Title: Grid-converged Solution and Analysis of the Unsteady Viscous Flow in a Two-dimensional Shock Tube,
Abstract: The flow in a shock tube is extremely complex with dynamic multi-scale
structures of sharp fronts, flow separation, and vortices due to the
interaction of the shock wave, the contact surface, and the boundary layer over
the side wall of the tube. Prediction and understanding of the complex fluid
dynamics is of theoretical and practical importance. It is also an extremely
challenging problem for numerical simulation, especially at relatively high
Reynolds numbers. Daru & Tenaud (Daru, V. & Tenaud, C. 2001 Evaluation of TVD
high resolution schemes for unsteady viscous shocked flows. Computers & Fluids
30, 89-113) proposed a two-dimensional model problem as a numerical test case
for high-resolution schemes to simulate the flow field in a square closed shock
tube. Though many researchers have tried this problem using a variety of
computational methods, there is not yet an agreed-upon grid-converged solution
of the problem at the Reynolds number of 1000. This paper presents a rigorous
grid-convergence study and the resulting grid-converged solutions for this
problem by using a newly-developed, efficient, and high-order gas-kinetic
scheme. Critical data extracted from the converged solutions are documented as
benchmark data. The complex fluid dynamics of the flow at Re = 1000 are
discussed and analysed in detail. Major phenomena revealed by the numerical
computations include the downward concentration of the fluid through the curved
shock, the formation of the vortices, the mechanism of the shock wave
bifurcation, the structure of the jet along the bottom wall, and the
Kelvin-Helmholtz instability near the contact surface.