A Parallel Algorithm for the Convection Diffusion Problem

Based on the second-order compact upwind scheme, a group explicit method for solving the two-dimensional time-independent convection-dominated diffusion problem is developed. The stability of the group explicit method is proven strictly. The method has second-order accuracy and good stability. This explicit scheme can be used to solve all Reynolds number convection-dominated diffusion problems. A numerical test using a parallel computer shows high efficiency. The numerical results conform closely to the analytic solution.     

Fast Multipole BEM for 3-D Elastostatic Problems with Applications for Thin Structures

The fast multipole method (FMM) has been used to reduce the computing operations and memory requirements in large numerical analysis problems. In this paper, the FMM based on Taylor expansions is combined with the boundary element method (BEM) for three-dimensional elastostatic problems to solve thin plate and shell structures. The fast multipole boundary element method (FM-BEM)requires O(N) operations and memory for problems with N unknowns. The numerical results indicate that for the analysis of thin structures, the FM-BEM is much more efficient than the conventional BEM and the accuracy achieved is sufficient for engineering applications.     

Daubechies Wavelet Meshless Method for 2-D Elastic Problems

This paper introduces a meshless method based on Daubechies （DB） wavelets for 2-D elastic problems. The scaling and wavelet functions of the DB wavelet are used as basis functions to approximate the unknown field functions, so there is no need to construct costly shape functions as in the finite element method （FEM） and other meshless methods. In addition, the properties of the DB wavelets facilitate implementation of the method. The new method is used to analyze the elastic problem of a plain plate with a circle hole, and the numerical results agree well with the FEM. This method is effective and can be extended to solve complicated two or three dimensional problems.     

An Improved Heat Transfer Model for Flame Resistant Fabric Used in Thermal Protective Clothing

An improved numerical heat transfer model considering pyrolysis effect is proposed to predict thermal performance of heat-resistant fabric subjected to radiant heat flux. The model incorporates the heat-induced changes in fabric thermophysical properties. The new model has been validated with data from modified Radiant Protective Performance （RPP） tests of flame-resistant cotton fabrics. Comparison with experimental data shows that the predictions of mass loss rates and temperature profiles within the charring material and skin simulant are in reasonably good agreement with the experiments. Results from the numerical model contribute to a better understanding of the heat transfer process within flame-resistant fabrics under high heat flux conditions, and also to establish a systematic method for analyzing heat transfer in other fibrous materials applications.     

Stability and Accuracy Analysis for Taylor Series Numerical Method

The Taylor series numerical method (TSNM) is a time integration method for solving problems in structural dynamics. In this paper, a detailed analysis of the stability behavior and accuracy characteristics of this method is given. It is proven by a spectral decomposition method that TSNM is conditionally stable and belongs to the category of explicit time integration methods. By a similar analysis, the characteristic indicators of time integration methods, the percentage period elongation and the amplitude decay of TSNM, are derived in a closed form. The analysis plays an important role in implementing a procedure for automatic searching and finding convergence radii of TSNM. Finally, a linear single degree of freedom undamped system is analyzed to test the properties of the method.     

Non-Fourier Heat Conduction Effects During High-Energy Beam Metalworking

Non-Fourier heat conduction induced by ultrafast heating of metals with a high-energy density beam was analyzed. The non-Fourier effects during high heat flux heating were illustrated by comparing the transient temperature response to different heat flux and material relaxation times. Based on the hyperbolic heat conduction equation for the non-Fourier heat conduction law, the equation was solved using a hybridmethod co mbining an analytical solution and numerical inversion of the Laplace transforms for a semiinfinite body with the heat flux boundary. Analysis of the temperature response and distribution led to a criterion for the applicability of the non-Fourier heat conduction law. The results show that at a relatively large heat flux, such as greater than 108 W/cm2, the heat-affected zone in the metal material experiences a strong thermal shock as the non-Fourier effects cause a large step increase in the surface temperature. The results provide a method for analyzing transient heat conduction problems using a high-energy density beam, such as electron beam deep penetration welding.     

An optimized staggered variable-grid finite-difference scheme and its application in cross-well acoustic survey

In this paper, an optimized staggered variable-grid finite-difference （FD） method is developed in velocity-stress elastic wave equations. On the basis of the dispersion-relation-preserving （DRP）, e fourth-order finite-difference operator on non-uniform grids is constructed. The proposed algorithm is e continuous variable-grid method. It does not need interpolations for the field variables between regions with the fine spacing end the coarse one. The accuracy of the optimized scheme has been veri-fled with an analytical solution end e regular staggered-grid FD method for the eighth order accuracy in space. The comparisons of the proposed scheme with the variable-grid FD method based on Taylor series expansion ere made. It is demonstrated that this optimized scheme has less dispersion errors than that with Teylor＇s series expansion. Thus, the proposed scheme uses coarser grids in numerical simulations than that constructed by the Teylor＇s series expansion. Finally, the capability of the opti-mized FD is demonstrated for e complex cross-well acoustic simulation. The numerical experiment shows that this method greatly saves storage requirements and computational time, and is stable.     

Singular and Regular Implementations of the Hybrid Boundary Node Method

The hybrid boundary node method （HdBNM） combines a modified function with the moving least squares approximation to form a boundary-only truly meshless method. This paper describes two implementations of the HdBNM, the singular hybrid boundary node method （ShBNM） and the regular hybrid boundary node method （RhBNM）. The ShBNM and RhBNM were compared with each other, and the parameters that influence their performance were studied in detail. The convergence rates and their applicability to thin structures were also investigated. The ShBNM and RhBNM are found to be very easy to implement and to efficiently obtain numerical solutions to computational mechanics problems.     

