Improved multi-scale finite element method for stimulating two-dimensional water flow movement in porous media

Abstract

The invention discloses an improved multi-scale finite element method for stimulating two-dimensional water flow movement in porous media. The method comprises the steps as follows: firstly, converting a problem to be solved into a variational form; determining a boundary condition, setting a grid cell size h, subdividing a research area, and obtaining coarse grid cells; subdividing each coarse grid cell; according to a permeability coefficient K and the boundary condition of a basis function, solving the problem of degenerating elliptic type, and determining the basis function; according to the basis function, obtaining cell stiffness matrixes, and adding the same to obtain a total stiffness matrix; according to the boundary condition of the research area and a source sink term, obtaining a right-hand side; adopting an effective calculating method to solve the simultaneous equations of the total stiffness matrix and the right-hand side; and obtaining the hydraulic heads of all nodes in the research area. Through various simulation tests, the obtained result coincides with the analytical solution. Compared with the prior art, the method disclosed by the invention is similar to the same in precision, but the calculating time of the method is less than 10% of the calculating time in the prior art. The efficiency is greatly improved when the method is used for solving wide-range, long-time or complicated problems.

Description

technical field

[0001] The invention relates to the field of hydraulics, in particular to an improved multi-scale finite element method for simulating two-dimensional water flow motion in porous media. Background technique

[0002] The issue of water resources is an important issue closely related to human survival. Many cities around the world draw most of their water from groundwater. In addition, in geological engineering activities, the distribution of groundwater is also a factor that must be considered. Therefore, it is of great significance to study the calculation method and simulation of groundwater level for measuring and forecasting the distribution of groundwater.

[0003] The general equation of groundwater flow describes the distribution of steady flow by elliptic equation, and its two-dimensional form is:

[0004] - ∂ ∂ x ( K xx ...

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