Title: Stable explicit schemes for simulation of nonlinear moisture transfer in porous materials,
Abstract: 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.