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We present a numerical scheme, based on Godunov's method (REA algorithm), for the statistical mean of the solution of the 1D random linear transport equation, with homogeneous random velocity and random initial condition. Numerical examples are considered to validate our method.
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 random initial condition. We obtain the stability conditions of the method and we also show its consistency with a deterministic nonhomogeneous advective-diffusive… (More)
We solve Burgers' equation with random Riemann initial conditions. The closed solution allows simple expressions for its statistical moments. Using these ideas we design an efficient algorithm to calculate the statistical moments of the solution. Our methodology is an alternative to the Monte Carlo method. The present approach does not demand a random… (More)
This paper deals with a numerical scheme to approximate the mth moment of the solution of the one-dimensional random linear transport equation. The initial condition is assumed to be a random function and 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… (More)
We present a formula to calculate the probability density function to the solution of the random linear transport equation in terms of the density functions of the velocity and the initial condition. We also present an expression to the joint probability density function of the solution in two different points. Our results have shown good agreement with… (More)