An average linear finite difference scheme for the numerical solution of the initial-boundary value problem of Generalized Rosenau-KdV equation is proposed. The existence, uniqueness, and conservation for energy of the difference solution are proved by the discrete energy norm method. It is shown that the finite difference scheme is 2nd-order convergent and unconditionally stable. Numerical experiments verify that the theoretical results are right and the numerical method is efficient and reliable.
In this work the previously developed Lattice Boltzmann-Direct Forcing/ Fictitious Domain (LB-DF/FD) method is adopted to simulate the sedimentation of eight circular particles under gravity at an intermediate Reynolds number of about 248. The particle clustering and the resulting Drafting-Kissing-Tumbling (DKT) motion which takes place for the first time are explored. The effects of initial particle-particle gap on the DKT motion are found significant. In addition, the trajectories of particles are presented under different initial particle-particle gaps, which display totally three kinds of falling patterns provided that no DKT motion takes place, i.e. the concave-down shape, the shape of letter “M” and “in-line” shape. Furthermore, the lateral and vertical hydrodynamic forces on the particles are investigated. It has been found that the value of Strouhal number for all particles is the same which is about 0.157 when initial particle-particle gap is relatively large. The wall effects on falling patterns and particle expansions are examined in the final.
The products generated by the electrochemical reaction in the PEM fuel cell (PEMFC) are mainly concentrated in the flow field on the cathode side of the bipolar plate, and the oxygen introduced on the cathode has higher requirements to improve its diffusion performance by using the flow field structure. For this reason, the optimization of the cathode flow field of the PEMFC is essential. Inspired by the structure of a spider web, this paper proposes a novel spider-web-type flow field. In this kind of flow field, the shape of a polygonal structure and the number of layers of spiral flow channels are the two most crucial variables. In order to explore the impact of these two variables on the cathode flow field, complete three-dimensional PEMFC models with different values of the two variables were established, and the models were simulated by the method of CFD. By observing the results of oxygen distribution, the water removal performance and fuel cell output performance of different schemes, the optimal scheme of the polygonal structure and layer number are determined. Compared with the traditional flow field, it is proved that the optimization scheme is desirable in improving the performance of the cathode flow field in PEMFC.
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