Transparent boundary conditions for wave propagation on unbounded domains

The numerical solution of the time dependent wave equation in an unbounded domain generally leads to a truncation of this domain, which requires the introduction of an artificial boundary with associated boundary conditions. Such nonreflecting conditions ensure the equivalence between the solution of the original problem in the unbounded region and the solution inside the artificial boundary. We consider the acoustic wave equation and derive exact transparent boundary conditions that are local in time and can be directly used in explicit methods. These conditions annihilate wave harmonics up to a given order on a spherical artificial boundary, and we show how to combine the derived boundary condition with a finite difference method. The analysis is complemented by a numerical example in two spatial dimensions that illustrates the usefulness and accuracy of transparent boundary conditions.

Preparation and anode property of Pt-CeO2 electrodes supported on carbon black for direct methanol fuel cell applications

A platinum (Pt) on pure ceria (CeO2) supported by carbon black (CB) anode was synthesized using a combined process of precipitation and coimpregnation methods. The electrochemical activity of methanol oxidation reaction on synthesized Pt-CeO2/CB anodes was investigated by cyclic voltammetry and chronoamperometry experimentation. To improve the anode property on Pt-CeO2/CB, the influence of particle morphology and particle size on anode properties was examined. The morphology and particle size of the pure CeO2 particles could be controlled by changing the preparation conditions. The anode properties (i.e., peak current density and onset potential for methanol oxidation) were improved by using nanosize CeO2 particles. This indicates that a larger surface area and higher activity on the surface of CeO2 improve the anode properties. The influence of particle morphology of CeO2 on anode properties was not very large. The onset potential for methanol oxidation reaction on Pt-CeO2/CB, which consisted of CeO2 with a high surface area, was shifted to a lower potential compared with that on the anodes, which consisted of CeO2 with a low surface area. The onset potential on Pt-CeO2/CB at 60 degrees C became similar to that on the commercially available Pt-Ru/carbon anode. We suggest that the rate-determining steps of the methanol oxidation reaction on Pt-CeO2/CB and commercially available Pt-Ru/carbon anodes are different, which accounts for the difference in performance. In the reaction mechanism on Pt-CeO2/CB, we conclude that the released oxygen species from the surface of CeO2 particles contribute to oxidation of adsorbed CO species on the Pt surface. This suggests that the anode performance of the Pt-CeO2/CB anode would lead to improvements in the operation of direct methanol fuel cells at 80 degrees C by the enhancement of diffusion of oxygen species created from the surface of nanosized CeO2 particles. Therefore, we conclude that fabrication of nanosized CeO2 with a high surface area is a key factor for development of a high-quality Pt-CeO2/CB anode in direct methanol fuel cells.