It is shown that this extension is quite straightforward due to the explicit use of the diffusion flux in the expression of the diffusion velocity.
A limiter on the auxiliary variable for approximating the gradient of the solution must be used so that the diffusion flux is positivity-preserving in the sense that DG schemes with this flux satisfies a weak positivity property.
However, most of them use a scalar diffusivity thus the diffusion flux is along gradient direction, which may blur edges.
In order to analyze the evolution of the concentration profile experimentally observed by MacDonald and Muller under shear-induced polymer migration in a rotating cone-and-plate device, we use a constitutive equation for the diffusion flux, where the gradient of a generalized non-equilibrium chemical potential appears instead of the concentration gradient.
With "activated" electrodes under illumination using a photon flux smaller than the diffusion flux, the apparent quantum efficiency is nearly equal to zero and no H2 evolution occurs.
(1) where J is the diffusion flux, D is the diffusivity, C is the concentration, and x the position in the direction of diffusion.
The coupling between the on-lattice and off-lattice regions uses the Two Regime Method (TRM) (Flegg et al., 2012; Flegg et al., 2014), which correctly calculates the diffusion flux of species through an interface between the subdomains.
Fig. 1f shows the mass diffusion cloak, the diffusion coefficient of the hollow cylinder fulfills Eq. (2), the diffusion flux lines are parallel outside the outer cylinder, no diffusion flux lines penetrate into the inner circle.
The parameters and diffusion time are the same as that in Fig. 11, the diffusion flux are parallel and equal.
(b) The horizontal lines are diffusion flux lines, and the diffusion flux is opposite to the direction of the concentration gradient.
