非协调单元在声学边界元法中的应用

摘要

To solve the problem of corner point in surface in BEM, discontinuous element is employed for the discretization of Helmholtz boundary integral equation.The polar coordinate transformation in discontinuous element is presented so as to eliminate the singularity in the integration.Meanwhile, the CHIEF method and the Lagrange multiplier are applied to deal with the non-unique solutions.The value of acoustic pressures at the nodes can be acquired by solving a set of linear algebraic equations, acoustic pressure in grid points are obtained by taking the node average values or element average values.In order to demonstrate the robustness and accuracy of the proposed method, two numerical examples of sound radiation from a pulsating sphere and a cube are presented.The results calculated by discontinuous element are compared with the results determined by continuous element.The results have verified the efficiency and adaptability of the proposed method.%利用非协调元离散Helmholtz边界积分方程,有效地解决协调元计算中的角点问题.为消除积分奇异性,提出了非协调元法中的极坐标变换方法.采用CHIEF法加Lagrange乘子法进行处理特征频率处解的不唯一性.解线性代数方程组获得结点处声压,网格点处的声压通过结点平均或单元平均的方法计算.通过计算脉动球和立方体的表面辐射声压,并将协调元和非协调元的计算结果做了比较,证明本文方法的有效性和对非光滑表面的适应性.