CN111611722B - A method and system for predicting groundwater pressure in tidal areas - Google Patents

Abstract

The invention relates to a method and a system for predicting underground water pressure in a tidal region, wherein the method comprises the following steps:S1: establishing a tide response underground water control equation based on a water-bearing stratum system of a tidal area, deducing a complete base of the control equation and meeting an approximate solution of the control equation;S2: establishing an underground water model of the tidal region by adopting a space-time coordinate system, and respectively dispersing a space coordinate axis and a time coordinate axis;S3: respectively enabling discrete time boundary points and space boundary points to meet given boundary values and initial values, respectively substituting the boundary values and the initial values into approximate solutions of a control equation, establishing a linear equation set and expressing the linear equation set as a matrix operation form;S4: solving the undetermined coefficient;S5: substituting any point in the space-time coordinate system into the approximate solution, calculating the water head value of any point in the tidal region, and realizing the prediction of the underground water pressure of the tidal region. The method and the system are beneficial to quickly, efficiently and accurately predicting the underground water pressure of the tidal region.

Description

A method and system for predicting groundwater pressure in tidal areas

technical field

The invention belongs to the technical field of groundwater pressure sensing, and in particular relates to a method and system for predicting groundwater pressure in tidal areas.

Background technique

Water resources are the foundation of human survival and development, and even more importantly, the energy center. It is closely related to the balance and stability of the ecosystem. While ensuring the continuation of human life, it is also of immeasurable significance to the sustainable development of society. Groundwater is one of the few water resources in the world that can be used by human beings. It is the main source of water supply for residents' lives, industrial production, and agricultural irrigation in my country, especially in coastal areas. Groundwater resources account for a large proportion.

The tidal area is the area where land freshwater and seawater meet. Due to the influence of geological processes and tidal fluctuations all year round, the groundwater level in this area will fluctuate accordingly with tidal fluctuations, that is, the tidal effect of groundwater. The tidal effect of groundwater will not only gradually change the beach structure, but also be closely related to the water volume exchange and material transfer between the aquifer and seawater. Therefore, the ecological environment in tidal areas has an inseparable relationship with groundwater, especially with the unreasonable exploitation of groundwater resources. With the development of engineering construction, the groundwater level and water quality have already undergone many changes due to water circulation imbalance and groundwater imbalance. Many environmental geological problems such as groundwater level drop, ground subsidence, seawater intrusion, and groundwater pollution have gradually appeared in tidal areas.

Contents of the invention

The object of the present invention is to provide a method and system for predicting groundwater pressure in tidal areas. The method and system are conducive to quickly, efficiently and accurately predicting groundwater pressure in tidal areas.

In order to achieve the above object, the technical solution adopted in the present invention is: a method for predicting groundwater pressure in a tidal region, comprising the following steps:

S1: Based on the aquifer system in the tidal region, establish the governing equation of the tidal response groundwater, derive the complete Trefftz base of the governing equation and the approximate solution satisfying the governing equation;

S2: Use the space-time coordinate system to establish the groundwater model in the tidal area, and discretize the space coordinate axis and the time coordinate axis into n ₁ points and n ₂ points respectively;

S3: Make the discrete time boundary point and space boundary point meet the given boundary value and initial value respectively, respectively substitute the boundary value and initial value into the approximate solution of the governing equation, establish a linear equation system and express it as a matrix operation of Aλ=B form;

S4: Solve the undetermined coefficient λ;

S5: Substitute any point in the space-time coordinate system into the approximate solution, and calculate the water head value h( _xi ,t _j ) at any point in the tidal area by Β=Αλ, so as to realize the prediction of groundwater pressure in the tidal area.

Further, in the step S1, the aquifer system in the tidal area includes a free aquifer and a spillover aquifer, assuming that the free aquifer in the tidal area is not affected by tidal fluctuations, and the groundwater level is the same as the mean sea level, And taking the mean sea level as the datum of the aquifer system, the corresponding tidal response groundwater governing equation of the aquifer system is as follows:

0≤x≤L_n，0≤t≤t_max

0≤x≤L _n , 0≤t≤t _max

Among them, x is the distance from the shore, t is the forecast time, h is the total hydraulic pressure of the groundwater, T is the hydraulic conductivity, L is the overflow coefficient, S is the water storage coefficient, L _n is the distance from the shore, and t _max is the final duration .

Further, in the step S1, a set of complete Trefftz basis functions satisfying the governing equation of the tidal response groundwater is derived by the method of separation of variables, and the approximate solution of the governing equation is represented by the linear superposition combination of the basis functions.

Further, in the space-time coordinate system in the step S2, time is defined as an independent variable based on the space-time coordinate system, and the space-time coordinate system is used to process the transient modeling of groundwater in tidal areas, and the established groundwater model in tidal areas A two-dimensional coordinate system includes one dimension in time and one dimension in space.

Further, in the step S3, the matrix A is a matrix with a scale of aa×bb formed by the Trefftz basis, the matrix B is a matrix with a scale of aa×1 formed by boundary values and initial values, and the undetermined coefficient λ is the scale is a bb×1 matrix, where aa=n ₁ +2n ₂ , bb=4(w+1), and w is the order of the approximate solution of the governing equation.

