An algorithm for solving fuzzy advection diffusion equation and its application to transport of radon from soil into buildings

Abstract

This paper deals with the numerical solution of fuzzy advection diffusion equation. An algorithm for solving this fuzzy advection diffusion equation using finite difference method has been developed and the new numerical method is named as fuzzy finite difference scheme. The algorithm has been tested by a case study in which the radon transport from subsurface soil into buildings in presence of the fuzziness of the input parameters of advection diffusion equation such as radon diffusion coefficient and flow velocity of radon in air has been presented. Fuzziness 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 trapezoidal 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. Advantage of this new algorithm is to have the possibility of a power of quantifying uncertainty of the radon concentration as solution of the governing fuzzy partial differential equation. Results of computed radon concentration with uncertainty can be applied further for assessing the uncertainty in health hazards.