METHOD OF DISTRIBUTIONS FOR SYSTEMS WITH STOCHASTIC FORCING

摘要

The method of distributions is developed for systems that are governed by hyperbolic conservation laws with stochastic forcing. The method yields a deterministic equation for the cumulative distribution function (CDF) of a system state, e.g., for flow velocity governed by an inviscid Burgers equation with random source coefficients. This is achieved without recourse to any closure approximation. The CDF model is verified against Monte Carlo (MC) simulations using spectral numerical approximations. Our analysis demonstrates that the CDF model accurately predicts the mean and standard deviation of the system state for Gaussian, normal, and beta distributions of the random coefficients.