A method to compute the thermal conductivity of a dilute gas from stochastic particle methods is described. The proposed approach is inspired by the Müller-Plathe method, in that the heat flux is imposed on the system and is precisely known, whereas the temperature gradient is sampled during the simulation. In this manner, the issue of large statistical scatter associated with sampling the heat flux is circumvented. The modified Müller-Plathe (MMP) method is first verified with a standard variable hard sphere direct simulation Monte Carlo calculation. Then, it is used in direct molecular simulation (DMS) equipped with an ab initio $\mathrm{N}_2+\mathrm{N}_2$ potential energy surface. The most significant sources of uncertainty are clearly identified and discussed. The DMS results for molecular nitrogen thermal conductivity agree remarkably well with the experimental evidence up to 2 000 K. The proposed MMP technique is applicable to arbitrary interatomic potentials and gas compositions, and it provides a direct way to evaluate thermal conductivity without relying on empirical extrapolations to high temperatures or approximations based on viscosity.

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• Compressible flows
• High-speed flow
• Interatomic & molecular potentials
• Transport phenomena