CN111103414A - Intelligent river channel supervision system - Google Patents

Intelligent river channel supervision system Download PDF

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CN111103414A
CN111103414A CN201911306335.5A CN201911306335A CN111103414A CN 111103414 A CN111103414 A CN 111103414A CN 201911306335 A CN201911306335 A CN 201911306335A CN 111103414 A CN111103414 A CN 111103414A
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river
data
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water
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李金页
叶舟
曾丽
尹胜奇
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Shangyi Environment Technology Jinhua Co ltd
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Abstract

The invention discloses an intelligent river channel monitoring system which comprises a river channel monitoring module (1), wherein the river channel monitoring module (1) is connected with a data processing module (2), and the data processing module (2) is connected with a real-time data display module (3), an area data display module (4), an alarm module (5), a report module (6), a water environment capacity calculation module (7) and an accident module (8). The method has the characteristic of timely and clearly reflecting the actual situation of the river channel.

Description

Intelligent river channel supervision system
Technical Field
The invention relates to a river channel monitoring system, in particular to an intelligent river channel supervision system.
Background
Current water quality monitoring mainly comprises fixed monitoring station and mobile monitoring equipment, monitors river course quality of water through above-mentioned equipment to transmit monitoring data to control center, finally show on control center's display screen, the staff can only obtain simple data, and inefficiently carries out the analysis to above-mentioned data and classifies, leads to the actual conditions of the unable quick river course of reflecting in time. In addition, the existing detection equipment is only used for simply detecting the water quality condition in the river channel, and the judgment can not be made when the pollutant in the river channel exceeds the water environment capacity which can be borne by the river channel. When the sudden pollution accident happens, real-time data acquisition can only be carried out on the polluted site and the river channel downstream of the polluted site through the mobile monitoring equipment, so that the pollution condition is monitored, a large amount of personnel are required to acquire the pollution accident, time and labor are consumed, and the acquired data samples are less, so that the pollution condition of the whole river channel cannot be rapidly and accurately known. Therefore, the prior art has the problem that the actual situation of the river channel cannot be reflected clearly in time.
Disclosure of Invention
The invention aims to provide an intelligent river channel supervision system. The method has the characteristic of timely and clearly reflecting the actual situation of the river channel.
The technical scheme of the invention is as follows: the intelligent river channel monitoring system comprises a river channel monitoring module, wherein the river channel monitoring module is connected with a data processing module, and the data processing module is connected with a real-time data display module, an area data display module, an alarm module, a report module, a water environment capacity calculation module and an accident module.
In the foregoing intelligent river monitoring system, the data processing module transmits the monitoring data obtained by monitoring by the river monitoring module to the real-time data display module, the area data display module, the alarm module, the report module, the water environment capacity calculation module and the accident module, respectively.
In the foregoing intelligent river monitoring system, the real-time data display module displays real-time dynamic, historical data and section information of the national control section, the provincial control section and the cross-over section.
In the foregoing intelligent river monitoring system, the area data display module displays water quality information in the designated area.
In the intelligent river monitoring system, the alarm module monitors the river water body in real time according to the monitoring data, and gives an alarm when the water body exceeds a set value.
In the foregoing intelligent river monitoring system, the report module performs statistics on monitored data obtained by monitoring in a form of a table to generate a report.
In the foregoing intelligent river monitoring system, the water environment capacity calculation module performs corresponding calculation according to the monitoring data to obtain the water environment capacity of the area;
when the pollution is discharged from a single point source, the specific calculation formula of the water environment capacity calculation module is as follows:
Figure BDA0002323219200000021
in the formula: w: water environment capacity, t/a; q: design flow at hydrological frequency, m3S; q: flow of waste water, m3S; when Q "Q," Q may be ignored; cs: target concentration of water quality, mg/L; co: taking the concentration of the incoming water, namely taking the background concentration of a river course, namely mg/L; x: river reach length, m; x is 0.4 times the actual calculated unit length; u: design flow rate, m/s.
