We compare the thickness of shock-wave fronts at different Mach numbers, modeled via NavierStokes ͑NS͒ equations, with experimental results from the literature. Monoatomic argon and helium are considered. In this modeling a finite-difference scheme with second-order spatial accuracy is employed. For argon the calculated density thickness is in good agreement with the experimental results. For helium the NS results agree well with those from the bimodal model and with the few available experimental data. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.1921267͔The strong gradients within a shock-wave lead to a number of associated effects of scientific and technological relevance which have attracted the attention of theoreticians and experimentalists for a long time. Though the main features of shock waves are well understood, much remains to be done to complete the prediction of their quantitative aspects. The structure of a stationary shock wave has often been employed as a testing problem for numerical models of rarefied gas flows. In this context the one-dimensional ͑1D͒ shock waves produced in atomic argon and helium have been usual test systems to check the numerical aspects of NavierStokes ͑NS͒ equations by comparison with experiment.From the work done around 1950-1965 it was claimed that the NS approach could yield a reliable description of the density profile of the shock waves just up to Mach number Maϳ 2. This is more or less in accordance with the general validity criteria for the continuum description, as obtained from the classical Chapman-Enskog expansion of Boltzmann equation. A discussion of these aspects has been given by Kogan, 1 Cercignani, 2 and others. [3][4][5] Moreover, due to the sparse experimental temperature and velocity data on welldefined 1D shock waves produced in shock tubes, little was known about the actual merits of NS equations to model the profiles of these quantities across the shock wave. This limitation has prevailed up to now in spite of the wealth of density and temperature data on 2D shock waves produced in jets. 6,7 Unfortunately, 2D flows pose a number of difficulties for numerical modeling of normal shock waves ͑complicated flow pattern, low temperature upstream of the shock, with poorly known dependence of the viscosity on the temperature͒. Therefore, 2D shock waves are not well suited for use in connection with the simple 1D mathematical formulation.The main source of experimental 1D shock-wave density data suited for the present purpose has been compiled and completed with accurate original data by Alsmeyer. 8 In this work the experimental reciprocal thickness of argon and helium 1D shock waves is shown to be well characterized up to Ma= 10, while a few sparse helium data points have been included. Complete argon experimental density profiles were also reported by Alsmeyer for several MaϽ 10 values. Due to the shortage of experimental data on helium, the results of bimodal calculations have been also used as a reference, 9 since they are known to be quite rel...

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We simulate the structure of the shock wave front in the range of Mach numbers from 1.5 to 10 using quasigasdynamic (QGD) equations and Navier -Stokes (NS) equations. The numerical results are compared with published experimental data. QGD and NS calculations produce close results that tightly fit the experimental data, especially for the monatomic argon and helium. The QGD algorithm is found to be more stable than the NS algorithm.