Different Kinds Of Boundary Conditions Research Articles

On arbitrary inlet and wall boundary conditions in cascade flows for the Navier–Stokes solver

The present unsteady three-dimensional compressible Navier–Stokes solver, using the pseudo-analytic functions with integral operators, can satisfy arbitrary boundary conditions at the inlet and along wall surfaces, simultaneously. The governing equations can deal with numerous parameters and variables appearing in complicated numerical experiments. In the solver three different kinds of computation surfaces, blade-to-blade, meridional and cross-sectional ones, those allow any deflections of their surfaces, were introduced. Thanks to the employed function theory the indirect method, which yields complete fitting of different kinds of boundary conditions, was incorporated in the present solution. An interchange of necessary informations between direct and indirect methods can be smoothly and sufficiently executed without any artificial technique. The code requires only moderate size of memory and CPU time consumption of standard type of computer systems and can obtain needful informations for the graphics. The additionally calculated results for a film-cooled flowfield proved the applicability of present method to flowfields with independently given boundary conditions. Stable numerical solutions were obtained for the flowfields.

Proximal Analysis and the Minimal Time Function

Under general hypotheses on the target set S and the dynamics of the system, we show that the minimal time function TS(\cdot) is a proximal solution to the Hamilton--Jacobi equation. Uniqueness results are obtained with two different kinds of boundary conditions. A new propagation result is proven, and as an application, we give necessary and sufficient conditions for TS(\cdot) to be Lipschitz continuous near S. A Petrov-type modulus condition is also shown to be sufficient for continuity of TS(\cdot) near S.

An approach to information propagation in 1-D cellular neural networks-Part I: Local diffusion

This is the first of two companion papers devoted to a deep analysis of the dynamics of information propagation in the simplest nontrivial Cellular Neural Network (CNN), which is one-dimensional and has connections between nearest neighbors only. We will show that two behaviors are possible: local diffusion of information between neighboring cells and global propagation through the entire array. This paper deals with local diffusion, of which we will first give an accurate definition, before computing the template parameters for which the CNN has this behavior. Next we will compute the number of stable equilibria, before examining the convergence of any trajectory toward them, for three different kinds of boundary conditions: fixed Dirichlet, reflective, and periodic.

Effect of internal radiative heat transfer on the convection in CZ oxide melt

A numerical study was carried out to investigate the effect of internal radiative heat transfer on the convection in the Czochralski oxide melt. Results were obtained for a wide range of the absorption coefficients of the melt. The flow and temperature fields showed a remarkable change with the variance in the absorption coefficient. In this study, we adopted two different kinds of boundary conditions for the radiative heat transfer at the melt surface, i.e., an opaque and a semitransparent diffuse gray surface, and for each case, the influence of Marangoni convection was investigated. The optical characteristic of the melt surface and the Marangoni effect greatly affected the convection and temperature field in the melt. When the surface was assumed to be semitransparent, in the range of a small absorption coefficient, the smaller the absorption coefficient was, the lesser the Marangoni effect became. This was caused by the disappearance of the temperature gradient at the melt surface, and consequently the flow became as weak as in the case without the Marangoni effect. These numerical results give a clue for discussion on the effect of internal radiative heat transfer in the melt of the Czochralski system.

Continuous Dependence for 2×2 Conservation Laws with Boundary

on the domain 0.[(t, x) # R : t 0 and x 9(t)], for some boundary profile 9: R [ R. As usual, (1.1) is assumed to be strictly hyperbolic and with each characteristic field either linearly degenerate or genuinely non linear. An initial data u(0, x)=u (x) having sufficiently small total variation is given. We consider two different kinds of boundary conditions along x=9(t) and in both cases we construct a Lipschitzean flow whose trajectories are solutions of an initial-boundary value problem for (1.1). Thus, we prove the continuous dependence of the solution upon the initial data, upon the boundary condition and upon the boundary profile. The existence theory for global BV solutions to the Cauchy Problem for (1.1) goes back to the fundamental paper [15] by Glimm. More recently, in [6], a new approach has been introduced. It relies on the construction of a Lipschitzean semigroup, the Standard Riemann Semigroup (SRS), whose trajectories extend the local standard Lax [17] solutions of Riemann Problems. At present, such a SRS has been constructed in the 2_2 case in [8, 9], while for the general n_n case see [7, 10] and [3] in article no. DE973274

