Abstract
Propagation of the oil spilling from a damaged oil tanker is considered in a limited sea area. The accident consequences are evaluated by means of direct and adjoint oil concentration estimates in ecologically sensitive zones. While the direct estimates are preferable to get a comprehensive idea of the oil spill impact on the whole area, the adjoint ones are useful and economical in studying the sensitivity of the oil concentration in some zones to variations in the accident site and oil spill rate from the tanker. Thanks to special boundary conditions set at the inflow and outflow parts of the open boundary, the main and adjoint oil transport problems are both well-posed according to Hadamard (1923). The estimates obtained in Skiba (1996a) are generalized to the three dimensions. Balanced, absolutely stable 2nd-order finite-difference schemes based on the splitting method are constructed for the two- and three-dimensional cases, both. The main and adjoint schemes are compatible in the sense that at every fractional step of the splitting algorithm, the one-dimensional split operators of both the schemes satisfy a discrete form of the Lagrange identity (Marchuk, 1995). In the special unforced and non-dissipative case, the schemes have two conservation laws each. Each split problem is solved by the factorization method.
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Skiba, Y.N. Direct and Adjoint Oil Spill Estimates. Environ Monit Assess 59, 95–109 (1999). https://doi.org/10.1023/A:1006055702786
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DOI: https://doi.org/10.1023/A:1006055702786