Boundary knot method for 2D and 3D Helmholtz and convection-diffusion problems under complicated geometry

The boundary knot method (BKM) of very recent origin is an inherently meshless, integration-free, boundary-type, radial basis function collocation technique for the numerical discretization of general partial differential equation systems. Unlike the method of fundamental solutions, the use of non-singular general solution in the BKM avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain. The purpose of this paper is to extend the BKM to solve 2D Helmholtz and convection-diffusion problems under rather complicated irregular geometry. The method is also first applied to 3D problems. Numerical experiments validate that the BKM can produce highly accurate solutions using a relatively small number of knots. For inhomogeneous cases, some inner knots are found necessary to guarantee accuracy and stability. The stability and convergence of the BKM are numerically illustrated and the completeness issue is also discussed.

Laboratory Study on Sediment Diffusion and Deposition into Blind Channels

Any waterway with one end closed and the other open is generally called a blind channel. The main flow tends to expand, separate, and cause circulation at the mouth of blind channels. The main flow continuously transfers momentum and sediment into the circulation region through the turbulent mixing region (TMR) between them, thus leading to a large amount of sediment deposition in the blind channels. This paper experimentally investigated the properties of the water flow and sediment diffusion in TMR, demonstrating that both water flow and sediment motion in TMR approximately coincide with a similar structure as in the free mixing layer induced by a jet. The similarity functions of flow velocity and sediment concentration are then assumed, based on observation, and the resulting calculation of these functions is substantially facilitated. For the kind of low velocity flow system of blind channels with a finite width, a simple formula for the sediment deposition rate in blind channels is established by analyzing the gradient of crosswise velocity and sediment concentration in TMR.

Diffusion mechanisms in the Fe3ASi

In this paper, the possible reasons for the high thermal vacancy concentration and the low migration barriers for the Fe atom diffusion in the DO3 structure Fe3Si have been discussed.

Molecular Dynamics Modeling of Diffusion Bonding

Molecular dynamics simulations on diffusion bonding of Cu-Ag showed that the thickness of the interfacial region depended on the stress. The interfacial region became amorphous during diffusion bonding, and it would normally transform from amorphous into crystalline structure when the structure was cooled to the room temperature.

Effect of diffusion on coating microstructure and oxidation resistance of aluminizing steel

The effect of diffuse treatment on coating microstructure and oxidation resistance at high-temperature of hot-dip aluminum were studied by means of TEM, SEM and XRD. The results show that, the diffusion temperature has significant effect on structure of coatings and its oxidation resistance. After diffusion at 750 degreesC, the coating consists of thick outer surface layer (Fe2Al5+ FeAl2), thin internal layer (FeAl + stripe FeAl2), and its oxidation resistance is poor. After diffusion at 950 degreesC, the outer surface layer is composed of single FeAl2 phase, the internal layer is composed of FeAl phase, and its oxidation resistance declines due to the occurrence of early stage internal oxidation cracks in the coating. After diffusion at 850 degreesC, the outer surface layer becomes thinner and consists of FeAl2 Fe2Al5(small amount), the internal layer becomes thicker and consists of FeAl+spherical FeAl2, and the spheroidized FeAl2 phase in the internal layer and its existing in FeAl phase steadily improve the oxidation resistance of the coating.

Observation Of Diffusion Process Of A Water Droplet Immersed In Protein Solution In Microgravity

Pure liquid - liquid diffusion driven by concentration gradients is hard to study in a normal gravity environment since convection and sedimentation also contribute to the mass transfer process. We employ a Mach - Zehnder interferometer to monitor the mass transfer process of a water droplet in EAFP protein solution under microgravity condition provided by the Satellite Shi Jian No 8. A series of the evolution charts of mass distribution during the diffusion process of the liquid droplet are presented and the relevant diffusion coefficient is determined.

Atomistic investigation of the effects of temperature and surface roughness on diffusion bonding between Cu and Al

Molecular dynamics (MD) simulations are carried out to analyze the diffusion bonding at Cu/Al interfaces. The results indicate that the thickness of the interfacial layer is temperature-dependent, with higher temperatures yielding larger thicknesses. At temperatures below 750 K, the interface thickness is found to increase in a stepwise manner as a function of time. At temperatures above 750 K, the thickness increases rapidly and smoothly. When surface roughness is present, the bonding process consists of three stages. In the first stage, surfaces deform under stress, resulting in increased contact areas. The second stage involves significant plastic deformation at the interface as temperature increases, resulting in the disappearance of interstices and full contact of the surface pair. The last stage entails the diffusion of atoms under constant temperature. The bonded specimens show tensile strengths reaching 88% of the ideal Cu/Al contact strength. (c) 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Diffusion dominated process for the crystal growth of a binary alloy

The pure diffusion process has been often used to study the crystal growth of a binary alloy in the microgravity environment. In the present paper, a geometric parameter, the ratio of the maximum deviation distance of curved solidification and melting interfaces from the plane to the radius of the crystal rod, was adopted as a small parameter, and the analytical solution was obtained based on the perturbation theory. The radial segregation of a diffusion dominated process was obtained for cases of arbitrary Peclet number in a region of finite extension with both a curved solidification interface and a curved melting interface. Two types of boundary conditions at the melting interface were analyzed. Some special cases such as infinite extension in the longitudinal direction and special range of Peclet number were reduced from the general solution and discussed in detail.

Numerical simulation of hypersonic viscous flow around space shuttle with method of diffusion analogy

Hypersonic viscous flow around a space shuttle with M(infinity) = 7, Re = 148000 and angle of attack alpha = 5-degrees is simulated numerically with the special Jacobian matrix splitting technique and simplified diffusion analogy method. With the simplified diffusion analogy method the efficiency of computation and resolution of the shock can be improved.

A perturbational h4 exponential finite-difference scheme for the convective diffusion equation

A perturbational h4 compact exponential finite difference scheme with diagonally dominant coefficient matrix and upwind effect is developed for the convective diffusion equation. Perturbations of second order are exerted on the convective coefficients and source term of an h2 exponential finite difference scheme proposed in this paper based on a transformation to eliminate the upwind effect of the convective diffusion equation. Four numerical examples including one- to three-dimensional model equations of fluid flow and a problem of natural convective heat transfer are given to illustrate the excellent behavior of the present exponential schemes, the h4 accuracy of the perturbational scheme is verified using double precision arithmetic.

H4 exponential finite-difference scheme for convective diffusion-equations

Perturbations are applied to the convective coefficients and source term of a convection-diffusion equation so that second-order corrections may be applied to a second-order exponential scheme. The basic Structure of the equations in the resulting fourth-order scheme is identical to that for the second order. Furthermore, the calculations are quite simple as the second-order corrections may be obtained in a single pass using a second-order scheme. For one to three dimensions, the fourth-order exponential scheme is unconditionally stable. As examples, the method is applied to Burgers' and other fluid mechanics problems. Compared with schemes normally used, the accuracies are found to be good and the method is applicable to regions with large gradients.

Diffusion analogy and shock capturing for solving aerodynamic equations

Improving the resolution of the shock is one of the most important subjects in computational aerodynamics. In this paper the behaviour of the solutions near the shock is discussed and the reason of the oscillation production is investigated heuristically. According to the differential approximation of the difference scheme the so-called diffusion analogy equation and the diffusion analogy coefficient are defined. Four methods for improving the resolution of the shock are presented using the concept of diffusion analogy.

Diffusion sliding rate in the binary gaseous mixture

radiation incident upon a test cell filled with gaseous SF6 has