DSMC Collision Model for the Lennard-Jones Potential: Efficient Algorithm and Verification

An efficient algorithm to implement elastic scattering using the Lennard-Jones (LJ) intermolecular potential in the direct simulation Monte Carlo (DSMC) method is presented. The exact elastic scattering angle for the LJ intermolecular potential obtained by numerical integration is used to construct a piecewise polynomial representation in terms of two collision parameters - the reduced impact parameter and the reduced relative energy. The 5 thdegree polynomials representation is obtained using the Chebyshev basis. The implementation valid for reduced relative energies ranging from 0.001 to 10.0 is verified by DSMC simulations of subsonic and supersonic Couette flow of Argon at temperatures of 273 K and 40 K and is shown to accurately reproduce the viscosity variation with temperature that corresponds to the LJ intermolecular potential. The LJ collision model is formulated in non-dimensional coordinates and is applicable to arbitrary gas species. For the Couette flow problem, the algorithm is shown to have a computational cost comparable to the variable hard sphere (VHS) model that is widely used in DSMC simulations