Yeh-multi-scale finite element method for simulating water flow Darcy velocity of porous medium

A porous medium and multi-scale technology, applied in the field of hydraulics, can solve the problems of lack of solution for Darcy permeation flow rate, and the inability to guarantee the continuity of velocity and flow, and achieve the effect of obvious efficiency advantage, high precision and high calculation efficiency

Active Publication Date: 2016-12-07
NANJING UNIV
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

However, the multi-scale finite element method lacks the means to solve the Darcy

Method used

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  • Yeh-multi-scale finite element method for simulating water flow Darcy velocity of porous medium
  • Yeh-multi-scale finite element method for simulating water flow Darcy velocity of porous medium
  • Yeh-multi-scale finite element method for simulating water flow Darcy velocity of porous medium

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Embodiment 1

[0070] Embodiment 1: two-dimensional oscillating medium model

[0071] The research area is a square unit: Ω=[0,1m]×[0,1m], the water flow equation is:

[0072] - ∂ ∂ x ( K ∂ H ∂ x ) - ∂ ∂ y ( K ∂ H ∂ y ) = W , - - - ( 4 )

[0073] The permeability coefficient is:

[0074] K = 1 2 + P 1 ...

Embodiment 2

[0085] Example 2: Two-dimensional gradient medium unsteady flow model

[0086] The research area is a square unit: Ω=[0,1m]×[0,1m], the water flow equation is:

[0087] S ∂ H ∂ t - ∂ ∂ x ( K ∂ H ∂ x ) - ∂ ∂ y ( K ∂ H ∂ ) = W , - - - ( 6 )

[0088] Permeability coefficient K(x,y)=(1+x)(1+y)m / d. The water storage coefficient is 0.1 / m, the aqui...

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Abstract

The invention discloses a Yeh-multi-scale finite element method for simulating water flow Darcy velocity of a porous medium, comprising the steps of: performing variation on the problem which needs resolution by a Galerkin method; subdividing a research area into coarse grid cells and subdividing all the coarse grid cells into fine grid units; resolving a degradation elliptic equation on each coarse grid cell to construct a basis function; resolving variational form by applying the basis function to obtain a total rigidity matrix; obtaining a right-hand term according to the source sink term and the boundary condition of the research area; performing simultaneous operation to obtain a waterhead equation set; resolving the equation set by an effective numerical method to obtain the node waterhead of the research area; and resolving a Darcy equation directly in the research area by combining a Galerkin finite element model of Yeh and applying the constructed basis function and the waterhead value of the research area to obtain continuous Darcy permeating velocity on the coarse-scale node, and linearly expressing the fine-scale Darcy permeating velocity by the basis function. Compared with the prior art, the method has similar precision and higher efficiency.

Description

technical field [0001] The invention belongs to the technical field of hydraulics, in particular to a Yeh-multiscale finite element method for simulating the Darcy velocity of two-dimensional water flow in a porous medium. Background technique [0002] Groundwater is mainly distributed in porous media and is an important part of water resources. When simulating the flow and solute migration of groundwater, it is very important to accurately simulate the velocity and flow of groundwater. Therefore, the research and numerical simulation of the calculation method of the Darcy seepage velocity of groundwater is of great significance for the investigation of the distribution of groundwater and the state of solute migration. [0003] Yeh’s Galerkin finite element model [Yeh 1981] is a classic method for solving the Darcy seepage velocity of groundwater. This method directly uses the finite element method to solve the Darcy equation in the study area, and has high calculation accur...

Claims

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Application Information

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IPC IPC(8): G06F17/50
CPCG06F30/23
Inventor 谢一凡吴吉春薛禹群谢春红
Owner NANJING UNIV
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