In the intelligent river channel monitoring system, the accident module comprises a hydrological water quality condition input unit, a pollutant concentration change calculation, drawing and analysis unit and a display unit, wherein the pollutant concentration change calculation, drawing and analysis unit comprises a calculation and analysis part and a curve drawing part; and the accident module calculates and analyzes the concentration change condition of the pollutants in the river channel when the river flow has an emergency by utilizing the pollutant concentration change calculation and drawing analysis unit.
In the foregoing intelligent river monitoring system, the operation process of the accident module includes the following steps: A. firstly, inputting the required hydrological water quality condition data into a hydrological water quality condition input module or importing the required hydrological water quality condition data according to monitoring data;
B. the calculation and analysis part reads the hydrological water quality condition data and performs calculation and analysis to obtain pollutant concentration data changing along with time;
C. the curve drawing part draws a time-varying curve of the pollutant concentration according to the time-varying pollutant concentration data and transmits the time-varying curve to the display unit;
D. the display unit displays the data of the change curve of the pollutant concentration along with time.
In the foregoing intelligent river monitoring system, the specific calculation process of the calculation and analysis part is as follows:
firstly, establishing an equation set 1 of a two-dimensional water quality model:
Figure BDA0002323219200000031
wherein η is water level, h is water depth, ZbTaking river bottom elevation, rho is water density, u and v are average flow velocity in x and y directions respectively, v is flow velocity, g is gravity acceleration, n is lake bottom roughness, t is time, x is longitudinal distance, and y is transverse distance;
τbx、τbyrespectively representing friction resistance items of the bottom, and the specific expression is as follows:
Figure BDA0002323219200000041
wherein C represents the contaminant concentration;
Fbxand FbyRespectively representing the Coriolis force terms, and the specific expression is as follows: fbx=fv=2ωsinφ·v, Fby=-fu=-2ωsinφ·u(ω=7.29×10-5rad/s, phi is latitude value);
and step two, solving the equation set 1), and the concrete process is as follows:
establishing a two-dimensional steady-state linear convective diffusion equation set 2) as follows:
Figure BDA0002323219200000042
wherein, omega is a bounded region on a plane, and the boundary gamma is gamma0∪Γ1Smooth and gamma-shaped sheet0And gamma1A (x, y) is not less than a0≥0,b(x,y)=(b1(x,y),b2(x, y)), c (x, y), f (x, y) and
Figure BDA0002323219200000043
β (x, y) are smooth, sigma is a constant larger than 0, a (x, y) represents permeability, b (x, y) represents potential function, f (x, y) represents source function;
carrying out triangle division on a bounded region omega, wherein the step length h is 1/n, n is an integer larger than 0, and the bounded region omega is divided into n2A triangle unit without overlapping inner part, denoted as ek(1≤k≤n2) I.e. by
Figure BDA0002323219200000044
And the nodes are numbered from left to right and from bottom to top in turn as 1,2, …, (n +1)2
In that
Figure BDA0002323219200000051
Arbitrarily take out a unit, denoted as e, and set its vertex as Pi,Pj,PmI.e. e ═ Δ PiPjPmThe coordinates thereof are respectively (x)i,yi),(xj,yj),(xm,ym) The three points are in a counterclockwise sequence;
taking the linear interpolation basis function Ni(x,y),Nj(x,y),Nm(x, y) as a basis function, the functions u (x, y) and v (x, y) being at node PsThe value on (s ═ i, j, m) is denoted usAnd vs(s ═ i, j, m), then equation set 3 is obtained),
Figure BDA0002323219200000052
wherein the content of the first and second substances,
Figure BDA0002323219200000053
Figure BDA0002323219200000054
substituting the two equations of equation set 3) into equation set 1) can respectively obtain the cell stiffness matrix on the cell e
Figure BDA0002323219200000055
Element convection term matrix
Figure BDA0002323219200000056
Cell mass matrix
Figure BDA0002323219200000057
Line element stiffness matrix
Figure BDA0002323219200000058
Unit load vector F(e)Sum line element load vector F0 (e)
Matrix of cell stiffness
Figure BDA0002323219200000059
Element convection term matrix
Figure BDA00023232192000000510
Cell mass matrix
Figure BDA00023232192000000511
Line element stiffness matrix
Figure BDA00023232192000000512
Unit load vector F(e)Sum line element load vector F0 (e)Expand into (n +1)2Dimension vectors are correspondingly superposed to generate a total stiffness matrix K and a total load vector F; and (4) processing the essential boundary conditions of the matrix K and the vector F by a row-dividing and column-dividing method to form a finite element equation set, and calculating the concentration of the pollutants.
