is perceived that they are independent of the chirality and aspect ratio. Effects of point mass and atomistic dust on the fundamental frequencies are also considered in order to investigate the possibility of using SLGSs as sensors. Results of exhibit the principle frequencies are highly sensitive to the added mass in the order of 10-6fg.... 

One important point in microflow study is the correct consideration of the Knudsen layer. In addition to the many complexities behind numerical simulation of the Knudsen layer near the solid walls, there are serious uncertainties at the microchannel inlet (the point at which the flow enters the microdomain). One major difficulty is the appearance of two singularities at the two corners of the inlet section. They seriously affect the solution in the entrance region of microchannels in which the lengths are comparable with the lengths of their hydrodynamic developing zones. Although the macro inlet flow problem has been largely investigated, there has been little attempt to study the issue in... 

This study investigates the chaotic response of the spring-pendulum system. In this system besides of strange attractors, multiple regular attractors may co-exist for some values of system parameters, and it is important to study the global behavior of the system using the basin boundaries of the attractors. Here multiple scales method is used to distinguish the regions of stable and unstable attractors. Early studies show that there are unstable regions for the spring-pendulum system. In this study using bifurcation diagrams and Poincaré maps, it is shown that in some cases the response becomes quasi-periodic or chaotic for some deviations from external and internal resonance frequencies.... 

In present paper the theory of the micropolar fluid based on a Cosserat continuum model has been applied for analysis of Couette flow. The obtained results for the velocity field have been compared with known results from experiments done by Reichardt at Max Plank institute for fluids in Gottingen [1,2] and analytical solution of the problem from Gradient theory by alizadeh[3].the boundary condition used here was the no slip one and Trostel's slip boundary condition[4].a good agreement between experimental results and the results of the problem for Reynolds near 18000 has beeen found. A new dimensionless number introduced that indicates the theoretical relation between cosserat theory and... 

The numerical solution of the fluid flow governing equations requires correct boundary condition implementations at suitable locations to produce well-posed problem. Most of numerical strategies exhibit weak performance and obtain inaccurate solutions if the boundary conditions are not placed at suitable locations. Unfortunately, many practical fluid flow problems such as those in oceanography pose difficulty at the boundaries because the required information for solving the PDE's is hardly available there. On the other hand, large solution domains with certain boundary conditions need huge number of mesh nodes. This can drastically increase the computer expenses. Such difficulties have... 

The use of collocated grid schemes in control-volume-based methods has resulted in developing different strategies for coupling mass and momentum governing equations. Defining two different velocity components at cell faces is one remedy to suppress the possible checkerboard problem in the solution domain. These velocity components are widely known as convected and convecting velocities which are normally used in the momentum and mass governing equations, respectively. However, the linearization of the nonlinear governing equations generates a number of lagged velocity components which must be carefully treated in a manner to preserve the conceptual definition of the convected and convecting... 

Recently, a group of novel devices based on conducting interfaces has been proposed. These conducting interfaces can be implemented, for example, by using the inversion layer of MOS structures, trapped charges, or depletion layer charges. It has been shown that these structures can support surface electromagnetic waves. In this paper, the coupling of surface electromagnetic waves supported by conducting interfaces is first analysed. Next, by direct solution of Maxwell's equations and applying appropriate boundary conditions; exact analytical formulation of the dispersion equation has also been derived. Results driven by a coupled mode theory approach are justified by solving the exact... 

The non-linear bubble dynamics equations in a compressible liquid have been modified by considering the effects of compressibility of both the liquid and the gas at the bubble interface. A new bubble boundary equation has been derived, which includes a new term resulting from the liquid bulk viscosity effect. The influence of this term has been numerically investigated by considering the effects of water vapour and chemical reactions inside the bubble. The results clearly indicate that the new term has an important damping role at the collapse, so that its consideration dramatically decreases the amplitude of the bubble rebounds after the collapse. This damping feature is more remarkable for... 

In this paper, the large amplitude free vibration of a cantilever Timoshenko beam is considered. To this end, first Hamilton's principle is used in deriving the partial differential equation of the beam response under the mentioned conditions. Then, implementing the Galerkin's method the partial differential equation is converted to an ordinary nonlinear differential equation. Finally, the method of multiple scales is used to determine a second order perturbation solution for the obtained ODE. The results show that nonlinearity acts in the direction of increasing the natural frequency of the thick-cantilevered beam  

An investigation on the nonlinear vibrations of a system with two degrees of freedom when subjected to saturation is presented. The method is especially applied to a system that consists of a DC motor with a nonlinear controller and subjected to a harmonic forcing voltage. Approximate solutions are sought using the method of multiple scales. Also, singular point analysis is used to study stability of solutions. These findings are then compared with the corresponding numerical results. Good agreement between the two is observed  

The Casimir forces on two parallel plates in conformally flat de Sitter background due to conformally coupled massless scalar field satisfying mixed boundary conditions on the plates is investigated. In the general case of mixed boundary conditions formulae are derived for the vacuum expectation values of the energy-momentum tensor and vacuum forces acting on boundaries. Different cosmological constants are assumed for the space between and outside of the plates to have general results applicable to the case of domain wall formations in the early universe  

In this paper, the unsteady state heat transfer equations with time dependent boundary conditions are coupled with a two-dimensional finite element method to predict the work-roll temperature distribution during the continuous hot slab rolling process. To achieve an accurate temperature field, the effects of various factors including the thermal relationship of the work-roll and the metal slab, the idling work-roll revolutions, the rolling speed, the slab/roll interfacial heat transfer coefficient, and the magnitude of the thickness reduction of the slab at each deformation pass are taken into account. Comparisons between the predicted and published experimental results are used to... 

An investigation into the dynamics of vehicle-occupant-structure-induced vibration of bridges traversed by moving vehicles is presented. The vehicle including the driver and passengers is modelled as a half-car planar model with six degrees-of-freedom, and the bridge is assumed to obey the Euler-Bernoulli beam theory with arbitrary conventional boundary conditions. Due to the continuously moving location of the variable loads on the bridge, the governing differential equations become rather complicated. The numerical simulations presented here are for the case of vehicle travelling at a constant speed on a uniform bridge with simply supported end conditions. The relationship between the...