Revisit viscous shock tube at low Reynolds number
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914507579719680 |
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| author | Zhang, Yue Xu, Kun |
| author_facet | Zhang, Yue Xu, Kun |
| contents | The viscous shock tube is a canonical test case for assessing Navier-Stokes (NS) solvers in the continuum-flow regime, widely used to validate numerical accuracy and probe flow physics. It features a rich set of interacting structures-shock and rarefaction waves, contact discontinuities, boundary layers, and their coupling-spanning multiple spatial and temporal scales. However, NS-based modeling, which presumes near-equilibrium behavior, may fail to capture important non-equilibrium effects even in nominally continuum conditions. This study investigates the viscous shock tube at low Reynolds numbers and demonstrates the presence of non-equilibrium phenomena within the conventional continuum regime. To obtain physically consistent solutions across scales, we employ the unified gas-kinetic scheme (UGKS) and compare its results with NS solutions computed using the gas-kinetic scheme (GKS). Discrepancies between UGKS and GKS solutions reveal pronounced non-equilibrium effects in regions where shock waves interact with boundary layers. For continuum flows at high Mach and low Reynolds numbers, such multiscale non-equilibrium transport becomes important, underscoring the need for multiscale methods in analysis and prediction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23319 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Revisit viscous shock tube at low Reynolds number Zhang, Yue Xu, Kun Fluid Dynamics Computational Physics The viscous shock tube is a canonical test case for assessing Navier-Stokes (NS) solvers in the continuum-flow regime, widely used to validate numerical accuracy and probe flow physics. It features a rich set of interacting structures-shock and rarefaction waves, contact discontinuities, boundary layers, and their coupling-spanning multiple spatial and temporal scales. However, NS-based modeling, which presumes near-equilibrium behavior, may fail to capture important non-equilibrium effects even in nominally continuum conditions. This study investigates the viscous shock tube at low Reynolds numbers and demonstrates the presence of non-equilibrium phenomena within the conventional continuum regime. To obtain physically consistent solutions across scales, we employ the unified gas-kinetic scheme (UGKS) and compare its results with NS solutions computed using the gas-kinetic scheme (GKS). Discrepancies between UGKS and GKS solutions reveal pronounced non-equilibrium effects in regions where shock waves interact with boundary layers. For continuum flows at high Mach and low Reynolds numbers, such multiscale non-equilibrium transport becomes important, underscoring the need for multiscale methods in analysis and prediction. |
| title | Revisit viscous shock tube at low Reynolds number |
| topic | Fluid Dynamics Computational Physics |
| url | https://arxiv.org/abs/2604.23319 |