Physical Valid Scale of General Continuum Models in Unsteady Flow (Communications in Computational Physics, 2019)
A variety of numerical simulations based on continuum medium modelshave been carried out in unsteady flows to explore the physical characteristics qualitatively. However, there still lack quantitative valid scales for these models, in whichscale the solutions by simulation can be treated as physically credible. In this work,Euler and Navier-Stokes models are implemented on the typical unsteady flow withdiscontinuities: Sod shock tube problem. Firstly, based on the Boltzmann model whosevalid scale is molecule kinetic scale, we compare the values of different moments ofEuler and Navier-Stokes to Boltzmann with the evolution of flow. The results providethe valid scales of Euler and Navier-Stokes models quantitatively. Secondly, followingthe real conditions and parameters in real air, the physical characteristics of waves’generation and evolution in Sod shock tube are observed and analyzed numericallyat the microscopic level for the first time. Our results present the reference scales forthe choice of minimal simulation scale in which the continuum medium models areused, and for the criteria whether the flow characteristics obtained by simulations canbe treated as real physical characteristics.
Keywords: Physical valid scale; continuum model; waves generation; contact discontinuity thickness.