加速摂動境界要素法による不均質媒体内流動挙動シミュレーション

抄録

The boundary element method (BEM) owes its elegance, computational efficiency and accuracy, to the existence of the free-space Green's function for the governing equation. If there is no such solution in a closed form, the BEM cannot be applied, and unfortunately, this is the case for flow problems in heterogeneous media.
To overcome this difficulty, the governing equation is decomposed into various order perturbation equations, for which the free-space Green's function can be found. At each level of perturbation, the solution is obtained by the BEM and the summation of various order perturbation solutions gives the complete solution for the original governing equation. To improve the perturbation series, Padé approximants are employed, which accelerate the rate of convergence of a slowly convergent series and convert a divergent series into a convergent series.
Two kinds of perturbation boundary element models are introduced: one for transient flow problems, associated with the modified Helmholtz operater in Laplace space and the other for steady-state flow problems, associated with the Laplace operator. The perturbation BEM shows its utility in streamline tracking and well testing problems in heterogeneous media. The sound mathematical foundations ensure the high order of computational accuracy.