Application of numerical modelling for the better design of radon preventive and remedial measures

The main aim of the presented work was to verify, whether soil gas radon concentrations measured directly on building sites at a depth of 0.8 m below ground level and used in several countries for the design of protective measures against radon from the soil are in agreement with concentrations measured under houses after they had been built on a corresponding site. The correlation between sub-slab concentrations and concentrations measured at a depth of 0.8 m below the uncovered soil surface has been studied using a numerical simulation with the help of the computer program Radon2D. Numerical predictions showed that radon concentrations under the houses could be significantly different from concentrations measured on the building site and used for the assessment of radon risk categories. The highest differences were predicted for soil profiles with highly permeable upper layers. In the case of houses resting on the ground level the sub-slab radon concentration can be up to 3.4 times higher compared to the concentration measured at a depth of 0.8 m. An even higher increase was predicted for houses with the floor embedded 2 m below ground level. In this case the sub-floor concentrations increased up to 9.3 times. Numerical modelling can thus be considered as a powerful tool that can ensure the higher reliability of radon preventive and remedial measures

Algebraic and Discretization Error Estimation by Equilibrated Fluxes for Discontinuous Galerkin Methods on Nonmatching Grids

International audienceWe derive a posteriori error estimates for the discontinuous Galerkin method applied to the Poisson equation. We allow for a variable polynomial degree and simplicial meshes with hanging nodes and propose an approach allowing for simple (nonconforming) flux reconstructions in such a setting. We take into account the algebraic error stemming from the inexact solution of the associated linear systems and propose local stopping criteria for iterative algebraic solvers. An algebraic error flux reconstruction is introduced in this respect. Guaranteed reliability and local efficiency are proven. We next propose an adaptive strategy combining both adaptive mesh refinement and adaptive stopping criteria. At last, we detail a form of the estimates avoiding any practical reconstruction of a flux and only working with the approximate solution, which simplifies greatly their evaluation. Numerical experiments illustrate a tight control of the overall error, good prediction of the distribution of both the discretization and algebraic error components, and efficiency of the adaptive strategy