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Volume 115
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Improvement of hard-sphere/pseudo-particle modeling (HS-PPM) for high Knudsen number gas-solid flows
Mingcan Zhao a, Feiguo Chen a, Yu Zhang a, Chengxiang Li a c, Tianhao Qiu b, Wei Ge a c *
a State Key Laboratory of Mesoscience and Process Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing, 100190, China
b School of Energy Science and Engineering, Harbin Institute of Technology (HIT), Harbin, 150001, China
c School of Chemical Engineering, University of Chinese Academy of Sciences, Beijing, 100049, China
10.1016/j.partic.2026.06.002
Volume 115, August 2026, Pages 292-308
Received 12 February 2026, Revised 16 May 2026, Accepted 1 June 2026, Available online 8 June 2026, Version of Record 16 June 2026.
E-mail: wge@ipe.ac.cn
Highlights

• HS-PPM is implemented with eliminated inlet-outlet coupling and triangular elements method for wall description.

• Simulation accuracy and efficiency are balanced for high Knudsen number situations.

• Temperature and flow fields of IRVE in rarefied gas are well predicted based on dimensionless numbers.

• The flow system of porous particle at atomic level can be simulated by the implemented HS-PPM.


Abstract

Hard-sphere/pseudo-particle modeling (HS-PPM) provides a parallel and more versatile implementation of molecular dynamics simulation based on hard-sphere model at large scales with remarkable performance. For more practical applications, however, more sophisticated and realistic boundary conditions have to be incorporated. In this work, the artifact of inlet-outlet coupling due to periodic boundary is basically eliminated by adding collisions at both ends and proportional-integral-differential (PID) control of density at the outlet based on implicit boundary conditions, maintaining reasonable flow field there for both high (up to 13.0) and low (down to 0.0) Mach numbers. Moreover, geometrically complex boundaries are approximated by a large number of polygonal (in particular, triangular) elements, instead of exact analytical descriptions, to balance the accuracy and efficiency. Given the challenges of nanoscale experimentation, the drag coefficients from simulation conducted at matching dimensionless numbers were compared with macroscopic results. With these improvements, the flow around a conical particle and the Inflatable Re-entry Vehicle Experiment (IRVE) was successfully simulated and demonstrated consistent to experiment and numerical results from direct simulation Monte Carlo (DSMC) towards the continuum flow limit (with the Knudsen number ranging from 0.1 to 1.7). Furthermore, the drag coefficient of nano-particles in fluid flow, which is challenging for experimental measurement, was obtained from simulation results, and the potential of HS-PPM in simulating particles and systems with complex structures is exemplified by the gas flow and diffusion in porous micro/nano-particles.

Graphical abstract
Keywords
HS-PPM; Implicit boundary conditions; Triangular elements; Flow around porous particles; Rarefied gas; Supersonic flow
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