It is well known that the standard finite element method ( FEM) is unreliable to compute approximate solutions to Helmholtz equation for high wave numbers due to numerical dispersion. The cell-based smoothed radial point interpolation method ( CS-RPIM) was extended to solve 2D acoustic problems and the formulation of CS-RPIM was presented for two-dimensional acoustic problems. With this method, the acoustic domain was discretized using triangular background cells, and each cell was further divided into several smoothing cells, the acoustic pressure gradient smoothing technique was implemented to each smooth cell. The system equations were derived using the smoothed Galerkin weak form, and the necessary boundary conditions were imposed directly according to the finite element method ( FEM). The CS-RPIM greatly reduced the numerical dispersion error and obtained accurate results for acoustic problems because it provided a properly softened model stiffness. Numerical examples including a tube and a 2D acoustic problem of a car were analyzed and the results showed that the CS-RPIM achieves more accurate solutions and higher convergence rates as compared with the corresponding finite element method, especially, for higher wave numbers.%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.
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