The numerical solution of the diffusion equation describing the flow of radon through cracks in a concrete slab

Numerical methods, finite differences and finite elements, have been used to solve the diffusion equation describing the flow of radon from soil through cracks in concrete slabs used in building foundations. Comparisons have been made with an analytical method in the case of a set of periodic cracks in a semi-infinite slab over soil. A more realistic model of a house considers a crack in a finite concrete raft which has side walls. The effect of placing a trench of a high porosity and/or a high diffusion coefficient material adjacent to the building as a remedial measure to reduce the emanation of radon from the crack has been investigated. Significant reduction of the radon flux was observed only when the crack was less than a diffusion length away from the trench. (author)