Novel multi-scale finite element method for simultaneously simulating underground water flow and Darcy speed

A technology of groundwater flow and simultaneous simulation, applied in the field of hydraulics, which can solve problems such as low computational efficiency

Active Publication Date: 2021-02-09
HOHAI UNIV
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

[0005] Purpose of the invention: In order to overcome the deficiencies in the background technology, the present invention discloses a novel multi-scale finite element method for simultaneously simulating groundwater flow and Darcy velocity. The multi-scale finite element method and Yeh's Galerkin finite element method were developed to improve the calculation efficiency of water head and Darcy velocity through multi-scale basis functions, and the velocity matrix was constructed through Yeh's Galerkin finite element method to ensure the continuity of Darcy velocity , by embedding the velocity matrix into the algorithm framework of the multi-scale finite element method to realize the simultaneous calculation of Darcy velocity and water head, which can ensure the mass conservation of Darcy velocity and water head, and solve the problem of solving the heterogeneous ground water head and continuous The calculation efficiency of Darcy's velocity is too low, and it is realized that two parameters of water head and Darcy's velocity can be obtained by solving one equation

Method used

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  • Novel multi-scale finite element method for simultaneously simulating underground water flow and Darcy speed
  • Novel multi-scale finite element method for simultaneously simulating underground water flow and Darcy speed
  • Novel multi-scale finite element method for simultaneously simulating underground water flow and Darcy speed

Examples

Experimental program
Comparison scheme
Effect test

Embodiment 1

[0083] Two-dimensional continuum steady flow model

[0084] The steady flow equation is:

[0085]

[0086] The research area Ω=[0,1]×[0,1], the aquifer thickness is 1, two different hydraulic coefficient fields are considered, K=K 1 = 1 and The Dirichlet boundary condition and the source-sink term W are given by the analytical head H = xy(1-x)(1-y).

[0087] In this example, FEM-F, NMSFEM, MSFEM and FEM are used to solve the water head field. NMSFEM, MSFEM and FEM divide each boundary of the study area Ω into 30 equal parts. NMSFEM and MSFEM divide the study area Ω into 900 (30×30) rectangular coarse units, and each coarse unit is divided into 128 (8×30) 8×2) triangular fine units; FEM divides the research area Ω into 1800 (30×30×2) triangular fine units; FEM-F divides the research area Ω into 240×240×2 units to ensure that its units The total is the same as the total number of elements for NMSFEM and MSFEM.

[0088] Such as image 3 Shown are the absolute errors of ...

Embodiment 2

[0091] Two-dimensional Steady Flow Model in Medium with Gradient Variation

[0092] The research area is a square area: Ω=[0,10km]×[0,10km], the research equation is Equation (11), and the permeability coefficient in the research area satisfies the relationship from left to right: The thickness of the aquifer is 1m.

[0093] In this example, the left and right boundaries of the study area are constant water head boundaries, which are 10m and 0m, respectively, and the upper and lower boundaries are water-isolated boundaries.

[0094] In this example, FEM-F, NMSFEM-O, NMSFEM-L, MSFEM-O, MSFEM-L and FEM are used to solve the water head field. NMSFEM, MSFEM and FEM divide each boundary of the study area Ω into 20 equal parts. NMSFEM and MSFEM divide the study area Ω into 400 (20×20) rectangular coarse units, and each rough unit is divided into 72 (6×6 ×2) triangular fine units; FEM divides the research area Ω into 800 (20×20×2) triangular fine units; FEM-F divides the research ...

Embodiment 3

[0098] Two-dimensional unsteady flow model in gradient media

[0099] The research equation is:

[0100]

[0101] The study area is: Ω=[0,10km]×[0,10km], the permeability coefficient in the study area satisfies the relationship from left to right: The left and right boundaries are constant water head boundaries, which are 10m and 0m respectively, and the upper and lower boundaries are water barrier boundaries. The unit water storage capacity is 10 -6 / m, the aquifer thickness is 1m. There is a pumping well at the point (6000m, 6000m), the constant flow rate is 100m / day, the total pumping time is 3 days, and the time step is 1 day. The initial water head in this example is H 0 =0.

[0102] In this example, FEM-F, NMSFEM-O, MSFEM-O and FEM are used to solve the water head field. NMSFEM, MSFEM and FEM divide the research area Ω into 20 equal parts, NMSFEM and MSFEM divide the research area Ω into 400 (20×20) rectangular coarse units, and each rough unit is divided into...

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Abstract

The invention discloses a novel multi-scale finite element method for simultaneously simulating underground water flow and Darcy speed, which comprises the following steps of: setting scales of coarseand fine grid units, dividing a research area into the coarse grid units, and dividing the coarse grid units into the fine grid units to obtain a multi-scale grid; solving a degraded elliptic equation on the coarse mesh unit, and constructing a primary function; solving a Darcy equation and a speed matrix on the coarse mesh unit; obtaining a variation form of the problem by using a Galerkin method and a Green formula, and dispersing the variation form to the coarse mesh; substituting the Darcy law into variational components on each coarse mesh, converting a water head partial derivative terminto a speed term, linearly expressing the Darcy speed term by applying a coarse-scale solution of a water head by applying a speed matrix to obtain a unit stiffness matrix of the coarse mesh, and adding to obtain a total equation of the water head; and solving a total equation by using an effective matrix solution, and meanwhile, obtaining a Darcy speed value through a speed matrix. Compared with various classic methods, the novel multi-scale finite element method has higher efficiency.

Description

technical field [0001] The invention belongs to the technical field of hydraulics, in particular to a novel multi-scale finite element method for simultaneously simulating groundwater flow and Darcy velocity. Background technique [0002] Groundwater is an essential part of water resources. It has the advantages of good water quality and stable water quantity. It is a very important source of human life and economic development. Due to the mismatch between the layout of my country's productive forces and the distribution of groundwater resources, it will not only cause the reduction of groundwater resources and water pollution, but also cause geological and environmental problems such as seawater intrusion, land subsidence, soil deterioration, and engineering geological disasters. Numerical simulation is an important technical means of groundwater research, it can predict the state of groundwater resources and environment and their changing trends. Therefore, it is of great...

Claims

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Application Information

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IPC IPC(8): G06F30/23G06F30/28G06F113/08G06F119/14
CPCG06F30/23G06F30/28G06F2113/08G06F2119/14
Inventor 谢一凡王益谢镇泽鲁春辉徐腾叶逾常勇
Owner HOHAI UNIV
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