In this article, a new hybrid approach combining Fokker Planck (FP) and Direct Simulation Monte Carlo (DSMC) is introduced. The FP approach, which is an approximation of the Boltzmann equation, has been recently introduced for modeling rarefied gas flows. Compared to standard molecular methods like DSMC, it has a lower computational cost. However, the FP model may provide erroneous results in modeling some flow features, including vortex region and shock waves. The DSMC approach is accurate enough; yet, it has a high computational cost, especially at low Knudsen/low Mach number conditions. The purpose of this article is to suggest an optimized hybrid algorithm to benefit from high-speed modeling and sufficient accuracy simultaneously. We show a modified form of the gradient length Knudsen number, i.e., KnGL/Kn, must be considered to define the range of accuracy of the FP method. We used KnGL/Kn as a parameter for switching between DSMC and FP. The cavity flow and the nozzle flow are considered for the investigation of the proposed hybrid algorithm. The dependence of the accuracy and computational cost on KnGL/Kn is reported. The results demonstrate that the optimized KnGL/Kn is between 3 to 4, which gives suitable computational cost and acceptable accuracy.

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