Non-equilibrium parameter for a hybrid Fokker-Planck/DSMC scheme

Abstract

In this work we investigate the kinetic Fokker-Planck (FP) model [1, 2] concerning its applicability to simulate hypersonic, rarefied gas flow. As in the direct simulation Monte Carlo (DSMC) algorithm, the FP model simulates the stochastic motion of a set of particles through the computational domain which results in a simple coupling of both methods. No collisions must be calculated in the FP approach and so larger cell and time step sizes than by DSMC calculations can be used. Because of this, the FP model holds the potential to be more efficient than DSMC where the Knudsen number is small. Further we present and investigate a hybridisation scheme for the FP and DSMC algorithms. We derive a non-equilibrium parameter from the Fokker-Planck-and Boltzmann-operator which indicates the validity of the FP model. In hybrid simulations this parameter is used to partition the computational domain in DSMC and FP regions. The particle motion is processed similarly in both regions, only the procedure for assigning new particle velocities differs. To achieve an equal number of particles per cell, weighting factors depended on the cell size are used. The hybridisation scheme is tested for one-dimensional shock and two-dimensional cylinder flows and gives results in agreement to pure DSMC simulations. An efficiency study shows, that the hybrid scheme is roughly five times faster than a pure DSMC simulation for a hypersonic cylinder flow test case.

On the conservative property of particle-based Fokker–Planck method for rarefied gas flows

“…Due to the particle nature of the FP method, it can be conveniently combined with other particle methods. For example, Fei and Fan 59 and Fei et al 60 proposed the diffusive information preservation (D-IP) method, and the hybrid FP-DSMC scheme [61][62][63][64][65] has been studied. The FP method has been applied to numerical investigations of high-speed aerodynamics including the supersonic flow over the leading edge of a flat plate, 66 the supersonic flow past a cylinder, 64,67 the nozzle expansion flow, 68 the re-entry aerodynamics of a slender configuration, 69 and the interior structure of normal shock waves.…”