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N ‐space collision model for rotation‐translation energy exchange in DSMC collisions
Author(s) -
Macrossan M. N.
Publication year - 2020
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4780
Subject(s) - physics , rotation (mathematics) , collision , direct simulation monte carlo , degrees of freedom (physics and chemistry) , mach number , translation (biology) , monte carlo method , classical mechanics , energy (signal processing) , relaxation (psychology) , molecular dynamics , internal energy , statistical physics , mechanics , geometry , mathematics , quantum mechanics , chemistry , computer science , dynamic monte carlo method , psychology , social psychology , biochemistry , statistics , computer security , messenger rna , gene
Summary A new discrete simulation Monte Carlo (DSMC) collision model for molecules possessing an integer number of classical degrees of freedom for molecular structure energy is proposed. The total molecular energy (translation plus molecular structure) is represented by a velocity in five‐dimensional space. Each collision is an elastic N ‐sphere collision in N ‐space, where N = 3, 4, or 5. For N =5, there is a maximum chance of exchange of energy between the two components of velocity, which represent the rotation energy and the three components that represent the translational velocity. For N =3, there is no change in the rotation energy of each molecule, and for N =4, there is an intermediate chance that rotation and translation energy will be exchanged. The exchange probability ϕ can be set to give the desired rotational relaxation rate. To achieve any realistic viscosity μ ( T ), the N ‐space model must be coupled with a modified collision procedure known as ν ‐DSMC. The new model is shown to match the results of molecular dynamics calculations for the internal structure of a Mach 7 shock, with a saving of about 20% in CPU time compared to standard DSMC using the standard Borgnakke‐Larsen exchange model.