Solving unsteady problems in water pollution using Lie symmetries

Abstract

This work proposes an analytic method to simulate the environmental damage caused by accidents with chemical substances in rivers and lakes. The two-dimensional transport equation is solved by rules based on the Lie algebra in situations in which the velocity field is considered locally constant. The exponential of the differential operator, which arises in the formal solution is locally approximated by the Taylor series. The initial condition is obtained by Lie symmetries. This method was by tested simulating scenarios that describe the blob's behavior through time and the results are compared with available data. Numerical results are shown.