Compared with the prior art, the river channel monitoring module reasonably optimizes and classifies the data acquired by the river channel monitoring module by arranging the real-time data display module, the regional data display module and the report module, so that workers can know needed data clearly and timely, the data searching efficiency can be effectively improved, and the actual condition of the river channel can be reflected timely and clearly; according to the invention, by arranging the alarm module, when the monitoring data exceeds the set value, the alarm is automatically given, so that the alarm speed can be increased, and the manual monitoring cost can be reduced. Meanwhile, the invention is additionally provided with a water environment capacity calculation module and an accident module for calculating the water environment capacity and prejudging the change condition of the concentration of the pollutants in the river channel within a certain time after the occurrence of the pollution accident, so that the working personnel can conveniently make response measures or emergency schemes in time, and the loss is reduced. In conclusion, the method and the device can clearly reflect the actual situation of the river channel in time, can also pre-judge the water environment capacity borne by the river channel, and can quickly and accurately reflect the pollution situation of the river channel in the face of sudden pollution accidents.
In addition, the accident module of the invention is composed of a hydrologic water quality condition input unit, a pollutant concentration change calculating and drawing analysis unit and a display unit, and only the hydrologic water quality condition is input, the pollutant concentration in the riverway water quality at the place and the downstream where the pollutant occurs in the set time can be calculated and a corresponding pollutant concentration change curve can be drawn, and manual sampling and collection on the spot are not needed, so that the invention not only can effectively save manpower, but also can shorten the required time and improve the efficiency, and can also greatly improve the precision of pollution condition prejudgment. According to the invention, the river pollution condition can be rapidly and accurately mastered by reasonably designing the algorithm of the pollutant concentration change calculation and drawing analysis unit.
Drawings
FIG. 1 is a schematic structural view of the present invention;
fig. 2 is a triangle unit formed by triangulating the bounded region Ω.
The labels in the figures are: the system comprises a river channel monitoring module, a data processing module, a real-time data display module, a 4-region data display module, an alarm module, a 6-report module, a 7-water environment capacity calculation module and an 8-accident module, wherein the river channel monitoring module, the data processing module, the real-time data display module, the 4-region data display module, the alarm module, the 6-report module, the 7-water environment capacity calculation.
Detailed Description
The invention is further illustrated by the following figures and examples, which are not to be construed as limiting the invention.
Examples are given. The intelligent river channel monitoring system is shown in fig. 1 and fig. 2, and comprises a river channel monitoring module 1, wherein the river channel monitoring module 1 is connected with a data processing module 2, and the data processing module 2 is connected with a real-time data display module 3, an area data display module 4, an alarm module 5, a meter reporting module 6, a water environment capacity calculation module 7 and an accident module 8.
The data processing module 2 transmits the monitoring data obtained by monitoring of the river channel monitoring module 1 to the real-time data display module 3, the area data display module 4, the alarm module 5, the report module 6, the water environment capacity calculation module 7 and the accident module 8 respectively.
