Analysis of a numerical solution to the one-dimensional stochastic convection equation |
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| Authors: | CA Oster AG Gibbs DH Tang |
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| Institution: | Battelle, Pacific Northwest Laboratory, Richland, Washington 99352, USA;INTERA Environmental Consultants, 11999 Katy Freeway, Houston, Texas 77079, USA |
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| Abstract: | Under certain conditions the concentration and flux of a substance moving in a stochastic flow field are described by the stochastic convection equation. A numerical method for solving the one-dimensional problem is studied here. The differential operator is replaced by a discrete linear operator based on finite differences. The resulting system of stochastic equations is then replaced by a system of equations whose solution is the mean concentration or mean flux. This final system is analysed and conditions for a stable numerical solution are obtained. Finally, numerical examples are given and are compared to an approximate analytical solution to the stochastic convection equation. |
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