一种带完美匹配层的非结构化有限体积亥姆霍兹方法用于非均匀两相声学
An unstructured finite-volume Helmholtz method with perfectly matched layers for heterogeneous two-phase acoustics
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中文总结 AI 辅助
提出一种带PML的非结构化有限体积亥姆霍兹方法，用于非均匀两相声学，通过体积分数和面分数处理界面，验证了压力二阶收敛及辐射力精度。
中文摘要 AI 辅助
本文提出了一种基于单元中心非结构化有限体积方法，用于求解时谐两相声学问题。体积分数表示提供了密度和声学压缩率。面分数平均可用的相邻平面界面切割，且与速度方向无关，保留了已建立的单场面密度闭合。笛卡尔复坐标拉伸提供了完美匹配层（PML）。实虚分裂产生实值块系统，通过修正的非正交通量和一致的边界贡献进行离散。验证涵盖均匀波、带PML截断的分层气液透射、带基尔霍夫远场重建的挡板活塞辐射，以及解析刚球辐射力。均匀波压力在正交网格和具有非正交内部及正交边界单元的网格上以约二阶收敛。重建速度在正交网格上以约二阶收敛，在后一类网格上观测阶数约为1.7。在一致细化下，分层情况的相对全域复压力$L_2$误差降至$2.657\ imes10^{-4}$。在测试的瑞利尺寸范围内，解析球力与Gorkov预测的差异最多为1.5%。结果量化了非均匀亥姆霍兹-PML公式的准确性和当前局限性。
英文摘要
This paper presents a cell-centred unstructured finite-volume method for time-harmonic two-phase acoustics. A volume-fraction representation supplies density and acoustic compressibility. Face fractions average available neighbouring planar interface cuts independently of velocity direction, retaining the established one-field face-density closure. Cartesian complex-coordinate stretching provides perfectly matched layers (PMLs). Real-imaginary splitting yields a real-valued block system, discretized with corrected non-orthogonal fluxes and consistent boundary contributions. Verification covers homogeneous waves, layered gas-liquid transmission with PML truncation, baffled-piston radiation with Kirchhoff far-field reconstruction, and resolved rigid-sphere radiation forces. Homogeneous-wave pressure converges at approximately second order on orthogonal meshes and on meshes with non-orthogonal interiors and orthogonal boundary cells. Reconstructed velocity converges at approximately second order on orthogonal meshes and with an observed order of about 1.7 on the latter mesh family. Under aligned refinement, the layered case's relative whole-domain complex-pressure $L_2$ error decreases to $2.657\times10^{-4}$. The resolved-sphere force differs from the Gorkov prediction by at most 1.5% over the tested Rayleigh size range. The results quantify the accuracy and current limitations of the heterogeneous Helmholtz-PML formulation.
发表机构
- TU Darmstadt（达姆施塔特工业大学）
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