Numerical simulation for nonstationary Mach reflection of a shock wave: A kinetic-model approach

Abstract

Abstract. A numerical simulation was performed for the process of formation of single Mach reflection on a wedge by soiving a BGK type kinetic equation for the reduced disl;ribution function with a finite difference ,;cheme. The calculations were carried out for a shock Math number 2.75 and wedge angle 250 in a monatomic gas, which corresponds to the conditions of single Mach reflection in the, classical yon Neumann theory. The calculations were performed for both diffuse and specular reflection of molecules at the wall surface. It is concluded that the diffuse reflection of molecules at the wall surface or the existence of the viscous or thermal layer is an essential factor for a nonstationary process at the initial stage of Mach reflection. Furthermore, the numerical results for diffuse reflection are found to simulate the experimental results very well, such as a transient process from regular reflection to Math reflection along with shock propagation.

Implementation of unsteady sampling procedures for the parallel direct simulation Monte Carlo method

“…The test case was chosen to correspond to one of the experimental conditions of Walenta [32] and subsequently investigated using a BGK scheme by Xu and Honma [33]. from the equivalent case simulated by Xu and Honma [33] is also given, which shows good qualitative agreement with the present results. Figure 20 shows the density contours at a further two points in the flow: when the shock reaches approximately 40λ 1 and 110λ 1 respectively.…”

“…Again, in each case the resolution of the flow structure is greatly enhanced by using DREAM. Figure 21 shows a comparison of the normalized density profile between the experimental data by Walenta [32], the BGK simulation by Xu and Honma [33] and the data from the present simulation at a point approximately 17.5λ 1 behind the leading edge when the shock reaches 40λ 1 . Both the simulated profiles agree qualitatively, as they both use specular walls, however they differ from the experimental data due to the different wall conditions in the experiment.…”

“…Experimental studies of relatively rarefied flows have been carried out by Walenta [31,32] and comparable simulations using both DSMC and BGK solvers have been carried out by Xu et al [22,33]. At the continuum level, the impingement of a planar Mach 2 shock of ideal air over a 46º wedge is frequently used as a bench mark test for advanced numerical schemes in gas dynamics.…”

DSMC approach to nonstationary Mach reflection of strong incoming shock waves using a smoothing technique

“…Seiler (1985) investigated the pseudo-stationary Mach reflection of relatively weak shock waves (Mach number 3) and the influence of the different reflection conditions on the surface in some detail by using the same method. In 1990, Xu et al (1991aXu et al ( , 1991b investigated the nonstationary process of shock wave reflection under different wedge surface conditions by using a kinetic-model approach, in which a BGK type kinetic equation was solved by using a MacCormack difference scheme combined with techniques of general transformation and operator splitting. The scheme was proved to be efficient for analyzing unsteady flow fields.…”

“…smoothing technique is verified to be useful to estima te the flow fields qualitatively and even quantitatively by using a relatively small sample size. The comparison between the present approach and the kineticmodel approach (Xu et al 1991a(Xu et al , 1991b on the application to unsteady rarefied flow fields was also carried out. …”