A high-order local artificial boundary condition for seepage and heat transfer

A high-order local artificial boundary condition (ABC) with a new approximation scheme is proposed for numerical analyses of seepage and heat transfer in unbounded domains. The proposed ABCs are first derived for a one-dimensional case and then extended to high-dimensional cases and transversely isotropic media. In the derivation, the irrational function in Laplace space with respect to time is approximated through numerical integration. The calculations show that the proposed ABCs provide more satisfactory results than those obtained by using existing approximation methods, especially for long-duration simulations. Moreover, the relation among the calculation accuracy, approximation order, and diffusivity is also investigated.