The real-time data display module 3 displays real-time dynamic, historical data and section information of the state control section, the provincial control section and the cross-over section.
The real-time dynamic state comprises real-time values of water quality indexes (COD, PH, NH3-N, DO and TP), real-time values of hydrological conditions (water level, hydrology, flow rate and flow rate) and real-time values of weather conditions (weather, wind power, temperature, humidity and air pressure).
The historical data is the section historical information in the user-defined time interval.
The section information is section background information, including position information, river channel, river length information, water quality type, section equipment maintenance information and the like.
The regional data display module 4 displays the water quality information in the designated region.
The regional data display module stores, subsumes and integrates the data collected in the same region, calculates a series of water quality health indexes which reflect the whole region, forms water quality information to display, and visually compares and understands the water quality condition of the region. By checking different areas, detailed water quality overall information, information of responsible persons and information of all equipment in the areas in different levels of administrative areas can be known; checking the exact numerical value of each water quality comprehensive index of each level area; real-time comparison of water quality conditions between the regions and historical ranking information are sensed.
And the alarm module 5 monitors the river water body in real time according to the monitoring data, and gives an alarm when the water body exceeds a set value. When alarming, a red alarm font is sent out and an alarm sound is accompanied.
The alarm module also comprises historical alarm section detailed information which comprises alarm time, an alarm section, an alarm trigger index, an alarm grade, an overproof rate and the like, and the historical alarm section detailed information is displayed in a form. Each piece of alarm information can also display the numerical value of each time of the alarm triggering index in a line graph mode, wherein the abscissa is time, and the ordinate is numerical value. Meanwhile, historical alarms can be screened according to time, alarm factors, the affiliated river channels and processing results.
And the report module 6 counts the monitored data obtained by monitoring in a form of a table to generate a report. Daily reports, weekly reports, annual reports, etc. can be generated. And the daily report forms are generated by recording the maintenance of each section background monitoring device, reagent replacement, comparison of monitoring data and fault repair in detail.
The water environment capacity calculation module 7 performs corresponding calculation according to the monitoring data to obtain the water environment capacity of the area; according to the water environment capacity, the integral pollutant carrying capacity in the river channel can be known, the optimal pollutant discharge point is simulated and planned according to the user-defined discharge amount and the discharge port position, and the influence of pollutants on the section is analyzed. The selected location can also be analyzed for maximum pollutant emissions and the remaining capacity of the water environment.
Based on the national water environment capacity approval guidelines, a one-dimensional water quality model is selected in the water environment capacity calculation process, and the one-dimensional water quality model has the following water quality conditions:
(1) wide and shallow river sections in the water body flow field;
(2) the pollutants can be mixed quickly and uniformly, and the mixing time is basically negligible;
(3) concentration gradient changes of longitudinal dispersion and transverse mixing of pollutants are not considered;
after the pollutants enter the drainage basin, the pollutants are rapidly moved in a advection mode to achieve a fully mixed state in a certain space, or the mixing process is not considered according to the precision requirement of water quality control management, and the uniform mixing is supposed to be instantly finished on the section of a sewage discharge port, so that the calculation process can be simplified according to one-dimensional problems no matter whether the water body belongs to any one of rivers, lakes and reservoirs.
W allowed is intended to be the allowed emission ratio; the ratio of the discharge to be allowed is selected according to the actual situation of the river channel and can be 80%.
Specific calculation of water environment capacity calculation module when pollution is discharged from single point sourceThe formula is as follows:
Figure BDA0002323219200000091
in the formula: w: water environment capacity, t/a; q: design flow at hydrological frequency, m3S; q: flow of waste water, m3S; when Q "Q," Q may be ignored; cs: target concentration of water quality, mg/L; co: taking the concentration of the incoming water, namely taking the background concentration of a river course, namely mg/L; x: river reach length, m; x is 0.4 times the actual calculated unit length; u: the design flow speed, m/s, is obtained by Lagrange interpolation based on the design flow.
