Axisymmetric and three-dimensional boundary integral simulations of bubble growth from an underwater orifice

The formation of bubbles from an underwater orifice is studied by means of a boundary integral method. Since the bubble process is highly transient the flow field is assumed to be irrotational. A potential-flow boundary-integral formulation is employed to simulate the growth of a bubble from a needle in an unbounded domain and in a tube. The geometry of the problem is axisymmetric in these cases. A good agreement is found between the simulations and the experiment for air bubbles of radii ranging from a few hundred microns to several millimeters in water. A three-dimensional boundary integral method is developed to simulate bubble detachment from a non-vertical needle in an unbounded domain. Numerical instabilities commonly associated with the boundary integral technique are found to be even more severe for the three dimensional case and therefore an artificial damping term is introduced to eliminate these instabilities. Even though the simulations often fail just before the pinchoff point, the results compare favorably with the experiment.     

On the choice of interpolation functions used in the dual-reciprocity boundary-element method

The dual-reciprocity boundary-element method is a very powerful technique for solving general elliptic equations of the type ²u=b. In this method, a series of interpolation functions is used to approximate b in order to convert the associated domain integral, which it is necessary to evaluate in a traditional boundary-element analysis, into boundary integrals only. Hence the choice of interpolation functions has direct effects on the numerical results. According to Partridge and Brebbia, the adoption of a comparatively simple form of interpolation function gives the best results. Unfortunately, when b contains partial derivatives of the unknown function u(x, y), the adoption of such a type of interpolation function inevitably leads to the creation of singularities on all boundary and internal nodes used in a dual-reciprocity boundary-element analysis, as was pointed out by Zhu and Zhang in 1992. To avoid this problem, a functional transformation, which applies only to linear governing equations, can be employed to eliminate these derivative terms and thus to obtain better numerical results. In this paper, two new interpolation functions are proposed and examined; they are proven to be generally applicable and satisfactory.     

A symmetric and positive definite variational BEM for 2-D free vibration analysis

A general BEM model for structural dynamics is derived by using a symmetric and positive definite variational formulation. The functional employed involves domain displacements and boundary tractions and displacements. These variables are taken to be independent of one another. The boundary variables are expressed in terms of their nodal values while the domain displacement field is approximated by a linear combination of static fundamental solutions. The source point of the latter is located outside the domain. The resolving system is a linear system and for free vibration a classic linear algebraic eigenvalue problem is inferred. The stiffness and mass matrices are symmetric and positive definite and the domain integral, when associated with the inertial term, can be transformed into a boundary integral. Numerical results are presented to prove the efficiency of the method.     

结构声辐射的源强声辐射模态分析方法

为了解决不易获取复杂结构振速声辐射模态和利用其计算复杂结构外辐射声场困难的问题,提出源强声辐射模态分析方法。该方法利用简单源积分公式将结构表面连续的源强分布等效为一组简单源源强分布,利用这组简单源源强分布构造了结构辐射声功率2次型表达式,其2次型系数定义一个辐射阻矩阵,辐射阻矩阵的特征向量就构成了源强声辐射模态,从而实现复杂结构总辐射声功率的解耦。只要获得声辐射模态的展开系数,声场中的声压、质点法向速度等声学量都可由源强声辐射模态叠加得到。球形声源和棱台体声源的分析表明：源强声辐射模态保留了传统的声辐射模态优点,更方便解决复杂结构声辐射问题。     

A fast higher-order integral equation method for solution of the full potential equation around airfoils

A method based on an integral equation formulation is described for solution of the full potential equation in terms of the velocity field. In addition to the conventional distribution of singularities over the boundaries of field, a field source distribution is added in the flow region in order to represent the non-linear compressibility effect. The unknown source distribution in the field is calculated from the full potential equation by iteratively updating the normal velocity boundary conditions. In order to treat more complex configurations, local transformations provided by higher-order elements are used. Computation time required for integration of the domain is improved by using a domain decomposition. Results of calculations demonstrate substantial improvement in computation time and are in good agreement with independent results.     

基于时域声辐射模态的结构噪声主动控制研究

以简支矩形板为例，提出了利用时域声辐射模态进行声辐射研究，并从物理和数学意义上对时域声辐射模态进行了解释。研究表明时域声辐射模态既与时间无关，也互相独立，使得计算和控制声功率得以简化。针对瞬时声功率主要由第一阶辐射模态的声功率所决定的特点，在时域里进行结构噪声的主动控制研究，通过抵消第一阶辐射模态的声功率使得总的声功率得以有效降低。在此基础上，建立基于最小二乘算法的自适应反馈控制系统，进行仿真计算，结果证明了主动控制策略是有效的。     

运动介质中奇异边界元积分式的精确求解

采用边界元方法求解与运动介质相关声学问题时,难点之一是如何精确计算场点与源点重合所导致的奇异积分式。论文提出一种将具有奇性的单元面积分式拆分为奇性和非奇性积分部分分别进行计算的新方法。对奇性积分部分,经过严格的数学推导给出解析解;而对非奇性积分部分则通过高斯积分法处理。新方法可有效地提高边界元计算精度和效率,对运动介质中的有关声学问题的边界元数值计算具有重要意义。     

A dual-reciprocity boundary element method for axisymmetric thermoelastostatic analysis of nonhomogeneous materials

The problem of determining the axisymmetric time-independent temperature and thermoelastic displacement and stress fields in a nonhomogeneous material is solved numerically by using a dual-reciprocity boundary element technique. Interpolating functions that are bounded in the solution domain but that are in relatively simple elementary forms for easy computation are constructed for treating the domain integrals in the dual-reciprocity boundary element formulation. The proposed numerical approach is successfully applied to solve several specific problems.     

Perfectly matched layers for frequency-domain integral equation acoustic scattering problems

Simulations of acoustic wavefields in inhomogeneous media are always performed on finite numerical domains. If contrasts actually extend over the domain boundaries of the numerical volume, unwanted, non-physical reflections from the boundaries will occur. One technique to suppress these reflections is to attenuate them in a locally reflectionless absorbing boundary layer enclosing the spatial computational domain, a perfectly matched layer (PML). This technique is commonly applied in time-domain simulation methods like finite element methods or finite-difference time-domain, but has not been applied to the integral equation method. In this paper, a PML formulation for the three-dimensional frequency-domain integral-equation-based acoustic scattering problem is derived. Three-dimensional acoustic scattering configurations are used to test the PML formulation. The results demonstrate that strong attenuation (a factor of 200 in amplitude) of the scattered pressure field is achieved for thin layers with a thickness of less than a wavelength, and that the PMLs themselves are virtually reflectionless. In addition, it is shown that the integral equation method, both with and without PMLs, accurately reproduces pressure fields by comparing the obtained results with analytical solutions.     

圆柱绕流噪声预报的流场与声场模拟方法对比研究

以三维圆柱为研究对象,使用Lighthill声类比法研究其绕流发声问题。第一步进行流场计算,分别用大涡模拟(LES)、脱体涡模拟(DES)和瞬态雷诺平均法(URANS)模拟声源区流场,通过对比流场压力和涡量等参数,据此选取合适的流场仿真方法;第二步用基于Lighthill方程FW-H积分法和边界元法预报远场直发声,通过和Revell试验结果比较,分析各种计算方法差别。研究表明:进行流场仿真时LES计算结果最好,IDDES法在保证计算精度条件下能有效减少流场网格数量,URANS法误差很大;进行辐射噪声预报时,FW-H积分法和边界元法基本相同。