Numerical computation for acoustic problem using a cell-based smoothed radial point interpolation method
YAO ling-yun; YU de-jie; ZANG xian-guo
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State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082
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出版日期
1900-01-01
1900-01-01
2011-10-25
发布日期
2011-10-25
摘要
针对标准的有限元法分析声学问题时由于数值色散导致高波数计算结果不可靠问题，将分区光滑径向点插值法(cell-based smoothed radial point interpolation method, CS-RPIM)应用到二维声学分析中，推导了分区光滑径向点插值法分析二维声学问题的原理公式。该方法将问题域划分为三角形背景单元，每个单元进一步分成若干个光滑域，对每个光滑域进行声压梯度光滑处理，运用光滑Galerkin弱形式构造系统方程，并按有限元中方法施加必要的边界条件。CS-RPIM提供了合适的模型硬度，能有效降低色散效应，提高计算精度。对管道和二维轿车声学问题的数值分析结果表明，与标准有限元法相比，CS-RPIM具有更高的精度和准确度，在高波数计算时这种优势特别明显。
Abstract
It is well known that the standard finite element method (FEM) is unreliable to compute approximate solutions of the Helmholtz equation for high wave numbers due to the numerical dispersion. The cell-based smoothed radial point interpolation method (CS-RPIM) is extended to solve the 2D acoustic problem and the formulation of CS-RPIM is presented for the two-dimensional acoustic problem. In present method, the acoustic domain is discretized using triangular background cells, and each cell is further divided into several smoothing cells, the acoustic gradient smoothing technique is implemented to each smoothing cell. The system equations are derived using the smoothed Galerkin weak form, and the essential boundary conditions are imposed directly as in the finite element method (FEM). The CS-RPIM will greatly reduce the numerical dispersion error and obtain accurate results for acoustic problems because of the properly softened stiffness. Numerical examples have been studied, including a tube and a 2D problem of a car acoustic problem and the results show that the CS-RPIM achieves more accurate results and higher convergence rates as compared with the corresponding finite elements, especially for high wave number.
YAO ling-yun;YU de-jie; ZANG xian-guo.
Numerical computation for acoustic problem using a cell-based smoothed radial point interpolation method[J]. Journal of Vibration and Shock, 2011, 30(10): 188-192
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