The accident module 8 comprises a hydrological water quality condition input unit, a pollutant concentration change calculation, drawing and analysis unit and a display unit, wherein the pollutant concentration change calculation, drawing and analysis unit comprises a calculation and analysis part and a curve drawing part; the accident module 8 calculates and analyzes the concentration change condition of the pollutants in the river channel when the river has an accident by using the pollutant concentration change calculation and drawing analysis unit.
The operation process of the accident module comprises the following steps: A. firstly, inputting the required hydrological water quality condition data into a hydrological water quality condition input module or importing the required hydrological water quality condition data according to monitoring data;
B. the calculation and analysis part reads the hydrological water quality condition data and performs calculation and analysis to obtain pollutant concentration data changing along with time;
C. the curve drawing part draws a time-varying curve of the pollutant concentration according to the time-varying pollutant concentration data and transmits the time-varying curve to the display unit;
D. the display unit displays the data of the change curve of the pollutant concentration along with time.
The specific calculation process of the calculation and analysis part is as follows:
firstly, establishing an equation set 1 of a two-dimensional water quality model:
Figure BDA0002323219200000101
wherein η is water level, h is water depth, ZbElevation of river bottom, rho is density of waterU and v are average flow velocities in x and y directions, respectively, g is gravity acceleration, n is lake bottom roughness, t is time, x is longitudinal distance, and y is transverse distance;
τbx、τbyrespectively representing friction resistance items of the bottom, and the specific expression is as follows:
Figure BDA0002323219200000111
wherein C represents the contaminant concentration;
Fbxand FbyRespectively representing the Coriolis force terms, and the specific expression is as follows: fbx=fv=2ωsinφ·v, Fby=-fu=-2ωsinφ·u(ω=7.29×10-5rad/s, phi is latitude value);
and step two, solving the equation set 1), and the concrete process is as follows:
the similarity of the homogeneous shallow water equation and the Euler equation in the mathematical form is utilized, so that the equation set 1) can be solved by a high-performance algorithm for calculating gas dynamics.
Firstly establishing a two-dimensional steady-state linear convection diffusion equation set 2) as follows:
Figure BDA0002323219200000112
wherein, omega is a bounded region on a plane, and the boundary gamma is gamma0∪Γ1Smooth and gamma-shaped sheet0And gamma1A (x, y) is not less than a0≥0,b(x,y)=(b1(x,y),b2(x, y)), c (x, y), f (x, y) and
Figure BDA0002323219200000113
β (x, y) are smooth, sigma is a constant larger than 0, a (x, y) represents permeability, b (x, y) represents potential function, f (x, y) represents source function;
carrying out triangle division on a bounded region omega, wherein the step length h is 1/n, n is an integer larger than 0, and the bounded region omega is divided into n2A triangle unit without overlapping inner part, denoted as ek(1≤k≤n2) I.e. by
Figure BDA0002323219200000114
And the nodes are numbered from left to right and from bottom to top in turn as 1,2, …, (n +1)2
In that
Figure BDA0002323219200000121
Arbitrarily take out a unit, denoted as e, and set its vertex as Pi,Pj,PmI.e. e ═ Δ PiPjPmThe coordinates thereof are respectively (x)i,yi),(xj,yj),(xm,ym) The three points are in a counterclockwise sequence;
taking the linear interpolation basis function Ni(x,y),Nj(x,y),Nm(x, y) as a basis function, the functions u (x, y) and v (x, y) being at node PsThe value on (s ═ i, j, m) is denoted usAnd vs(s ═ i, j, m), then equation set 3 is obtained),
Figure BDA0002323219200000122
wherein the content of the first and second substances,
Figure BDA0002323219200000123
Figure BDA0002323219200000124
substituting the two equations of equation set 3) into equation set 1) can respectively obtain the cell stiffness matrix on the cell e
Figure BDA0002323219200000125
Element convection term matrix
Figure BDA0002323219200000126
Cell mass matrix
Figure BDA0002323219200000127
Line element stiffness matrix
Figure BDA0002323219200000128
Unit load vector F(e)Sum line element load vector F0 (e)
Matrix of cell stiffness
Figure BDA0002323219200000129
Element convection term matrix
Figure BDA00023232192000001210
Cell mass matrix
Figure BDA00023232192000001211
Line element stiffness matrix
Figure BDA00023232192000001212
Unit load vector F(e)Sum line element load vector F0 (e)Expand into (n +1)2Dimension vectors are correspondingly superposed (the number-matching seating is carried out), and a total stiffness matrix K and a total load vector F are generated; and (4) processing the essential boundary conditions of the matrix K and the vector F by a row and column dividing method to form a finite element equation set, and calculating the concentration of the pollutants.
