A spatial interpolation for a stochastic particle Fokker-Planck model using a polynomial reconstruction

Abstract

The stochastic particle Fokker-Planck (FP) model describes the behavior of rarefied gases while reducing the computational cost compared to the direct simulation Monte Carlo (DSMC) method, particularly for gas flows in the continuum regime. Many studies using FP models rely on cell-averaged macroscopic properties to update particle velocities, limiting spatial resolution in regions with large macroscopic gradients. To overcome this limitation, this paper introduces a spatial interpolation method based on the polynomial reconstruction. This method provides more accurate estimations of macroscopic properties using cell-averaged values and allows for extension to higher-order spatial accuracy. The spatial interpolation method is evaluated through three numerical simulations: Couette flow, lid-driven cavity flow, and hypersonic flow over a flat plate. The results demonstrate that the polynomial reconstruction method significantly improves accuracy. The second-order polynomial reconstruction method consistently outperforms the first-order polynomial reconstruction method, while the fourth-order polynomial reconstruction method does not consistently surpass the second-order polynomial reconstruction method due to challenges in boundary treatment. The study also examines accuracy improvements by interpolating a combined property of the viscous stress and density in the hypersonic flow over a flat plate, where large viscous stress gradients are present. The result demonstrates that interpolating the combined property enhances the overall accuracy of flow predictions by capturing large gradients. (c) 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) license