A direct simulation Monte Carlo approach on the Riemann problem for gas mixtures

Abstract

The Direct Simulation Monte Carlo method is employed to solve the "1D -Sod-Shock tube problem", a special case of Riemann problems, for gas mixtures. Initially, two different gas species are distributed separately in the high and low pressure sides of the tube without interacting with each other. For time greater than zero the species start mixing and shock and rarefaction waves are formed moving in opposite directions. In this work, the mixing process between different kinds of gas species was investigated by observing differences in waves' formation. The influence of the mass and diameter ratio between the species was studied in detail. It was found that greater mass differences had very strong effect on the mixing process, while the effects due to diameter differences were relatively small. Finally, it is shown that in case of single species the interaction molecular models of hard sphere, variable hard sphere and variable soft sphere gave the same results, while for gas mixtures the variable hard sphere and variable soft sphere models gave slightly different results.

Mesoscopic Kinetic Approach of Nonequilibrium Effects for Shock Waves

“…This section will introduce the methodology for studying fluid systems using nonequilibrium effects. This approach was proposed and developed by Professor Xu’s research group [ 3 , 8 , 42 ], and we, inspired by their work, have introduced a method to understand and apply nonequilibrium effects from the perspective of molecular motion [ 43 , 44 ]. Here, we will primarily focus on the fundamental ideas of this method, the interpretation based on molecular motion kinematics, and the physical significance of the strength and direction of nonequilibrium effects.…”

“…The following provides an overview of the research progress in this area. It is important to note that in the following research progress, the double-distribution-function LBM model used in references [ 38 , 43 ] is different from the research conducted by Professor Xu’s group, which is based on the Discrete Boltzmann Method (DBM) [ 3 , 17 , 28 , 29 , 30 , 31 ]. The primary objective of this paper is to comprehensively review the advancements in research on the nonequilibrium effects of shock waves.…”

“…Recently, we conducted research on the nonequilibrium effects of the one-dimensional Riemann problem [ 43 ]. The initial conditions are specified as follows: represents density, denotes the transverse velocity, stands for pressure, and represents the reference length.…”

“…By solving the unsteady shock wave reflection problem, the process involves the formation of moving curved shock waves, exhibiting richer shock wave characteristics. We conducted a study on the formation process of two-dimensional shock waves and the nonequilibrium behavior of the system reaching a steady state [ 43 ]. The following is a brief introduction using symbols and to represent nonequilibrium moments.…”

“…It is worth noting that the nonequilibrium moments characterizing system nonequilibrium effects, as described above, encompass information about both macroscopic quantities and particle fluctuations. In the literature [43][44][45], nonequilibrium moments in this form have been utilized to represent nonequilibrium effects. Additionally, in the literature [3,17,[28][29][30][31]46,47], the macroscopic velocity's influence has been subtracted during the moment calculation processes, as shown in Equations ( 7)-( 9) and ( 11)- (12).…”