An improved explicit scheme for whole-building hygrothermal simulation
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Although implicit methods require extra calculation, they have been largely used for obtaining numerical approximations of time-dependent differential conservation equations in the building science domain, thanks to their stability conditions that enable the use of larger time steps. Nevertheless, they require important sub-iterations when dealing with highly nonlinear problems such as the combined heat and moisture transfer through porous building elements or when the whole-building is simulated and there is important coupling among the building elements themselves and among neighbouring zones and HVAC systems. On the other hand, the classical explicit Euler scheme is generally not used because its stability condition imposes very fine time discretisation. Hence, this paper explores the use of an improved explicit approach - the Dufort-Frankel scheme - to overcome the disadvantage of the classical explicit one and to bring benefits that cannot be obtained by implicit methods. The Dufort-Frankel approach is first compared to the classical implicit and explicit Euler schemes to compute the solution of both linear and nonlinear heat and moisture transfer through porous materials. Then, the analysis of the Dufort-Frankel unconditionally stable explicit scheme is extended to the coupled heat and moisture balances on the scale of a one- and a two-zone building models. The Dufort-Frankel scheme has the benefits of being unconditionally stable, second-order accurate in time O(dt^2) and to compute explicitly the solution at each time step, avoiding costly sub-iterations. This approach may reduce the computational cost by twenty as well as it may enable perfect synchronism for whole-building simulation and co-simulation. In addition, it can be easier parallelised on high-performance computer systems.
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