Parametric uncertainty analysis of solute transport process using fuzzy lattice Boltzmann scheme

Abstract

Uncertainty analysis of groundwater flow and solute transport model is important from the point of safety measures in the field of nuclear science and technology. Researchers have already carried out this uncertainty analysis using traditional Monte Carlo simulations. However, in practice, Monte Carlo simulation may not be possible because of lack of data obtained from the field experiments. Therefore, demand is to investigate the uncertainty by using imprecise based method. In order to fulfill this demand, we have carried out the parametric uncertainty analysis of solute transport model using a fuzzy set method. This paper, proposes an innovative methodology for solving advection diffusion equation describing tracer transport through geological media in presence of imprecise measurements of model parameters such as tracer dispersion coefficient and groundwater flow velocity. Measurement around most likely value provides a spread causing an imprecision of the model parameters. Imprecision 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. The governing advection dispersion equation is numerically solved using lattice Boltzmann scheme along with fuzzy parameters of the representative model and due to this the present numerical approach is named as fuzzy lattice Boltzmann. Uncertainty quantification of the solute concentration as solution of the governing fuzzy differential equation is carried out and by using this uncertainty modeling, advantage of the fuzzy lattice Boltzmann approach for obtaining the numerical solution of a fuzzy partial differential equation is shown.