Statistical properties of pseudo-particle systems

Pseudo-particle modeling （PPM）, a molecular modeling method which combines time-driven algorithms and hard molecule modeling, was originally developed for simulating gas in complex multiphase systems （Ge ＆ Li, 2003; Ge et al., 2005; Ge, 1998）. In this work, the properties of two- and three-dimensional pseudo-particle systems, namely, mean free path, compressibility factor, self-diffusion coefficient and shear viscosity, are systematically measured by using PPM. it is found that in terms of an effective diameter, the results well conform to the Chapman-Enskog theory, thus suggesting that PPM can be employed to simulate the micro- and meso-scale behavior of ordinary gas and fluid flows.

Macro-scale pseudo-particle modeling for particle-fluid systems

Pseudo-particle modeling (PPM) is a particle method (PM) proposed in 1996. Though it is effective for the simulation of microscopic particle-fluid systems, its application to practical systems is still limited by computational cost. In this note, we speed up the computation by using a combination of weighted averaging with finite difference techniques to upgrade the particle interactions to a fluid element level, which conforms to the Navier-Stokes equation. The approach, abbreviated to MaPPM, is then applied to the problem of one-dimensional Poiseuille flow with a quantitative comparison to the results of another related PM--smoothed particle hydrodynamics (SPH), where the accuracy and efficiency of MaPPM is found to be much better than that of SPH. Flows around a cylinder and multiple freely moving particles are also simulated with the new model, resulting in reasonable flow pattern and drag coefficient. The convergence and robustness of the algorithm prove promising.

Parallelizing of macro-scale pseudo-particle modeling for particle-fluid systems

A parallel algorithm suitable for simulating multi-sized particle systems and multi- phase fluid systems is proposed based on macro-scale pseudo-particle modeling (MaPPM). The algorithm employs space-decomposition of the computational load among the processing ele- ments (PEs) and multi-level cell-subdivision technique for particle indexing. In this algorithm, a 2D gas-solid system is simulated with the temporal variations of drags on solids, inter-phase slip velocities and solids concentration elaborately monitored. Analysis of the results shows that the algorithm is of good parallel efficiency and scalability, demonstrating the unique advantage of MaPPM in simulating complex flows.

Parallelization of pseudo-particle modeling and its application in simulating gas-solid fluidization

Pseudo-Particle Modeling （PPM） is a particle method proposed by Ge and Li in 1996 [Ge, W., ＆ Li, J. （1996）. Pseudo-particle approach to hydrodynamics of particle-fluid systems, in M. Kwauk ＆ J. Li （Eds.）, Proceedings of the 5th international conference on drculating fluidized bed （pp. 260-265）. Beijing： Science Press] and has been used to explore the microscopic mechanism in complex particle-fluid systems. But as a particle method, high computational cost remains a main obstacle for its large-scale application; therefore, parallel implementation of this method is highly desirable. Parallelization of two-dimensional PPM was carried out by spatial decomposition in this paper. The time costs of the major functions in the program were analyzed and the program was then optimized for higher efficiency by dynamic load balancing and resetting of particle arrays. Finally, simulation on a gas-solid fluidized bed with 102,400 solid particles and 1.8 × 10^7 pseudo-particles was performed successfully with this code, indicating its scalability in future applications.

PARTICLE METHODS FOR COMPLEX FLOWS IN CHEMICAL ENGINEERING ——THE PSEUDO-PARTICLE APPROACH

The multi-scale structures of complex flows in chemical engineering have been great challenges to the design and scaling of such systems, and multi-scale modeling is the natural way in response. Particle methods (PMs) are ideal constituents and powerful tools of multi-scale models, owing to their physical fidelity and computational simplicity. Especially, pseudo-particle modeling (PPM, Ge & Li, 1996; Ge & Li, 2003) is most suitable for molecular scale flow prediction and exploration of the origin of multi-scale structures; macro-scale PPM (MaPPM, Ge & Li, 2001) and similar models are advantageous for meso-scale simulations of flows with complex and dynamic discontinuity, while the lattice Boltzmann model is more competent for homogeneous media in complex geometries; and meso-scale methods such as dissipative particle dynamics are unique tools for complex fluids of uncertain properties or flows with strong thermal fluctuations. All these methods are favorable for seamless interconnection of models for different scales. However, as PMs are not originally designed as either tools for complexity or constituents of multi-scale models, further improvements are expected. PPM is proposed for microscopic simulation of particle-fluid systems as a combination of molecular dynamics (MD) and direct simulation Monte-Carlo (DSMC). The collision dynamics in PPM is identical to that of hard-sphere MD, so that mass, momentum and energy are conserved to machine accuracy. However, the collision detection procedure, which is most time-consuming and difficult to be parallelized for hard-sphere MD, has been greatly simplified to a procedure identical to that of soft-sphere MD. Actually, the physical model behind such a treatment is essentially different from MD and is more similar to DSMC, but an intrinsic difference is that in DSMC the collisions follow designed statistical rules that are reflection of the real physical processes only in very limited cases such as dilute gas. PPM is ideal for exploring the mechanism of complex flows ab initio. In final analysis, the complexity of flow behavior is shaped by two components on the micro-scale: the relative displacements and interactions of the numerous molecules. Adding to the generality of the characteristics of complex system as described by Li and Kwauk (2003), we notice that complex structures or behaviors are most probably observed when these two components are competitive and hence they must compromise, as in the case of emulsions and the so-called soft-matter that includes most bio-systems. When either displacement or interaction is dominant, as in the case of dilute gas or solid crystals, respectively, complexity is much less spectacular. Most PMs consist explicitly of these two components, which is operator splitting in a numerical sense, but it is physically more meaningful and concise in PPM. The properties of the pseudo-particle fluid are in good conformance to typical simple gas (Ge et al., 2003; Ge et al., 2005). The ability of PPM to describe the dynamic transport process on the micro-scale in heterogeneous particle-fluid systems has been demonstrated in recent simulations (Ge et al., 2005). Especially, the method has been employed to study the temporal evolution of the stability criterion in the energy minimization multi-scale model (Li & Kwauk, 1994), which confirms its monotonously asymptotic decreasing as the model has assumed (Zhang et al., 2005). Massive parallel processing is also practiced for simulating particle-fluid systems in PPM, indicating an optimistic prospect to elevate the computational limitations on their wider applications, and exploring deeper underlying mechanism in complex particle-fluid systems.

General approach for discrete simulation of complex systems

By applying a general algorithm to different particle models, i.e. molecular dynamic (MD) and macro-scale pseudo-particle models (MaPPM), two physical phenomena of distinct nature and scale differences, i.e. the mutual diffusion of two gases and the instability on the interface between two fluids, are simulated successfully. It demonstrates the possibility that the general algorithms of good parallelism and software of modular architecture can be established for complex physical systems based on the particle methods (PMs), which will thereby develop into a mainstream approach as finite element (FE) and finite difference (FD) approaches.