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.

A Numerical Study of Indentation Using Indenters of Different Geometry

Finite element simulation of the Berkovich, Vickers, Knoop, and cone indenters was carried out for the indentation of elastic-plastic material. To fix the semiapex angle of the cone, several rules of equivalence were used and examined. Despite the asymmetry and differences in the stress and strain fields, it was established that for the Berkovich and Vickers indenters, the load-displacement relation can closely be simulated by a single cone indenter having a semiapex angle equal to 70.3degrees in accordance with the rule of the volume equivalence. On the other hand, none of the rules is applicable to the Knoop indenter owing to its great asymmetry. The finite element method developed here is also applicable to layered or gradient materials with slight modifications.

High-Resolution Finite Compact Difference Schemes for Hyperbolic Conservation Laws

A finite compact (FC) difference scheme requiring only bi-diagonal matrix inversion is proposed by using the known high-resolution flux. Introducing TVD or ENO limiters in the numerical flux, several high-resolution FC-schemes of hyperbolic conservation law are developed, including the FC-TVD, third-order FC-ENO and fifth-order FC-ENO schemes. Boundary conditions formulated need only one unknown variable for third-order FC-ENO scheme and two unknown variables for fifth-order FC-ENO scheme. Numerical test results of the proposed FC-scheme were compared with traditional TVD, ENO and WENO schemes to demonstrate its high-order accuracy and high-resolution.

Using internal fibre geometry to improve the performance of pin-loaded holes in composite materials

The anisotropic nature of fibre reinforced composites leads to large stress concentrations around pin-loaded holes through standard weave cloths. Proper understanding of how this anisotropic nature affects the load distribution around holes can be utilised to reduce these con-centrations if sufficient thought is given to the internal fibre geometry near to the hole. Such local reinforcements need not be highly complex and can be readily produced without excessive effort, producing significant improvements in performance. © 1996 Kluwer Academic Publishers.

A geometry model for tortuosity of flow path in porous media

A simple geometry model for tortuosity of flow path in porous media is proposed based on the assumption that some particles in a porous medium are unrestrictedly overlapped and the others are not. The proposed model is expressed as a function of porosity and there is no empirical constant in this model. The model predictions are compared with those from available correlations obtained numerically and experimentally, both of which are in agreement with each other. The present model can also give the tortuosity with a good approximation near the percolation threshold. The validity of the present tortuosity model is thus verified.

Fractal geometry model for effective thermal conductivity of three-phase porous media

An approximate model, a fractal geometry model, for the effective thermal conductivity of three-phase/unsaturated porous media is proposed based on the thermal-electrical analogy technique and on statistical self-similarity of porous media. The proposed thermal conductivity model is expressed as a function of porosity (related to stage n of Sierpinski carpet), ratio of areas, ratio of component thermal conductivities, and saturation. The recursive algorithm for the thermal conductivity by the proposed model is presented and found to be quite simple. The model predictions are compared with the existing measurements. Good agreement is found between the present model predictions and the existing experimental data. This verifies the validity of the proposed model. (C) 2004 American Institute of Physics.