Homogeneous relaxation and shock wave problems: Assessment of the simplified and generalized Bernoulli trial collision schemes

Abstract

The impetus of this paper is to assess the newly suggested direct simulation Monte Carlo (DSMC) collision schemes, that is, the “Simplified Bernoulli Trails (SBT)” and “Generalized Bernoulli Trials (GBT)” schemes in the prediction of the higher-order moments of the velocity distribution function for both confined and non-confined gas flows. Two fundamental rarefied gas dynamics problems are considered: spatially homogeneous relaxation process of a gas flow from a non-Maxwellian condition given by Bobylev–Krook–Wu exact (analytical) solution of the Boltzmann equation and the stationary shock wave problem. To perform the relaxation test, SBT and GBT schemes were implemented in the DSMC0F program. For the shock wave test, changes were made in the DSMC1 code to include the SBT and GBT schemes. A detailed comparison of the SBT and GBT collision schemes in treating the higher-order moments of the velocity distribution function and comparison with theory and the solution of the standard No-Time-Counter (NTC) method and its new variant, nearest neighbor scheme, using the DS1 code, is reported. Some higher moments beyond the usual moments were computed. The results of the fourth moment of the velocity distribution function in the homogeneous relaxation problem show that while both collision schemes produce identical results at an ample time, the initial relaxation process indicates the difference between the schemes. Even though the NTC schemes required a large number of particles per cell to produce the same results as the theory, the SBT scheme successfully simulates the solution using a low number of particles per cell.

Simulation of Relaxation Processes in Hypersonic Flows with One-Temperature Non-Equilibrium Model

“…It is also interesting to compare the results computed with the results obtained with a more general approach to the simulation of hypersonic flows, for example Direct Simulation Monte Carlo (DSMC). The cases of stationary shock wave and assessment of various collision schemes are presented in [42]. At this stage, the results computed with the onetemperature model were compared with the temperature approach.…”

Numerical investigation of rarefied vortex loop formation due to shock wave diffraction with the use of rorticity

“…In rarefied conditions, shock waves have been investigated numerically using various techniques, such as direct simulation Monte Carlo (DSMC), kinetic solvers, and by hybrid numerical methods in shock tubes 36,49,52 , hypersonic flows 7,13,14,[39][40][41] , and in plasma flow 26 . Investigations of nozzle exit jet flow in the rarefied condition are mainly restricted to steady-state flow, such as hybrid numerical simulation of rarefied supersonic flow from micro-nozzles by Torre et al 20 , rarefied nozzle flow by Deschenes and Grot 8 , and transition regime flow in a diffuser investigated by Groll 16 .…”

Nonequilibrium effects of reactive flow based on gas kinetic theory*

“…For example, on the basis of the distribution function, Nagnibeda et al established the kinetic theory of transport processes and discussed the features of complex system strongly deviating from the thermal and chemical equilibrium [3]. Besides, on the microscopic level, the distribution function can be obtained by using the direct simulation Monte Carlo [13,14], or molecular dynamics [15,16]. As a kinetic mesoscopic methodology, the discrete Boltzmann method (DBM) is a special discretization of the Boltzmann equation in particle velocity space, and has been successfully developed to recover and probe the velocity distribution functions of nonequilibrium physical systems [11,[17][18][19][20].…”