We present a new algorithm based on Wiener–Hermite functionals combined with Fourier collocation to solve the advection equation with stochastic transport velocity. We develop different stategies of representing the stochastic input, and demonstrate that this approach is orders of magnitude more efficient than Monte Carlo simulations for comparable accuracy.
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Jardak, M., Su, CH. & Karniadakis, G.E. Spectral Polynomial Chaos Solutions of the Stochastic Advection Equation. Journal of Scientific Computing 17, 319–338 (2002). https://doi.org/10.1023/A:1015125304044