The numerical calculation and graphic display functions of the open-source JavaScript library and matlab for interactive map development based on the leaf let can reflect the calculation result on the map in real time.

Claims (10)

1. River course intelligence supervisory systems, its characterized in that: the river channel monitoring system comprises a river channel monitoring module (1), wherein the river channel monitoring module (1) is connected with a data processing module (2), and the data processing module (2) is connected with a real-time data display module (3), an area data display module (4), an alarm module (5), a report module (6), a water environment capacity calculation module (7) and an accident module (8).
2. The intelligent river supervision system according to claim 1, wherein: the data processing module (2) transmits monitoring data obtained by monitoring of the river channel monitoring module (1) to the real-time data display module (3), the area data display module (4), the alarm module (5), the report module (6), the water environment capacity calculation module (7) and the accident module (8) respectively.
3. The intelligent river supervision system according to claim 1, wherein: and the real-time data display module (3) displays real-time dynamic, historical data and section information of the state control section, the provincial control section and the cross-over section.
4. The intelligent river supervision system according to claim 1, wherein: the regional data display module (4) displays the water quality information in the designated region.
5. The intelligent river supervision system according to claim 1, wherein: and the alarm module (5) monitors the river water body in real time according to the monitoring data, and gives an alarm when the water body exceeds a set value.
6. The intelligent river supervision system according to claim 1, wherein: and the report module (6) counts the monitored data obtained by monitoring in a form of a table to generate a report.
7. The intelligent river supervision system according to claim 1, wherein: the water environment capacity calculation module (7) performs corresponding calculation according to the monitoring data to obtain the water environment capacity of the area;
when the pollution is discharged from a single point source, the specific calculation formula of the water environment capacity is as follows:
Figure FDA0002323219190000021
in the formula: w: water environment capacity, t/a; q: design flow at hydrological frequency, m3S; q: flow of waste water, m3S; when Q < Q, Q can be ignored; cs: target concentration of water quality, mg/L; co: incoming water concentrationTaking the background concentration of the river channel as mg/L; x: river reach length, m; x is 0.4 times the actual calculated unit length; u: design flow rate, m/s.
8. The intelligent river supervision system according to claim 1, wherein: the accident module (8) comprises a hydrological water quality condition input unit, a pollutant concentration change calculation, drawing and analysis unit and a display unit, wherein the pollutant concentration change calculation, drawing and analysis unit comprises a calculation and analysis part and a curve drawing part; the accident module (8) calculates and analyzes the concentration change condition of the pollutants in the river channel when the river has an emergency by utilizing the pollutant concentration change calculation and drawing analysis unit.
