TY - GEN
T1 - Consistent implementation of state-to-state collision models for direct simulation Monte Carlo
AU - Zhang, Chonglin
AU - Schwartzentruber, Thomas E.
PY - 2014
Y1 - 2014
N2 - A general framework for implementing state-to-state collision models in the DSMC method is presented. In developing a state-to-state DSMC collision model, one key as- pect is to propose effcient algorithms to correctly simulate the state-to-state collision cross-sections, hence the state-to-state collision (or transition) rates. This includes the calculation of the total collision rate, the selection of potential collision pairs, and the pro- cedure to perform actual state-to-state collisions in the DSMC method. To achieve these tasks in a computationally effcient manner, we proposed the detailed implementation of a general rovibrational state-to-state collision model for the DSMC method. The proposed model implementation successfully achieved microscopic reversibility, detailed balance, and equipartition of energy under equilibrium conditions. This was first demonstrated using qualitatively-constructed state-to-state cross-sections. With the algorithms verified, we further developed a vibrational state-to-state DSMC collision model using the transition probabilities of the forced harmonic oscillator (FHO) model, where the transition prob- abilities are modified to satisfy microscopic reversibility, and a power law temperature dependent viscosity is imposed. Furthermore, DSMC simulation results of isothermal vi- bration relaxation using the modified FHO cross-sections are compared with master equa- tion simulation results, where the transition rates in the master equation are obtained from integrating the state-to-state cross-sections used in the DSMC simulation. Overall, excel- lent agreement is observed for both the vibrational temperature relaxation history and the time dependent vibrational energy distribution functions, between DSMC and master equation simulations.
AB - A general framework for implementing state-to-state collision models in the DSMC method is presented. In developing a state-to-state DSMC collision model, one key as- pect is to propose effcient algorithms to correctly simulate the state-to-state collision cross-sections, hence the state-to-state collision (or transition) rates. This includes the calculation of the total collision rate, the selection of potential collision pairs, and the pro- cedure to perform actual state-to-state collisions in the DSMC method. To achieve these tasks in a computationally effcient manner, we proposed the detailed implementation of a general rovibrational state-to-state collision model for the DSMC method. The proposed model implementation successfully achieved microscopic reversibility, detailed balance, and equipartition of energy under equilibrium conditions. This was first demonstrated using qualitatively-constructed state-to-state cross-sections. With the algorithms verified, we further developed a vibrational state-to-state DSMC collision model using the transition probabilities of the forced harmonic oscillator (FHO) model, where the transition prob- abilities are modified to satisfy microscopic reversibility, and a power law temperature dependent viscosity is imposed. Furthermore, DSMC simulation results of isothermal vi- bration relaxation using the modified FHO cross-sections are compared with master equa- tion simulation results, where the transition rates in the master equation are obtained from integrating the state-to-state cross-sections used in the DSMC simulation. Overall, excel- lent agreement is observed for both the vibrational temperature relaxation history and the time dependent vibrational energy distribution functions, between DSMC and master equation simulations.
UR - http://www.scopus.com/inward/record.url?scp=85087188370&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85087188370&partnerID=8YFLogxK
U2 - 10.2514/6.2014-0866
DO - 10.2514/6.2014-0866
M3 - Conference contribution
AN - SCOPUS:85087188370
SN - 9781624102561
T3 - 52nd AIAA Aerospace Sciences Meeting - AIAA Science and Technology Forum and Exposition, SciTech 2014
BT - 52nd AIAA Aerospace Sciences Meeting - AIAA Science and Technology Forum and Exposition, SciTech 2014
PB - American Institute of Aeronautics and Astronautics Inc.
T2 - 52nd AIAA Aerospace Sciences Meeting - AIAA Science and Technology Forum and Exposition, SciTech 2014
Y2 - 13 January 2014 through 17 January 2014
ER -