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

Abstract

Abstract. The direct simulation Monte Carlo (DSMC)method is applied to simulation of nonstationary Mach reflection of strong shock waves. Normally the DSMC method is very time consuming in solving unsteady flow field problems especially for high Mach numbers, because of the necessity of iterative calculations to eliminate the inherent statistical fluctuation caused by a finite sample size. A centrail weighted smoothing technique is introduced to process the DSMC results, so that the iteration time can be significantly reduced. In spite of some relaxations of the shock wave structure, the. 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.

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

“…This is because reducing the statistical scatter significantly in time-averaged data necessitates a very large number of simulation particles with consequent large computational times. Other researchers have attempted to use data smoothing to prepare their results for presentation [22], however ultimately this removes data which may have physical significance.…”

“…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.…”

“…The associated high computational expense and large memory requirements mean that investigations in the literature tend to be restricted to one-dimensional problems, such as shock tube flow [21] or the shock waves generated by moving pistons [1]. Two dimensional unsteady problems have been attempted, and one method of decreasing the statistical scatter of the results is to using statistical smoothing procedures [22]. Bird's two-dimensional axisymmetric code DS2V [8] incorporates unsteady sampling techniques in which a number of time intervals close to the sampling point are averaged (usually termed "time-averaging"), however this single processor code is unable to model processes such as PP-CVD with acceptable run-times [23].…”