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Revisit viscous shock tube at low Reynolds number
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DOI：10.1017/jfm.2026.11797.png)
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Abstract
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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 couplings – spanning multiple spatial and temporal scales. However; NS-based modelling; which presumes near-equilibrium behaviour; 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.
Keywords:
compressible boundary layers
shock waves
Journal
IF:
3.9
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2.0W
Citations:
9.4W
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