Harmonic Balance Unified Gas-Kinetic Scheme for Multiscale Periodic Flows
Abstract
A time-domain harmonic balance unified gas-kinetic scheme (HB-UGKS) is developed for simulating periodic non-equilibrium flows across all Knudsen regimes. By applying a time-spectral operator, the unsteady periodic problem is reformulated into a block-coupled, quasi-steady system. To preserve the intrinsic multiscale transportcollision flux coupling of the UGKS, a source-separated formulation incorporates the harmonic balance coupling strictly at the cell-residual level. This allows the periodic limit cycle to be resolved directly via pseudo-time marching with local time-stepping, advancing all temporal collocation points simultaneously and completely bypassing physical startup transients. The framework is validated against three complementary benchmarks: two small-amplitude sheardriven oscillatory flows and a thermally driven cavity under finite-amplitude excitation. The scheme accurately captures intricate non-equilibrium kinetic phenomena, including aspectratio anti-resonance scaling, dynamic shear traction, nonlinear waveform distortions, and acoustic streaming. Across all cases, the HB-UGKS preserves the fidelity of standard timeaccurate simulations, while achieving order-of-magnitude speedups in high-frequency regimes where long transient timescales dominate.
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BibTeX
@misc{zhu2026harmonic,
title = {{Harmonic Balance Unified Gas-Kinetic Scheme for Multiscale Periodic Flows}},
author = {Yuze Zhu and Hangkong Wu and Yufeng Wei and Kun Xu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.03479},
eprint = {2605.03479},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.03479},
}
RIS
TY - UNPB
TI - Harmonic Balance Unified Gas-Kinetic Scheme for Multiscale Periodic Flows
AU - Yuze Zhu
AU - Hangkong Wu
AU - Yufeng Wei
AU - Kun Xu
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2605.03479
UR - https://arxiv.org/abs/2605.03479
AB - A time-domain harmonic balance unified gas-kinetic scheme (HB-UGKS) is developed for simulating periodic non-equilibrium flows across all Knudsen regimes. By applying a time-spectral operator, the unsteady periodic problem is reformulated into a block-coupled, quasi-steady system. To preserve the intrinsic multiscale transportcollision flux coupling of the UGKS, a source-separated formulation incorporates the harmonic balance coupling strictly at the cell-residual level. This allows the periodic limit cycle to be resolved directly via pseudo-time marching with local time-stepping, advancing all temporal collocation points simultaneously and completely bypassing physical startup transients. The framework is validated against three complementary benchmarks: two small-amplitude sheardriven oscillatory flows and a thermally driven cavity under finite-amplitude excitation. The scheme accurately captures intricate non-equilibrium kinetic phenomena, including aspectratio anti-resonance scaling, dynamic shear traction, nonlinear waveform distortions, and acoustic streaming. Across all cases, the HB-UGKS preserves the fidelity of standard timeaccurate simulations, while achieving order-of-magnitude speedups in high-frequency regimes where long transient timescales dominate.
ER -