Revisit viscous shock tube at low Reynolds number

TL;DR

This paper examines the viscous shock tube at low Reynolds numbers, revealing non-equilibrium effects in continuum flows and demonstrating the importance of multiscale methods like UGKS over traditional Navier-Stokes solutions.

Contribution

It highlights the significance of non-equilibrium phenomena in low Reynolds number flows and compares UGKS with GKS to improve multiscale flow modeling.

Findings

UGKS captures non-equilibrium effects missed by NS solutions.

Discrepancies between UGKS and GKS are pronounced near shock-boundary layer interactions.

Multiscale methods are essential for accurate continuum flow predictions at low Reynolds numbers.

Abstract

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.