Abstract
The unified stochastic particle method based on the Bhatnagar-Gross-Krook model (USP-BGK) has been proposed recently to overcome the low accuracy and efficiency of the traditional stochastic particle methods, such as the direct simulation Monte Carlo (DSMC) method, for the simulation of multi-scale gas flows. However, running with extra virtual particles and space interpolation, the previous USP-BGK method cannot be directly transplanted into the existing DSMC codes. In this work, the implementation of USP-BGK is simplified using new temporal evolution and spatial reconstruction schemes. As a result, the present algorithm of the USP-BGK method is similar to the DSMC method and can be implemented efficiently based on any existing DSMC codes just by modifying the collision module.
Highlights
Multi-scale gas flows widely exist in aerospace engineering [1] and micro-electromechanical systems (MEMS) [2]
The CFD-DSMC hybrid method [3,4,5] implements the CFD solver and direct simulation Monte Carlo (DSMC) method in different regions. Another example is the general synthetic iterative scheme (GSIS) [6] developed recently, which is solved by the CFD and discrete velocity method (DVM) together in the whole region but at different levels
Besides the hybrid methods, a straightforward approach is to extend the application of the kinetic methods to the continuum regime
Summary
Multi-scale gas flows widely exist in aerospace engineering [1] and micro-electromechanical systems (MEMS) [2]. (9) and (13) have the same form as the solutions of the particle motion and collision steps of the traditional SP-BGK method [23] except for the different target distribution In this way, virtual particles are not needed for simulation. From Eq (13), we can obtain f ðc; x; ΔtÞ after the collision step, and it is directly applied to particle motions in the time step Note that this technique has been first introduced in the USPBGK-DSMC hybrid method [23]. In the particle motion step, the particle tracking is exactly solved; in the collision step, to reconstruct the target distribution at the location of the simulated particle, the mean velocity and temperature with secondorder accuracy need to be interpolated based on the flow field. Combining Eqs. (20) and (22), the error between U(xp, t) and U ' (xp, t) is calculated as
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