二维声学数值计算的梯度最小二乘加权

发布时间：2019-02-16 10:50

【摘要】：针对传统有限元法求解声学问题由于刚度矩阵过硬导致较大的色散误差,以及在较高波数和网格扭曲时计算精度过低甚至错误的问题,采用移动最小二乘权函数对传统有限元法的声压梯度进行加权重构,推导了梯度移动最小二乘加权(Gradient weighted by moving least-squares,GW-MLS)的二维声学计算公式。对声压梯度的加权重构使得GW-MLS模型的刚度相对于FEM模型得以软化,刚度更接近真实模型刚度。采用与有限元法相同的方式构造质量矩阵和边界积分矢量,保证质量矩阵和边界条件的正确施加和积分精度。通过二维管道声腔模型和二维车内声腔模型算例对所提出的算法进行验证,数值分析结果表明,GW-MLS有效地减少了色散误差的影响,提高了计算精度,尤其是对较高波数和网格扭曲时表现出良好的适应性。
[Abstract]:In order to solve acoustic problems by traditional finite element method (FEM), the stiffness matrix stiffening leads to large dispersion error, and the accuracy of calculation is too low or even wrong when the wave number is higher and the mesh is distorted. The moving least square weight function is used to reconstruct the sound pressure gradient of the traditional finite element method and the two-dimensional acoustic calculation formula of the gradient moving least square weighted (Gradient weighted by moving least-squares,GW-MLS is derived. The weighted reconstruction of the sound pressure gradient makes the stiffness of the GW-MLS model softer than that of the FEM model, and the stiffness is closer to that of the real model. The mass matrix and the boundary integral vector are constructed in the same way as the finite element method to ensure the correct application of the mass matrix and boundary conditions and the accuracy of the integration. The numerical results show that GW-MLS can effectively reduce the influence of dispersion error and improve the accuracy of calculation. Especially, it has good adaptability to higher wave number and mesh distortion.
【作者单位】：湖南大学汽车车身先进设计制造国家重点实验室;
【基金】：国家自然科学基金(11472101);国家自然科学基金重点项目(61232014) 湖南省自然科学基金(2015JJ3037)资助项目
【分类号】：U461.4

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