Further, in the step S4, the undetermined coefficient λ is solved by Matlab left division method, so as to improve the solution speed.

The present invention also provides a groundwater pressure prediction system in a tidal area, which includes a memory and a processor, the memory stores a computer program, and the processor can realize the steps of the above method when running the computer program.

Compared with the prior art, the present invention has the following beneficial effects: a method and system for predicting groundwater pressure in tidal areas are proposed, and the method and system can obtain the tidal response groundwater control equation through establishment, derivation and solution, which can realize fast and efficient , Accurately predict the groundwater pressure in tidal areas, and further understand and analyze the distribution and evolution of groundwater pressure in tidal areas affected by tidal fluctuations, and provide a basis for rationally deploying relevant strategies for sustainable coastal development.

Description of drawings

FIG. 1 is a flow chart for implementing a method in an embodiment of the present invention.

Fig. 2 is a schematic diagram of space-time allocation in an embodiment of the present invention.

Fig. 3 is the actually measured fluctuation curve of tidal water level and groundwater level in the embodiment of the present invention.

Fig. 4 is a comparison of groundwater level fluctuations measured and predicted by the present invention in the embodiment of the present invention.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

Referring to Fig. 1, the method for predicting underground water pressure in tidal areas proposed by the present invention comprises the steps:

S1: Based on the aquifer system in the tidal area, establish the governing equation of the tidal response groundwater, deduce the complete Trefftz base of the governing equation and the approximate solution satisfying the governing equation.

S2: Establish the groundwater model in the tidal area by using the space-time coordinate system, and discretize the space coordinate axis and the time coordinate axis into n ₁ points and n ₂ points respectively.

S3: Make the discrete time boundary point and space boundary point meet the given boundary value and initial value respectively, respectively substitute the boundary value and initial value into the approximate solution expression of the governing equation, establish a linear equation system and express it as Aλ=B Matrix operation form.

S4: Solve the undetermined coefficient λ.

S5: Substitute any point in the space-time coordinate system into the approximate solution, and calculate the water head value h( _xi ,t _j ) at any point in the tidal area by Β=Αλ, so as to realize the prediction of groundwater pressure in the tidal area.

Taking Xingda Port in Taiwan, China as an example, the relevant content involved in the present invention will be further described below. Fig. 3 is the measured fluctuation curve of the tidal water level and groundwater level in this embodiment.

In the step S1, the aquifer system in the tidal area includes a free aquifer and a spillover aquifer, assuming that the free aquifer in the tidal area is not affected by tidal fluctuations, the groundwater level is the same as the mean sea level water level, and the average Sea level is used as the datum of the aquifer system, and the corresponding tidal response groundwater governing equation of the aquifer system is as follows:

0≤x≤L_n，0≤t≤t_max

0≤x≤L _n , 0≤t≤t _max

Among them, x is the distance from the shore, t is the forecast time, h is the total hydraulic pressure of the groundwater, T is the hydraulic conductivity, L is the overflow coefficient, S is the water storage coefficient, L _n is the distance from the shore, and t _max is the final duration .

A set of complete Trefftz basis functions satisfying the tidal response groundwater governing equations are derived by the method of separation of variables:

Then, the approximate solution to the governing equations is represented by a linear superposition combination of basis functions:

Wherein, A ₀₁ , B ₀₁ , A ₀₂ , B ₀₂ , A _1p , B _1p , A _2p , and B _2p are arbitrary constants, and w is the order of the approximate solution of the governing equation. In this embodiment, w=15.

In the space-time coordinate system of step S2, time is defined as an independent variable based on the space-time coordinate system, and the space-time coordinate system is used to process the transient modeling of groundwater in tidal areas, and the two-dimensional coordinates of the established groundwater model in tidal areas The system includes one dimension in time and one dimension in space. The simulation duration is t _max =30h, and the farthest distance from the shore is L _n =3000m. The space boundary is discretized into n ₁ points, and the time boundary is discretized into n ₂ points, where n ₁ =601, n ₂ =31. FIG. 2 is a schematic diagram of space-time allocation in this embodiment.

作为内陆边界。In the step S3, the tidal boundary at the junction of land and sea meets the tidal level data h ₁ (x,t)| _x=0 measured by the Yongan tide level station, and the initial groundwater level of the aquifer is consistent with the mean sea level, and v(x, t)| _t＝0 ＝0 is used as the initial boundary, and the position far enough away from the coastline is regarded as the same as the groundwater level and the sea level.

as an inland border.

The approximate solution expression satisfying the tidal boundary conditions is as follows:

where i=1, t=1, 2, . . . , 31.

The approximate solution expression satisfying the initial boundary conditions is as follows:

Where i=1, 2, . . . , 601, j=1.

The approximate solution expression satisfying the inland boundary conditions is as follows:

where i=601, j=1, 2, . . . , 31.

