Diagonal form fast multipole boundary element method for 2D acoustic problems based on Burton-Miller boundary integral equation formulation and its applications

This paper describes formulation and implementation of the fast multipole boundary element method (FMBEM) for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the FMBEM are described in details. They are moment calculation, moment to moment translation, moment to local translation, and local to local translation. A data structure for the quad-tree construction is proposed which can facilitate implementation. An analytical moment expression is derived, which is more accurate, stable, and efficient than direct numerical computation. Numerical examples are presented to demonstrate the accuracy and efficiency of the FMBEM, and radiation of a 2D vibration rail mode is simulated using the FMBEM.     

Wideband fast multipole boundary element method: Application to acoustic scattering from aerodynamic bodies

A wideband adaptive multi‐level fast multipole method (MLFMM) is used to accelerate the matrix–vector products arising from a boundary element method (BEM) formulation which solves the Burton–Miller boundary integral equation (BIE). The wideband MLFMM presented here applies a plane wave expansion formulation with fast interpolation and filtering for calculations in the high‐frequency regime and a partial wave expansion formulation with rotation‐coaxial translation in the low‐frequency regime. The iterative solvers GMRES, Bi‐CGSTAB and CGS are tested and compared and a block diagonal preconditioner is used to improve the condition number of the BEM matrices and to accelerate the convergence of the iterative solvers. Details on the implementation of the formulations are described, including the treatment of singular integrals. Results for acoustic scattering from a wing plus engine nacelle configuration for a prescribed source in a subsonic uniform flow are presented for a broad range of frequencies in order to assess the implemented capability. Copyright © 2010 John Wiley & Sons, Ltd.     

One-dimensional piston process in strong gravitational field

In this paper, the dynamic process driven by one-dimensional piston in strong gravitational field was studied on the Cartesian, cylinderical and spherical coordinates. The gasdynamic equations were numerically solved by the characteristic method. The solution which satisfies the velocity condition at piston and the boundary conditions connect the flow region and the quiet region is obtained. The present paper analyses especially the influence of coordinate systems on the field of compressible flow, uniform flow and rarefaction flow region, the shock velocity and the temperature distribution at the piston.     

New type of dual bem and Green's-function-library strategy for fracture analysis in complex structures

A new type of dual boundary integral equations (DBIE) is presented first, through which, a smaller system of equations needs to be solved in fracture analysis. Then a non-conforming crack tip element in two-dimensional problems is proposed. The exact formula for the hypersingular integral over the non-conforming crack tip element is given next. By virtue of Green's-function-library strategy, a series of stress intensity factors (SIF) of different crack orientations, locations and/or sizes in a complicated structure can be obtained easily and efficiently. Finally, several examples of fracture analysis in two dimensions are given to demonstrate the accuracy and efficiency of the method proposed. Partially supported by the Aeronautical Science Foundation of China (No. 99C53026)     

应用SBFEM研究波浪与薄板的相互作用问题

应用比例边界有限元法(SBFEM)求解了频域下波浪与刚性薄板防波堤相互作用问题。求解中将整个计算区域分为薄板周围的有限子域和直到无限远处的无限子域。有限子域的比例中心设置在薄板的下端,这时薄板的两侧为侧边面,而无限子域的比例中心设置在无限子域与有限子域的交界上,同时将水底和自由水面做为平行侧边面。应用加权余量法在每个子域内推导出比例边界有限元方程,然后在有限子域与无限子域交界上匹配求解。通过与解析解的对比,证明了这种方法的精确性,而后对不同类型的薄板防波堤进行了计算,并给出了反射和透射系数的变化规律。     

Application of dual kriging to structural shape optimization based on the boundary contour method

Summary The paper presents an approach in which the coupling of dual kriging and the boundary contour method (BCM) is applied to structural shape optimization problems in mechanical engineering design. The problems consist of optimizing the shape of an elastic body, which requires minimizing an objective function subject to some given constraints, such as those of displacement, stress or manufacturing. The originality of the present work is involved with the use of two novel methods that are combined here to solve structural shape optimization problems. The first one, called dual kriging, is a general, versatile interpolation and geometric modeling tool. The second one is a new variant of the boundary element method (BEM), called the BCM, which achieves a further reduction in dimensionality of analysis problems. Based on the advantages of these two methods, the coupling approach presented here is expected to offer an effective as well as a straightforward manner for solving shape optimal design problems. Received 18 December 1997; accepted for publication 21 April 1998     

Natural convection in porous media—dual reciprocity boundary element method solution of the Darcy model

This paper describes the solution of a steady state natural convection problem in porous media by the dual reciprocity boundary element method (DRBEM). The boundary element method (BEM) for the coupled set of mass, momentum, and energy equations in two dimensions is structured by the fundamental solution of the Laplace equation. The dual reciprocity method is based on augmented scaled thin plate splines. Numerical examples include convergence studies with different mesh size, uniform and non‐uniform mesh arrangement, and constant and linear boundary field discretizations for differentially heated rectangular cavity problems at filtration with Rayleigh numbers of Ra*=25, 50, and 100 and aspect ratios of A=1/2, 1, and 2. The solution is assessed by comparison with reference results of the fine mesh finite volume method (FVM). Copyright © 2000 John Wiley & Sons, Ltd.     

Perturbation solution to the nonlinear problem of oblique water exit of an axisymmetric body with a large exit-angle

In this paper,a nonlinear,unsteady3-D free surface problem of the oblique water exitof an axisymmetric body with a large water exit-angle was investigated by means of theperturbation method in which the complementary angle a of the water exit angle waschosen as a small parameter.The original3-D problem was solved by expanding it into apower series of a and reduced to a number of2-D problems.The integral expressions forthe first three order solutions were given in terms of the complete elliptic functions of thefirst and second kinds.The zeroth-order solution didn‘t turn out to be a linear problem asusual but a nonlinear one corresponding to the vertical water exit for the same body.Computational results were presented for the free surface shapes and the forces exerted upto the second order during the oblique water exit of a series of ellipsoids with various ratiosof length to diameter at different Froude numbers.     

Reissner型板表面裂纹应力强度因子的线弹簧-不连续位移边界积分方程解法

本文由Reissner型板的不连续位移基本解，根据Betti互换定理，导出了Reissuer型板的不连续位移边界积分方程；结合平面问题的不连续位移边界积分方程─—边界元方法和线弹簧模型，给出了Rrissner型板表面裂纹应力强度因子的线弹簧-不连续位移边界积分方程解法。     

自由面势流问题的域外奇点边界元法及其数值误差分析

讨论了域外奇点边界元法在自由面势流问题计算中的作用,并以连续及离散Fourier分析对该方法(就m阶面元的一般情况)进行数值误差分析,导出了计及面元阶数、奇点至自由面垂向距离、配置点移动、差分格式等因素影响的数值误差一般表达式。从理论上证明了自由面势流问题计算中采用域外奇点法可改善离散产生的数值色散误差并能结合配置点前移(向上游)等方法以数值满足辐射条件。