# 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.
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Submitted on : Tuesday, March 28, 2017 - 10:21:58 AM
Last modification on : Friday, November 6, 2020 - 3:34:23 AM
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### Citation

Suelen Gasparin, Julien Berger, Denys Dutykh, Nathan Mendes. Stable explicit schemes for simulation of nonlinear moisture transfer in porous materials. Journal of Building Performance Simulation, Taylor & Francis, 2018, 11 (2), pp.129-144. ⟨10.1080/19401493.2017.1298669⟩. ⟨hal-01404578v4⟩

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