An unstructured finite-volume Helmholtz method with perfectly matched layers for heterogeneous two-phase acoustics
Abstract
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 L2 error decreases to 2.657×10−4. 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.
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BibTeX
@misc{xu2026unstructured,
title = {{An unstructured finite-volume Helmholtz method with perfectly matched layers for heterogeneous two-phase acoustics}},
author = {Chuanchao Xu and Jun Liu and Jan Helge Dörsam and Mario Kupnik and Tomislav Maric and Dieter Bothe},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01593},
eprint = {2610.01593},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01593},
}
RIS
TY - UNPB
TI - An unstructured finite-volume Helmholtz method with perfectly matched layers for heterogeneous two-phase acoustics
AU - Chuanchao Xu
AU - Jun Liu
AU - Jan Helge Dörsam
AU - Mario Kupnik
AU - Tomislav Maric
AU - Dieter Bothe
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.01593
UR - https://arxiv.org/abs/2610.01593
AB - 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 2.657×10^−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.
ER -