FM-BEM Evaluation for Effective Elastic Moduli of Microcracked Solids

A fast multipole boundary element method (FM-BEM) was applied for the analysis of microcracked solids. Both the computational complexity and memory requirement are reduced to O(N), where N is the number of degrees of freedom. The effective elastic moduli of a 2-D solid containing thousands of randomly distributed microcracks were evaluated using the FM-BEM. The results prove that both the differential method and the method proposed by Feng and Yu provide satisfactory estimates to such problems. The effect of a non-uniform distribution of microcracks has been studied using a novel model. The numerical results show that the non-uniform distribution induces a small increase in the global stiffness.     

Finite Point Method for the Simulation of Solidification and Heat Transfer in Continuous Casting Mold

A 2-D finite point meshless model was used to simulate the heat transfer and solidification of steel in continuous casting molds to illustrate its use in metallurgy. The latent heat of the pure metal was treated using the temperature recovery method and the latent heat of the alloy was treated using an apparent heat capacity method. The model was validated by calculating the classical Stefan moving boundary problem. Analysis of the solid shell growth and temperature distribution of a billet in a mold shows that the solution by the finite point meshless model is quite reasonable, which indicates that the model has potential in metallurgical engineering applications.     

轴对称问题中的无网格Galerkin法

采用无网格Galerkin法分析轴对称问题，得到弹性力学中的对称问题的无网格离散方程．将这一方法与有限元耦合，即在边界处布置有限单元，这样就可以用传统有限元方法方便地处理力学边界条件．算例考察表明：本文方法通过了分片检验，计算结果达到了较高的精度，最大误差不超过5％．     

无网格法计算误差分析

探讨了无网格法中形函数的性态及对计算结果的影响 ,讨论了无网格法产生误差的原因 .主要分析了无网格伽辽金法 (EFGM )节点不良分布以及采用一般高次多项式基构造形函数时 ,致使形函数中矩阵A(X)病态 ,从而导致全局数值解振荡的原因 .就不同的基函数对插值函数及无网格法的计算精度的影响作了分析比较 ,得出了基函数的选取标准 ,算例说明使用三次基函数计算精度最高 .     

无网格伽辽金法(EFGM)求解接触问题

本文考虑到无网格伽辽金法只需节点信息,不需将节点连成单元,并且有精度高,后处理方便等优点,从而用它求解接触问题。这里采用的方法是将Ｋａｔｏｎａ界面单元引入ＥＦＧＭ,迭代求得两物体间的接触状态。算例表明,本文方法基本可行。     

用加权最小二乘无网格法求解抛物方程

加权最小二乘无网格法是一种新的高效无网格法,鉴于传统数值方法求解动态问题网格限制的缺陷,将传统差分法和加权最小二乘无网格法结合构造差分一加权最小二乘无网格方法,应用于求解一维与时间相关的线性抛物方程;该方法在空间域上的离散彻底摆脱了网格的束缚,算例表明：该方法计算量较小,并能够保证较高的精度．     

次弹性材料的无网格分析方法研究

次弹性材料在实际工程中是常见的，传统计算中大多数采用有限元方法。利用无网格伽辽金法对次弹性材料进行数值计算，并通过罚参数来实现本质边界条件，推导了求解此类问题的无网格伽辽金法离散格式。算例结果表明，无网格伽辽金法处理次弹性材料时，具有较高的计算精度，是一种有效的数值计算方法。     

Signorini问题的插值型边界无单元法

本文将改进的移动最小二乘插值法和边界积分方程结合,提出了求解Signorini问题的一种新的边界类型无网格方法——插值型边界无单元法.该方法用投影算子处理Signorini问题中的非线性边界不等式条件,然后将Signorini问题归化为边界积分方程,并用改进的移动最小二乘插值法近似未知的边界变量,然后本文分析了该方法的收敛性.数值算例表明该方法在求解Signorini问题时的可行性和有效性,相对于边界元方法也具有更好的精度和收敛速度.     

三维瞬态热传导问题的无网格对称粒子法

为了准确分析瞬态热传导问题,构造了一种三维无网格对称粒子法。首先,基于泰勒级数展开和加权最小二乘方法导出了一阶导数的对称粒子近似。然后,利用得到的粒子近似离散一阶导数,建立了求解三维瞬态热传导问题的无网格对称粒子法。应用该方法计算了各向同性介质中的瞬态热传导问题,得到了典型时刻的温度分布,计算结果与解析解吻合良好,验证了该方法的正确性。进一步将该方法应用于各向异性介质热传导和非线性热传导问题,计算结果与有限元法的计算结果非常接近,说明该方法对于复杂热传导问题的求解也是可行的。     

无网格法中一种新型权函数研究和应用

文章基于概率论和误差理论,提出了一种新的权函数——正态权函数(Normal weight function),从理论和实践上证明了它的实用、可行性。通过一维杆和二维梁实例,把正态权函数与现有流行的权函数进行比较,说明它是一种受影响域半径变化的影响较小、高效实用的权函数。最后给出了正态权函数影响域半径的确定规则。     

无网格伽辽金法在裂纹扩展计算中的应用

采用了一种基于t-分布的新型权函数，提高了无网格伽辽金法的计算精度；采用完全变换法处理本质边界条件，实现了本质边界条件在节点处的精确施加；针对裂纹扩展中的实际情况，对动态影响半径法作了进一步的补充和改进．算例验证了方法的正确性和有效性．     

基函数的阶数对无单元伽辽金方法精度的影响

无单元伽辽金(Element-Free Galerkin)方法是无网格方法中很重要的一种数值计算方法,利用无单元伽辽金方法求解二维稳态热传导方程,当选取基函数为线性基、二次基时,分别将数值解和解析解对比,分析了基函数的阶数对无单元伽辽金方法精度的影响,并说明无单元伽辽金方法是一种高精度的数值计算方法 .