The application of the improved Talbot's inverse Laplace transformation method in solving the flow problem of porous materials

In this paper, we extend the fixed Talbot's method to the complex-valued function in order to get the general solutions for the Biot's consolidation in the physical domain. We derive a solution for the unsteady flow field of layered porous media with anisotropic permeability under a point fluid source. By a Laplace and two-dimensional(2D) Fourier transform, the continuity equation of the fluid can be solved, and the flow field can be expressed in an analytical form in the transformed domain. Using the boundary and interface condition, the flow field for general layered porous media can be solved in the transform domain. The actual solutions in the physical domain can be obtained by inverting the Laplace-2D Fourier transform. Numerical examples are given to demonstrate the validity of the extended fixed Talbot's inverse Laplace transformation method, and its application in solving dymanic problems of porous materials.