Cubic spline multi-scale finite element method for simulating two-dimension flow movement

A finite element, multi-scale technology, applied in the field of hydraulics, can solve problems such as the inability to obtain continuous Darcy seepage velocity field and the inability to accurately describe the state of groundwater movement, and achieve the effects of saving calculation costs, high efficiency, and ensuring continuity

Inactive Publication Date: 2016-02-24
NANJING UNIV
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  • Application Information

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Problems solved by technology

[0004] For the problems referred to above, the object of the present invention is to provide a cubic spline multiscale finite element method for simulating two-dimensional water flow movement, which organically combines the cubic spline method (Zhang et al.1994) with the multiscale finite element method to achieve Solve the problem that the continuous and accurate Darcy seepage velocity field cannot be obtained through Darcy's law in the prior art, and the groundwater movement state cannot be accurately described

Method used

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  • Cubic spline multi-scale finite element method for simulating two-dimension flow movement
  • Cubic spline multi-scale finite element method for simulating two-dimension flow movement
  • Cubic spline multi-scale finite element method for simulating two-dimension flow movement

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Embodiment 1

[0048] Example 1: Two-dimensional continuum model

[0049] The research area is a square unit: Ω=[0,1m]×[0,1m], the permeability coefficient K(x,y)=(1+x)(1+y)m / d, and the flow equation is:

[0050] - ∂ ∂ x ( K x x ∂ H ∂ x + K x y ∂ H ∂ y ) - ∂ ∂ y ( K y x ∂ H ...

Embodiment 2

[0062] Example 2: Two-dimensional high oscillation head model

[0063] The research area is a square unit: Ω=[0,1m]×[0,1m], permeability coefficient K(x,y)=10m / d. The equation is the formula:

[0064] - ∂ ∂ x ( K x x ∂ H ∂ x + K x y ∂ H ∂ y ) - ∂ ∂ y ( K y x ∂ H ...

Embodiment 3

[0070] Embodiment 3: two-dimensional submerged flow model (non-linear model)

[0071] The current equation is the submerged flow equation:

[0072] - ▿ · K ( x , y , H ) ▿ H = W ,

[0073] K ( x , y , H ) = T ( H - b ) 0 0 T ( H ...

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Abstract

The present invention discloses a cubic spline multi-scale finite element method for simulating two-dimension flow movement. The method comprises: firstly converting a problem that needs resolution into a variational version; determining a boundary condition of a research area, setting a coarse grid cell dimension h, dissecting the research area to obtain a coarse grid cell, and dissecting the coarse grid cell into a fine grid cell; resolving a degradation elliptic problem on each coarse grid cell to construct a basis function; resolving a total rigidity matrix and a right-hand side simultaneous equations system by using an effective calculation matrix method; obtaining a water head of each node (the coarse dimension) on the research area; obtaining a coarse dimension water head derivative by using the cubic spline technique, and obtaining Darcy flow velocity of the coarse dimension according to Darcy's Law; obtaining a water head of each node (the fine dimension) by using the basis function and an interpolation formula; and obtaining a fine dimension water head derivative by using the cubic spline technique, and obtaining Darcy flow velocity of the fine dimension according to the Darcy's Law. Compared to the prior art, the method disclosed by the present invention has similar precision, but has higher calculation efficiency.

Description

technical field [0001] The invention belongs to the technical field of hydraulics, and in particular relates to a cubic spline multi-scale finite element method for simulating two-dimensional water flow motion in porous media. Background technique [0002] Groundwater is a very important water body and an important part of water resources. Many cities around the world draw most of their water from groundwater. At the same time, the distribution and migration of groundwater is an important factor in geological engineering activities. Therefore, it is of great significance to study the calculation method and numerical simulation of groundwater level and seepage velocity for the investigation and prediction of groundwater distribution. [0003] The multi-scale finite element method (Hou and Wu1997) is a method proposed by scientists to solve the problem of groundwater flow in heterogeneous media. The core idea of ​​the multi-scale finite element method is to make the basis f...

Claims

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Application Information

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Patent Type & Authority Applications(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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