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Yeh-Multiscale Finite Element Method for Simulation of Darcy Velocity of Water Flow in Porous Media

A porous medium, multi-scale technology, applied in the field of hydraulics, can solve the problems such as the inability to guarantee the continuity of velocity and flow, and the lack of solving the Darcy infiltration velocity, etc., to achieve the effect of high precision, obvious efficiency advantages, and high computing efficiency.

Active Publication Date: 2019-04-16
NANJING UNIV
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

However, the multi-scale finite element method lacks the means to solve the Darcy seepage velocity, and cannot guarantee the continuity of velocity and flow at nodes

Method used

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  • Yeh-Multiscale Finite Element Method for Simulation of Darcy Velocity of Water Flow in Porous Media
  • Yeh-Multiscale Finite Element Method for Simulation of Darcy Velocity of Water Flow in Porous Media
  • Yeh-Multiscale Finite Element Method for Simulation of Darcy Velocity of Water Flow in Porous Media

Examples

Experimental program
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Effect test

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]

[0073] The permeability coefficient is:

[0074]

[0075] where P 1 =1.965,P 2 = 1.99, the source-sink term W and the constant head boundary are determined by the analytical solution H=xy(1-x)(1-y).

[0076] The model is solved using MSFEM-Y, Method-Yeh, Method-Zhang and Method-Yeh-F. In order to ensure the same number of coarse grid nodes, MSFEM-Y, Method-Yeh and Method-Zhang all divided each side of the study area into the same 30 parts (N=30), a total of 1800 (2NN) triangular units ( figure 1 ). MSFEM-Y divides each unit into 25 fine grid units ( figure 2 ). In order to ensure that the number of cells is the same as the number of fine grid cells in MSFEM-Y, Method-Yeh-F divided each side of the study area into 150 parts (N=150), with a total of 45,000 fine grid cells.

[0077] Coarse-scale Darcy per...

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]

[0088] Permeability coefficient K(x,y)=(1+x)(1+y)m / d. The water storage coefficient is 0.1 / m, the aquifer thickness is 1 m, the time step is 1 day, and the total time is 5 days. The source-sink term W and the fixed head boundary are solved analytically: H=xy(1-x)(1-y)e -t Sure.

[0089] The model is solved using MSFEM-Y, Method-Yeh, Method-Zhang and Method-Yeh-F. The subdivision is the same as in the first embodiment above, that is, MSFEM-Y, Method-Yeh and Method-Zhang subdivide the study area into 1800 units, MSFEM-Y subdivides each coarse grid into 25 fine units, and Method- Yeh-F divided the study area into 45000 units.

[0090] Coarse-scale Darcy percolation velocity

[0091]Same as the above-mentioned Example 1, MSFEM-Y and Method-Yeh-F obtained more accurate head values ​​than other methods, MS...

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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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Patent Type & Authority Patents(China)
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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