The penetration rate of solid-liquid phase-change heat transfer interface with different kinds of boundary conditions

The penetration rate of solid-liquid phase-change heat transfer interface with different kinds of boundary conditions

An investigation about the relations between the results of heat conduction problems with and without phase change

There are physical relations between the velocities of the isotherms for two heat conduction problems having the same initial and boundary conditions, but one of them has phase change while the other one has not. The main idea of this study is to find these relations mathematically, which stand on a physical base, depending on the physical properties of the phases and the common parameters of these two different problems. If such kind of relations are known, then it will be possible to find the position of solid-liquid interface by using the analytical solutions and the relation itself, not solving the phase change problem. This idea is applied to heat conduction problem in semi infinite media and one dimensional phase change problem is solved for three different kind of boundary conditions via the Enthalpy Method. The results are correlated with the analytical solutions of the problem having same geometry and conditions but without phase change and obtained some relations having correlation coefficients changing between 0.91 and 0.98. This result shows that the regression analysis made is statistically meaningful.

The penetration rate of solid-liquid phase-change heat transfer interface with different kinds of boundary conditions

The penetration rate of solid-liquid phase-change heat transfer interface with different kinds of boundary conditions

Coupled FEM-BEM approach for mean flow effects on vibro-acoustic behavior of planar structures

The originality of the present paper lies in the development of a formulation accounting for mean flow effects on the forced vibro-acoustic response of a baffled plate. The importance of these effects on the vibrational behavior of the plate, as well as on its acoustic radiation pattern, is investigated for a baffled plate with different kinds of boundary conditions. The analysis is based on a finite element method for the calculation of the plate transverse vibrations and the use of the extended Kirchhoff's integral equation to account for fluid loading with mean flow. A variational boundary element method is used to compute the acoustic radiation impedance. The formulation shows explicitly the effects of mean flow in terms of added mass, stiffness, and radiation damping. Details of the formulation as well as its numerical implementation are expounded, and results showing the effect of mean flow hi light and heavy fluid on the vibro-acoustic quantities, such as mean square velocity and radiated acoustic power, are presented. It is seen that the effects of a mean flow amount to a decrease of the natural frequencies of the plate, a small damping effect on the vibrations, and a change in the radiated acoustic power when compared with the no-flow case. Besides, these effects increase with the flow speed. The negative stiffness added by the flow is shown to be mainly responsible for the natural frequency shift effect. The changes in the radiated acoustic power are explained in terms of important changes in the radiation efficiencies and modal cross-coupling induced by the flow.

K+ uptake by root systems grown in soil under salinity: II. Sensitivity analysis

A numerical algorithm for the solution of multicomponent transport of Ca2+, Mg2+, Na+, K+, Cl− in soil and their uptake by plant roots has been developed. The model emphasizes adsorptiondesorption due to cation exchange mechanism, dissolution-precipitation of CaCO3, and pH changes at the root surface controlled by the anion-cation influx balance. A fully implicit finite difference scheme is used for numerical implementation. Sensitivity analysis was conducted to evaluate the effect of each parameter on nutrient uptake. Each parameter (independent of all others) was varied between 0.25 to 4 times its speculated ‘average’ level. Predicted K+ uptake was found to be more sensitive to changes of root radius and the parameter indicating maximal influx of K+. Effective diffusion coefficient and soil moisture are less influential. The influence of CaCO3 dissolution and different kinds of boundary conditions were also considered.

