A local absorbing boundary condition for 3D seepage and heat transfer in unbounded domains

摘要

For the parabolic problems in an infinite space, previous methods basically focused on the one- and two-dimensional artificial boundary. Here, a high-order local absorbing boundary condition (ABC) used for the fluid seepage and heat transfer in unbounded one- and two-dimensional domains is extended to the relative three-dimensional analysis. The local ABCs are first derived for the problem in an isotropic media and then stretched to the case in an orthotropic media. The function including time-related variables in Laplace-Fourier space is approximated through the Gauss-Legendre quadrature formula. By using the inverse Laplace-Fourier transformation, the local ABCs in Laplace-Fourier space are inverted into the ones in time space. The numerical examples indicate that the local ABCs can provide satisfactory results with high computational efficiency, especially for the long-term analysis. Moreover, the relationship among the diffusion coefficient, maximum simulation time and approximation order value is also investigated.

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