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
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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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