Some applications require tracking the evolution of the H partial pressure in an enclosure in contact with permeable membranes.
For example, see this TMAP verification case.
The way we did it in this case was using an explicit scheme. But thanks to @jorgensd 's scifem package, we can use Real elements and include these equations in the variational formulation.
Boundary conditions:
$$
c(x=0, t) = 0
$$
$$
c(x=l, t) = K_H \ P(t)
$$
Governing equation:
$$
\frac{dc}{dt} = \nabla \cdot (D \nabla c)
$$
$$
\frac{dP}{dt} = \varphi(x=l) \ \frac{A \ R\ T}{V}
$$
where $\varphi = -D \nabla c \cdot n$, $n$ being the surface normal.
Some applications require tracking the evolution of the H partial pressure in an enclosure in contact with permeable membranes.
For example, see this TMAP verification case.
The way we did it in this case was using an explicit scheme. But thanks to @jorgensd 's
scifempackage, we can use Real elements and include these equations in the variational formulation.Boundary conditions:
Governing equation:
where$\varphi = -D \nabla c \cdot n$ , $n$ being the surface normal.