Heat transfer analysis of a second grade fluid over a stretching sheet

The heat tranfer and flow of a non‐Newtonian fluid past a stretching sheet is analyzed in this paper. Results in a non‐dimensional form are presented here for the velocity and temperature profiles assuming different kind of boundary conditions.

Calculus of variations in the context of exterior differential systems

A new approach to the study of variational problems defined through functionals given by multiple integrals is presented. This work is based on techniques from the theory of exterior differential systems. Different kinds of boundary conditions are formulate for well-posed variational problems. Sufficient conditions for an integral manifold to be a local extremum are established. Applications to the study of string theory as well as some other examples are discussed.

A semi-analytic treatment of three-dimensional statics of marine cables

A semi-analytic approach is presented in this paper which is capable of predicting the static performance of marine cables. The solution is derived as a function of only three parameters which can be solved numerically by implementing different kinds of boundary conditions. The efficiency and accuracy of the method permit quick parametric studies for optimal selection of the system particulars which is undoubtedly useful for preliminary design. A number of numerical examples demonstrates the validity of the approach adopted.

Long-time behavior of the one-particle distribution function for the Knudsen gas in a convex domain.

In this paper some insight into the behavior of the one-particle distribution function describing the Knudsen gas in a convex-plane domain is given. The influence of different kinds of boundary conditions is studied, namely of those following ergodic or chaotic reflection laws and of those with a stable periodic orbit. By applying numerical and theoretical methods it is shown that, under appropriate boundary conditions and after a sufficiently long period of time, there appear enclaves free of particles in the configuration space, and moreover the collection of limiting velocities reached by every particle is finite. On the basis of this result we prove that the one-particle distribution function becomes nonanalytic after a sufficiently long period of time, independent of the initial conditions. On the other hand, it turns out that in our model ergodicity or chaotic properties of the reflection law imply ergodicity or chaotic behavior of the Knudsen gas, respectively. From this result some related properties of the one-particle distribution function of the corresponding Knudsen gas for long periods of time are deduced.

On the coerciveness property of the biharmonic operator

We consider the weak formulation of the bilurmonic equation under two different kinds of boundary conditions. It is shown, in one case, that the coerciveness of the bilinear form associated can be easily deduced by using the continuous- dependence result for the Laplace equation with Dirichlet data. In the second case, a generalized l'oincare inequality is readily employed.

The extended rigorous cellular method: Theory and applications to thin films

The extended rigorous cellular method is derived in a form which allows different kinds of boundary conditions for the wave function. Within the resulting computing scheme it is possible to calculate the electronic structure of crystals with and without a surface, of molecular clusters and of solid films on the basis of local potentials. The method works both for metals and semiconductors and can easily be modified to include relativistic effects. Results of the two-dimensional band structure for (001) films of lithium, copper, palladium and tungsten consisting of one or three layers are presented.

Stochastic analysis of a chemical reaction with spatial and temporal structures

A stochastic analysis of the spatial and temporal structures in the Prigogine-Lefever-Nicolis model (the Brusselator) is presented. The analysis is carried out through a Langevin equation derived from a multivariate master equation using the Poisson representation method, which is used to calculate the spatial correlation functions and the fluctuation spectra in the Gaussian approximation. The case of an infinite three-dimensional system is considered in detail. The calculations for the spatial correlation functions and the fluctuation spectra for a finite system subject to different kinds of boundary conditions are also given.

Numerical solution of static and dynamic equations of cables

Abstract The mechanical equations of an extensible, perfectly flexible curvilinear material (cable) are formulated. The static problem can be solved either by a minimization technique or by an iterative finite difference method which also permits dealing with forces that are not derived from a potential. In the dynamic alternative the solution of the equations is obtained from finite difference discretization explicit in time - this can apply to different kinds of constitutive laws and to different kinds of boundary conditions. Application of these numerical methods to electric transmission lines subject to electromagnetic forces shows a good agreement between computation and experimental data.