Stable explicit schemes for simulation of nonlinear moisture transfer in porous materials
  Implicit schemes have been extensively used in building physics to compute
the solution of moisture diffusion problems in porous materials for improving
stability conditions. Nevertheless, these schemes require important
sub-iterations when treating non-linear problems. To overcome this
disadvantage, this paper explores the use of improved explicit schemes, such as
Dufort-Frankel, Crank-Nicolson and hyperbolisation approaches. A first case
study has been considered with the hypothesis of linear transfer. The
Dufort-Frankel, Crank-Nicolson and hyperbolisation schemes were compared to the
classical Euler explicit scheme and to a reference solution. Results have shown
that the hyperbolisation scheme has a stability condition higher than the
standard Courant-Friedrichs-Lewy (CFL) condition. The error of this schemes
depends on the parameter \tau representing the hyperbolicity magnitude added
into the equation. The Dufort-Frankel scheme has the advantages of being
unconditionally stable and is preferable for non-linear transfer, which is the
second case study. Results have shown the error is proportional to O(\Delta t).
A modified Crank-Nicolson scheme has been proposed in order to avoid
sub-iterations to treat the non-linearities at each time step. The main
advantages of the Dufort-Frankel scheme are (i) to be twice faster than the
Crank-Nicolson approach; (ii) to compute explicitly the solution at each time
step; (iii) to be unconditionally stable and (iv) easier to parallelise on
high-performance computer systems. Although the approach is unconditionally
stable, the choice of the time discretisation $\Delta t$ remains an important
issue to accurately represent the physical phenomena.
