Statistical Moments of the Random Linear Transport Equation

This paper deals with a numerical scheme to approximate the $m$th moment of the solution of the one-dimensional random linear transport equation. The initial condition is assumed to be a random functionand the transport velocity is a random variable. The scheme is based on local Riemann problem solutions and Godunov's method. We show that the scheme is stable and consistent with an advective-diffusive equation. Numerical examples are added to illustrate our approach.