Indoor Air Quality Campaign in an Occupied Low-Energy House with a High Level of Spatial and Temporal Discretization

Background and gaps. The topic of indoor air quality (IAQ) in low-energy buildings has received increasing interest over the past few years. Often based on two measurement points and on passive measurements over one week, IAQ studies are struggling to allow the calculation of pollutants exposure. Objectives. We would like to improve the evaluation of the health impacts, through measurements able to estimate the exposure of the occupants. Methodology. This article presents detailed IAQ measurements taken in an energy-efficient occupied house in France. Two campaigns were conducted in winter and spring. Total volatile organic compounds (TVOC), formaldehyde, the particle numbers and PM2.5, carbon dioxide (CO2), relative humidity (RH), temperature (T), ventilation airflows, and weather conditions were dynamically measured in several points. Laboratory and low-cost devices were used, and an inter-comparison was carried out for them. A survey was conducted to record all the daily activities of the inhabitants. IAQ performance indicators based on the different pollutants were calculated. Results. PM2.5 cumulative exposure did not exceed the threshold available in the literature. Formaldehyde concentrations were high, in the kitchen, where the average concentrations exceeded the threshold. However, the formaldehyde cumulative exposure of the occupants did not exceed the threshold. TVOC concentrations were found to reach the threshold. With these measurements performed with high spatial and temporal discretization, we showed that such detailed data allow for a better-quality health impacts assessment and for a better understanding of the transport of pollutants between rooms.

Uniformly Convergent Numerical Scheme for Singularly Perturbed Parabolic PDEs with Shift Parameters

In this article, singularly perturbed parabolic differential difference equations are considered. The solution of the equations exhibits a boundary layer on the right side of the spatial domain. The terms containing the advance and delay parameters are approximated using Taylor series approximation. The resulting singularly perturbed parabolic PDEs are solved using the Crank–Nicolson method in the temporal discretization and nonstandard finite difference method in the spatial discretization. The existence of a unique discrete solution is guaranteed using the discrete maximum principle. The uniform stability of the scheme is investigated using solution bound. The uniform convergence of the scheme is discussed and proved. The scheme converges uniformly with the order of convergence O N − 1 + Δ t 2 , where N is number of subintervals in spatial discretization and Δ t is mesh length in temporal discretization. Two test numerical examples are considered to validate the theoretical findings of the scheme.

Spatio-Temporal Discretization Uncertainty of Distributed Hydrological Models

Quantifying the uncertainty linked to the degree to which the spatio-temporal variability of the catchment descriptors (CDs), and consequently calibration parameters (CPs), represented in the distributed hydrology models and its impacts on the simulation of flooding events is the main objective of this paper. Here, we introduce a methodology based on ensemble approach principles to characterize the uncertainties of spatio-temporal variations. We use two distributed hydrological models (WaSiM and Hydrotel) and six catchments with different sizes and characteristics, located in southern Quebec, to address this objective. We calibrate the models across four spatial (100, 250, 500, 1000 $m^2$) and two temporal (3 hours and 24 hours) resolutions. Afterwards, all combinations of CDs-CPs pairs are fed to the hydrological models to create an ensemble of simulations for characterizing the uncertainty related to the spatial resolution of the modeling, for each catchment. The catchments are further grouped into large ($>1000 km^2$), medium (between 500 and 1000 $km^2$) and small ($<500km^2$) to examine multiple hypotheses. The ensemble approach shows a significant degree of uncertainty (over $100\%$ error for estimation of extreme streamflow) linked to the spatial discretization of the modeling. Regarding the role of catchment descriptors, results show that first, there is no meaningful link between the uncertainty of the spatial discretization and catchment size, as spatio-temporal discretization uncertainty can be seen across different catchment sizes. Second, the temporal scale plays only a minor role in determining the uncertainty related to spatial discretization. Third, the more physically representative a model is, the more sensitive it is to changes in spatial resolution. Finally, the uncertainty related to model parameters is dominant larger than that of catchment descriptors for most of the catchments. Yet, there are exceptions for which a change in spatio-temporal resolution can alter the distribution of state and flux variables, change the hydrologic response of the catchments, and cause large uncertainties.

An efficient localized collocation solver for anomalous diffusion on surfaces

This paper introduces an efficient collocation solver, the generalized finite difference method (GFDM) combined with the recent-developed scale-dependent time stepping method (SD-TSM), to predict the anomalous diffusion behavior on surfaces governed by surface time-fractional diffusion equations. In the proposed solver, the GFDM is used in spatial discretization and SD-TSM is used in temporal discretization. Based on the moving least square theorem and Taylor series, the GFDM introduces the stencil selection algorithms to choose the stencil support of a certain node from the whole discretization nodes on the surface. It inherits the similar properties from the standard FDM and avoids the mesh generation, which is available particularly for high-dimensional irregular discretization nodes. The SD-TSM is a non-uniform temporal discretization method involving the idea of metric, which links the fractional derivative order with the non-uniform discretization strategy. Compared with the traditional time stepping methods, GFDM combined with SD-TSM deals well with the low accuracy in the early period. Numerical investigations are presented to demonstrate the efficiency and accuracy of the proposed GFDM in conjunction with SD-TSM for solving either single or coupled fractional diffusion equations on surfaces.

Robust numerical method for singularly perturbed parabolic differential equations with negative shifts

This paper deals with numerical treatment of singularly perturbed parabolic differential equations having delay on the zeroth and first order derivative terms. The solution of the considered problem exhibits boundary layer behaviour as the perturbation parameter tends to zero. The equation is solved using ?-method in temporal discretization and exponentially fitted finite difference method in spatial discretization. The stability of the scheme is proved by using solution bound technique by constructing barrier functions. The parameter uniform convergence analysis of the scheme is carried out and it is shown to be accurate of order O(N-2/N-1+c?+(?t)2) for the case ?= 1/2, where N is the number of mesh points in spatial discretization and ?t is the mesh size in temporal discretization. Numerical examples are considered for validating the theoretical analysis of the scheme.