A practical deviational particle method for variance reduction of polyatomic gas DSMC simulation

The DSMC method is a prevalent numerical method to solve the Boltzmann equation, but it can suffer from statistical fluctuations especially when the distributions do not change much along with the flow. The deviational particle method is proposed to reduce statistical variations, by defining deviational distribution from prescribed reference and generating sample particles only from it. However, the increasing number of particles due to the collision process of this method is a problem. The low-variance deviational simulation Monte Carlo (LVDSMC) method successfully overcame this issue by utilizing the Hilbert form of the collision operator that leads to a source-sink formulation. Yet, a limitation of the LVDSMC method is that it is only usable for monoatomic gas flows, while polyatomic gases are used in most industrial applications. Therefore, in this research, we have formulated a practical deviational particle method for polyatomic gas flows. The Larsen-Borgnakke (LB) model is used for polyatomic molecular interactions, and we calculate its elastic collisions with the LVDSMC method in the literature and inelastic collisions with conventional collision calculation and the newly introduced particle reduction algorithm. The concept of this particle reduction algorithm is to maintain the number of computational particles while conserving the energy exchange between different modes calculated by the LB model.

We conducted a numerical experiment involving calculations of one-dimensional evaporation flows. Such evaporation flows encompass heat and mass transfer through vapor, and find applications in various industrial processes like desalination and cooling devices. During the demonstration, we varied the flow velocity and compared the accuracy and computational costs with the DSMC method for validation. According to the results, the present method successfully replicates the results obtained by the DSMC method, with reasonable computational expenses up to a certain degree of non-equilibrium.