عنوان مقاله [English]
In this study, numerical solutions to one dimensional transient linear and nonlinear oil flow in both homogeneous and heterogeneous media are achieved, based on the newly developed Green Element Method (GEM). GEM is a new numerical method based on a singular theory of the boundary element method. However, utilizing the discretization feature of finite element methods leads to forming a sparse and banded global matrix, which is easier to solve.
Solution procedure in this method commences by formation of free space green function and conversion of original partial differential equation and implementation of boundary conditions.
By applying GEM, some examples of linear and nonlinear flow are solved and the results are compared with the available analytical solution. The comparison shows good agreement between them.