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Diffusion-Based Coarse Graining in Hybrid Continuum-Discrete Solvers: Theoretical Formulation and A Priori Tests
Coarse graining is an important ingredient in many multi-scale
continuum-discrete solvers such as CFD--DEM (computational fluid
dynamics--discrete element method) solvers for dense particle-laden flows.
Although CFD--DEM solvers have become a mature technique that is widely used in
multiphase flow research and industrial flow simulations, a flexible and
easy-to-implement coarse graining algorithm that can work with CFD solvers of
arbitrary meshes is still lacking. In this work, we proposed a new coarse
graining algorithm for continuum--discrete solvers for dense particle-laden
flows based on solving a transient diffusion equation. Via theoretical analysis
we demonstrated that the proposed method is equivalent to the statistical
kernel method with a Gaussian kernel, but the current method is much more
straightforward to implement in CFD--DEM solvers. \textit{A priori} numerical
tests were performed to obtain the solid volume fraction fields based on given
particle distributions, the results obtained by using the proposed algorithm
were compared with those from other coarse graining methods in the literature
(e.g., the particle centroid method, the divided particle volume method, and
the two-grid formulation). The numerical tests demonstrated that the proposed
coarse graining procedure based on solving diffusion equations is theoretically
sound, easy to implement and parallelize in general CFD solvers, and has
improved mesh-convergence characteristics compared with existing coarse
graining methods. The diffusion-based coarse graining method has been
implemented into a CFD--DEM solver, the results of which are presented in a
separate work (R. Sun and H. Xiao, Diffusion-based coarse graining in hybrid
continuum-discrete solvers: Application in CFD-DEM solvers for particle laden
flows)
Diffusion-Based Coarse Graining in Hybrid Continuum-Discrete Solvers: Applications in CFD-DEM
In this work, a coarse-graining method previously proposed by the authors in
a companion paper based on solving diffusion equations is applied to CFD-DEM
simulations, where coarse graining is used to obtain solid volume fraction,
particle phase velocity, and fluid-particle interaction forces. By examining
the conservation requirements, the variables to solve diffusion equations for
in CFD-DEM simulations are identified. The algorithm is then implemented into a
CFD-DEM solver based on OpenFOAM and LAMMPS, the former being a
general-purpose, three-dimensional CFD solver based on unstructured meshes.
Numerical simulations are performed for a fluidized bed by using the CFD-DEM
solver with the diffusion-based coarse-graining algorithm. Converged results
are obtained on successively refined meshes, even for meshes with cell sizes
comparable to or smaller than the particle diameter. This is a critical
advantage of the proposed method over many existing coarse-graining methods,
and would be particularly valuable when small cells are required in part of the
CFD mesh to resolve certain flow features such as boundary layers in wall
bounded flows and shear layers in jets and wakes. Moreover, we demonstrate that
the overhead computational costs incurred by the proposed coarse-graining
procedure are a small portion of the total costs in typical CFD-DEM simulations
as long as the number of particles per cell is reasonably large, although
admittedly the computational overhead of the coarse graining often exceeds that
of the CFD solver. Other advantages of the present algorithm include more
robust and physically realistic results, flexibility and easy implementation in
almost any CFD solvers, and clear physical interpretation of the computational
parameter needed in the algorithm. In summary, the diffusion-based method is a
theoretically elegant and practically viable option for CFD-DEM simulations
Guest editorial for the special issue on software-defined radio transceivers and circuits for 5G wireless communications
Yichuang Sun, Baoyong Chi, and Heng Zhang, Guest Editorial for the Special Issue on Software-Defined Radio Transceivers and Circuits for 5G Wireless Communications, published in IEEEE Transactions on Circuits and Systems II: Express Briefs, Vol. 63 (1): 1-3, January 2016, doi: https://doi.org/10.1109/TCSII.2015.2506979.Peer reviewedFinal Accepted Versio
INFLUENCE OF EDUCATIONAL REFORM ON TEACHERSā ANXIETY UNDER BIM COLLABORATIVE MANAGEMENT MODE
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