Fuzzy Finite Difference Scheme to Simulate Radon Transport from Subsurface Soil to Buildings

In this paper, a methodology for solving the advection diffusion equation describing the radon transport from subsurface soil into buildings in presence of the imprecision in the measurements of model parameters such as radon diffusion coefficient and flow velocity of radon in air has been explored. Imprecision of the model parameters is addressed as a fuzzy variable and the membership function of each such fuzzy variable is expressed in the form of a triangular fuzzy number. Explicit finite difference numerical method along with fuzzy parameters of the representative model is applied to obtain the solution of the governing advection diffusion equation and due to this the present numerical approach is named as fuzzy finite difference. Uncertainty quantification of the radon concentration as solution of the governing fuzzy partial differential equation is carried out and by using this uncertainty modeling, advantage of the fuzzy finite difference approach for obtaining the numerical solution of a fuzzy partial differential equation is shown. Results of computed radon concentration with uncertainty can be possible to use for assessing further the uncertainty in health hazards.