9. The intelligent river supervision system according to claim 8, wherein the operation process of the accident module comprises the following steps: A. firstly, inputting the required hydrological water quality condition data into a hydrological water quality condition input module or importing the required hydrological water quality condition data according to monitoring data;
B. the calculation and analysis part reads the hydrological water quality condition data and carries out calculation and analysis to obtain pollutant concentration data changing along with time;
C. the curve drawing part draws a time-varying curve of the pollutant concentration according to the time-varying pollutant concentration data and transmits the time-varying curve to the display unit;
D. the display unit displays the data of the change curve of the pollutant concentration along with time.
10. The intelligent river supervision system according to claim 9, wherein the specific calculation process of the calculation and analysis part is as follows:
firstly, establishing an equation set 1 of a two-dimensional water quality model:
Figure FDA0002323219190000031
wherein η is water level, h is water depth, ZbLet u and v be the elevation of river bottom, ρ be the density of water, and u and v be in x and y directions, respectivelyG is the gravity acceleration, n is the lake bottom roughness, t is the time, x is the longitudinal distance, and y is the transverse distance;
τbx、τbyrespectively representing friction resistance items of the bottom, and the specific expression is as follows:
Figure FDA0002323219190000032
and
Figure FDA0002323219190000033
wherein C represents the contaminant concentration;
Fbxand FbyRespectively representing the Coriolis force terms, and the specific expression is as follows: fbx=fv=2ωsinφ·v,Fby=-fu=-2ωsinφ·u(ω=7.29×10-5rad/s, phi is latitude value);
and step two, solving the equation set 1), and the concrete process is as follows:
establishing a two-dimensional steady-state linear convective diffusion equation set 2) as follows:
Figure FDA0002323219190000034
Figure FDA0002323219190000041
wherein, omega is a bounded region on a plane, and the boundary gamma is gamma0∪Γ1Smooth and gamma-shaped sheet0And gamma1A (x, y) is not less than a0≥0,b(x,y)=(b1(x,y),b2(x, y)), c (x, y), f (x, y) and
Figure FDA0002323219190000046
β (x, y) are smooth, sigma is a constant larger than 0, a (x, y) represents permeability, b (x, y) represents potential function, f (x, y) represents source function;
carrying out triangle division on the bounded region omega, wherein the step length h is 1/n, and n is an integer larger than 0Number, divided into n2A triangle unit without overlapping inner part, denoted as ek(1≤k≤n2) I.e. by
Figure FDA0002323219190000042
And the nodes are numbered from left to right and from bottom to top in turn as 1,2, …, (n +1)2
In that
Figure FDA0002323219190000043
Arbitrarily take out a unit, denoted as e, and set its vertex as Pi,Pj,PmI.e. e ═ Δ PiPjPmThe coordinates thereof are respectively (x)i,yi),(xj,yj),(xmYx), the order of these three points is counterclockwise;
taking the linear interpolation basis function Ni(x,y),Nj(x,y),Nm(x, y) as a basis function, the functions u (x, y) and v (x, y) being at node PsThe value on (s ═ i, j, m) is denoted usAnd vs(s ═ i, j, m), then equation set 3 is obtained),
Figure FDA0002323219190000044
wherein the content of the first and second substances,
Figure FDA0002323219190000045
Figure FDA0002323219190000051
substituting the two equations of equation set 3) into equation set 1) can respectively obtain the cell stiffness matrix on the cell e
Figure FDA0002323219190000052
Element convection term matrix
Figure FDA0002323219190000053
Cell mass matrix
Figure FDA0002323219190000054
Line element stiffness matrix
Figure FDA0002323219190000055
Unit load vector F(e)Sum line element load vector F0 (e)
Matrix of cell stiffness
Figure FDA0002323219190000057
Element convection term matrix
Figure FDA0002323219190000058
Cell mass matrix
Figure FDA0002323219190000059
Line element stiffness matrix
Figure FDA00023232191900000510
Unit load vector F(e)Sum line element load vector F0 (e)Expand into (n +1)2Dimension vectors are correspondingly superposed to generate a total stiffness matrix K and a total load vector F; and (4) processing the essential boundary conditions of the matrix K and the vector F by a row-dividing and column-dividing method to form a finite element equation set, and calculating the concentration of the pollutants.
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