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Numerical analysis of stochastic advection-diffusion equation via Karhunen-Loéve expansion

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Figure 1: A realization of the random field for σ = 1. Left: G N , right: a N . We use the bound (29) to truncate the field in the series (13)
Figure 2: The mean spread and dispersion computed for various numbers of MC simulations M and with fixed P = 50000 particles and a variance σ = 1.
Figure 5: The mean spread and mean dispersion computed for various numbers particles P and with fixed M = 600 MC simulations and a variance σ = 1.
Figure 7: The mean spread and mean dispersion computed for various numbers particles P and with fixed M = 600 MC simulations and a variance σ = 3.
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