Operated by Universities Space Research AssociationAccurate Finite Difference Methods for Time-harmonic Wave Propagation*
Operated by Universities Space Research AssociationAccurate Finite Difference Methods for Time-harmonic Wave Propagation*
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DOI：
10.1006/jcph.1995.1134
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发表时间：
1995-07
影响因子：
4.1
通讯作者：
中科院分区：
文献类型：
--
作者：
发展和分析了求解时谐声学问题的有限差分方法。多维非均匀问题的变量，可能是不连续的，系数被认为是，占采用非均匀网格的影响。与标准逐点表示法相比，加权平均表示法对波分辨率的变化不太敏感（由于波数可变或网格不均匀）。方法性能的进一步增强是通过基于推广的帕德近似，或广义定义的衍生物，减少虚假的色散，各向异性和反射，并通过提高源项的表示。所得到的格式在均匀网格上具有四阶精度的局部截断误差，在非均匀网格上具有三阶精度。有关网格方向和分辨率的离散化准则。
Finite difference methods for solving problems of time-harmonic acoustics are developed and analyzed. Multi-dimensional inhomogeneous problems with variable, possibly discontinuous, coefficients are considered, accounting for the effects of employing non-uniform grids. A weighted-average representation is less sensitive to transition in wave resolution (due to variable wave numbers or non-uniform grids) than the standard pointwise representation. Further enhancement in method performance is obtained by basing the stencils on generalizations of Pade approximation, or generalized definitions of the derivative, reducing spurious dispersion, anisotropy, and reflection, and by improving the representation of source terms. The resulting schemes have fourth order accurate local truncation error on uniform grids and third order in the non-uniform case. Guidelines for discretization pertaining to grid orientation and resolution are presented.