Gridless Modeling of Oil Spreading and Transport in the Sea

B. V. Arkhipov, V. N. Koterov, V. V. Solbakov, D. A. Shapochkin, and Yu. S. Yurezanskaya

We consider features of the application of a discrete particle statistical method to solve the transport and diffusion equation in the case of the time-dependent (contaminant transport by turbulent flow) or nonlinear (thin slick spreading on the water surface) diffusion rate. For the problem of contaminant dispersion by turbulent flow, an algorithm is developed for discrete particle technique application in the case of the diffusion rate change governed by “4/3 law,” and a good agreement of numerical and analytical results is demonstrated. For the problem of oil slick spreading, as described by the quasi-linear transport–diffusion equation, an algorithm of the particle random walk is developed, in which the walk step dispersion depends on the unknown function. The solution using a discrete particle technique for both volley and continuous discharge is in good agreement with analytical and/or numerical solutions using the grid method (the latter is practically equivalent to the analytical solution due to small time and space steps for a one-dimensional axisymmetric case).

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