Establish a linear equation system and express it as a matrix operation form of Aλ=B, as shown in the following formula:

Wherein, matrix A is a matrix of aa×bb (in this embodiment, 663×64) formed by the Trefftz basis, and matrix B is aa×1 (in this embodiment, in this embodiment) formed by boundary values and initial values. is a matrix of 663×1), and the undetermined coefficient λ is a matrix with a scale of bb×1 (64×1 in this embodiment). Where aa=n ₁ +2n ₂ , bb=4(w+1).

In the step S4, the undetermined coefficient λ is solved by Matlab left division method, so as to improve the solution speed.

In the traditional Matlab operation, the right division in the form of matrix operation needs to calculate the inverse of the matrix before multiplying, while the left division does not need to calculate the inverse matrix, and can be directly divided, and can also avoid the singularity of the matrix. When calculating When the dimension reaches tens of thousands of dimensions, the calculation speed of "A\B" is much faster than that of "inv(A)*B".

In the step S5, any point in the Xingda Port area of Taiwan, China is substituted into the approximate solution obtained above, and the water head value h( _xi , t _j ) of any point can be calculated by Β=Αλ:

Where i=1,2,...,601, j=1,2,...,31.

Thus, the prediction of groundwater pressure in tidal areas can be realized. Fig. 4 is a comparison of groundwater level fluctuations measured in this embodiment and predicted by the present invention.

The present invention also provides a groundwater pressure prediction system in a tidal area for implementing the above prediction method, including a memory and a processor, the memory stores a computer program, and the processor can realize the above method when running the computer program step.

The above are the preferred embodiments of the present invention, and all changes made according to the technical solution of the present invention, when the functional effect produced does not exceed the scope of the technical solution of the present invention, all belong to the protection scope of the present invention.

Claims (5)

1. A groundwater pressure prediction method in a tidal area, is characterized in that, comprises the steps: S1: Based on the aquifer system in the tidal area, establish the governing equation of the tidal response groundwater, derive the complete Trefftz basis function of the governing equation and approximate solution satisfying the governing equation; In the step S1, a set of complete Trefftz basis functions satisfying the tidal response groundwater governing equation are derived by the method of separation of variables:

Then, the approximate solution to the governing equations is represented by a linear superposition combination of basis functions:

Among them, A ₀₁ , B ₀₁ , A ₀₂ , B ₀₂ , A _1p , B _1p , A _2p , B _2p are arbitrary constants, and w is the order of the approximate solution of the governing equation; S2: Use the space-time coordinate system to establish the groundwater model in the tidal area, and discretize the space coordinate axis and the time coordinate axis into n ₁ points and n ₂ points respectively; S3: Make the discrete time boundary point and space boundary point meet the given boundary value and initial value respectively, respectively substitute the boundary value and initial value into the approximate solution of the governing equation, establish a linear equation system and express it as a matrix operation of Aλ=B form; In the step S3, the approximate solution expression satisfying the tidal boundary condition is as follows:

where i=1, t=1,2,...,31; The approximate solution expression satisfying the initial boundary conditions is as follows:

where i=1, 2, ..., 601, j=1; The approximate solution expression satisfying the inland boundary conditions is as follows:

where i=601, j=1,2,...,31; S4: Solve the undetermined coefficient λ; S5: Substituting any point in the space-time coordinate system into the approximate solution, and calculating the water head value h( _xi ,t _j ) at any point in the tidal area by Β=Αλ, realizing the prediction of groundwater pressure in the tidal area:

where i=1,2,...,601, j=1,2,...,31; In the step S1, the aquifer system in the tidal area includes a free aquifer and a spillover aquifer, assuming that the free aquifer in the tidal area is not affected by tidal fluctuations, the groundwater level is the same as the mean sea level water level, and the average Sea level is used as the datum of the aquifer system, and the corresponding tidal response groundwater governing equation of the aquifer system is as follows:

Among them, x is the distance from the shore, t is the forecast time, h is the total hydraulic pressure of the groundwater, T is the hydraulic conductivity, L is the overflow coefficient, S is the water storage coefficient, L _n is the distance from the shore, and t _max is the final duration . 2. groundwater pressure prediction method in tidal area according to claim 1, is characterized in that, in the space-time coordinate system of described step S2, time is defined as the independent variable based on space-time coordinate system, adopts space-time coordinate system to process sense Transient modeling of groundwater in tidal areas, the established two-dimensional coordinate system of the groundwater model in tidal areas includes one dimension in time and one dimension in space. 3. method for predicting groundwater pressure in tidal area according to claim 1, is characterized in that, in described step S3, matrix A is that the scale that is made of Trefftz base is aa * bb matrix, and matrix B is by boundary value and The initial value constitutes a matrix with a scale of aa×1, and the undetermined coefficient λ is a matrix with a scale of bb×1, where aa=n ₁ +2n ₂ , bb=4(w+1), and w is the approximate solution of the governing equation Order. 4. The method for predicting groundwater pressure in tidal areas according to claim 1, characterized in that, in the step S4, the undetermined coefficient λ is solved by Matlab left division. 5. A groundwater pressure prediction system in a tidal area, characterized in that it comprises a memory and a processor, the memory is stored with a computer program, and when the processor runs the computer program, it can realize Any one of the described method steps.

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