A numerical scheme for the variance of the solution of the random transport equation

We present a numerical scheme, based on Godunov's method (REA algorithm), for the variance of the solution of the 1D random linear transport equation, with homogeneous random velocity and stochastic initial condition. We obtain the stability conditions of the method and we also show its consistency with a deterministic nonhomogeneous advective-diffusive equation, which means convergency. Numerical results are considered to validate our scheme.