Institute of Computational Mathematics and Mathematical Geophysics

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Стохастическое моделирование в геофизике и физике атмосферы

We employ the methods of splitting and domain decomposition for constructing artificial boundary conditions (ABCs) for the advection-diffusion-reaction equation when the region of interest is a 3D open set with a piecewise smooth artificial boundary. We begin from a domain decomposition, representing the infinite space as a union of an interior (computational) and exterior domains with an overlap. Then we perform the splitting by physical processes and consider the advective and diffusive terms separately. The exterior advective problem admits the analytical solution, which is imposed as the exact local ABC for the interior advective problem. For the exterior diffusive problem we first apply the Laplace transform in time and then use the operator splitting by coordinates and spline interpolation. Therefore, we obtain an infinite family of functions approximating the exterior solution with higher and higher accuracy. These functions are used as local ABCs for the interior diffusive problem. We also prove that the resulting boundary value problems are well-posed in the sense of existence, uniqueness and stability of solution, and present results of the numerical experiments that confirm the theoretical study.

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    Дата последней модификации: 06-Jul-2012 (11:52:46)