CN115796075A - River network hydrodynamic process simulation method based on branch point water quantity conservation - Google Patents
River network hydrodynamic process simulation method based on branch point water quantity conservation Download PDFInfo
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Abstract
The invention discloses a river network hydrodynamic process simulation method based on branch point water conservation, which comprises the following specific steps of: collecting basic data of each river section and each branch point of the river network; establishing a topological relation between the branch point and an adjacent river reach; carrying out grid division on the river network by using a finite volume method to disperse a one-dimensional Saint-Wei-nan equation; determining the time step length by adopting a Runge-Kutta method and limiting; calculating interface flux, and solving water surface gradient source items and friction source items of each grid unit of the independent river reach; calculating the water quantity and the water level at the branch point based on a water conservation equation according to the flux value of the branch point adjacent to the river reach; updating the river network computational grid, and outputting a simulation result after the simulation time reaches the set total time. The method simulates the hydrodynamic process of the complex river network, can accurately simulate the complex water flow movement process of the complex river reach, and is simple and efficient in branch point calculation method and free of iterative calculation.
Description
Technical Field
The invention belongs to the technical field of hydraulic engineering, and particularly relates to a river network hydrodynamic process simulation method based on branch point water conservation.
Background
The river network is an integral body formed by connecting a series of river sections, and a connection point between a river section and a river section is called a branch point and can be generally divided into a tree-shaped river network and a ring-shaped river network according to the arrangement condition of the river network. River network systems are very common in practical engineering, such as urban drainage river networks, irrigation drainage channels, natural river systems and the like. The numerical simulation of the hydrodynamic process of the river network system is an important basis for mastering the river hydraulic conditions, and the numerical simulation of the hydrodynamic process of the river network system also becomes a hotspot and difficulty of research.
The current one-dimensional river network unsteady flow mathematical model is usually based on the saint-wien equation system to perform discrete solution, and for the selection of the differential format, there are two main types, implicit differential and explicit differential. In the existing model, in order to ensure the simulation stability, the river network is generally solved by adopting implicit difference to obtain key hydraulic information, but the method has poor effect when the phenomenon of rapid flow or shock wave existing in the river reach is processed. The explicit difference method has the advantages of easy understanding and convenience in programming a calculation program, and along with the improvement of the numerical simulation method, the method for solving the river network hydrodynamic process by adopting the explicit difference method is also widely applied. Particularly, the Godunov-based finite volume method becomes a research hotspot and difficulty for river flood, surface overflow and dam break. In the river network system solving process, each river reach is generally solved independently, and branch points connected with the river reach are regarded as inner boundary conditions. The conventional methods comprise a prediction correction algorithm, a characteristic line method and the like, and all the methods need iterative calculation, so that the calculation process is complex, the calculation amount is large, the operation efficiency is low, and the accuracy is low.
Disclosure of Invention
The invention aims to provide a river network hydrodynamic process simulation method based on branch point water conservation, and solves the problems of complex calculation process, low operation efficiency and low accuracy of the existing complex river network hydrodynamic process simulation.
The technical scheme adopted by the invention is that a river network hydrodynamic process simulation method based on branched point water conservation is implemented according to the following steps:
step 1, collecting basic section data such as geometric shapes, section lengths and the like of the net meshes of the river network, and conveniently determining the roughness of the section material;
step 6, regarding the branched points as boundary water level conditions, performing numerical reconstruction by adopting an MUSCL format, calculating interface flux by using an approximate Riemann solver of an HLL format, and acquiring flux of the branched points adjacent to the grids;
step 7, solving water surface gradient source items and friction source items of each grid unit of the independent river reach, and updating hydraulic elements of each unit to t + delta t moment;
step 8, updating the water quantity at the branch point according to a water quantity conservation equation through the flux obtained in the step 6, and further obtaining a water level value of the branch point at the t + delta t moment;
step 9, updating the time by enabling t = t + delta t, and repeating the steps 5-8 until the simulation time reaches the total duration;
and step 10, outputting results, obtaining the hydraulic element values of each grid unit at each moment, and outputting the flow of the overflow section and a water depth map.
The present invention is also characterized in that,
in step 2, the branch points are generalized to grid nodes with a water storage effect, a water level volume relation at the branch points is established according to adjacent grids, the volume at the branch points is the sum of half of the volume of the grids of adjacent grid units, and a calculation expression is as follows:
in the formula, j is a branch point number; i is the river section grid unit number adjacent to the branch point; k is the number of grid cells adjacent to the branch point j; v is the volume at the branch point; b is the water surface width; z is the water surface elevation at the branch point; h is i The water depth of the grid cells; dx is the length of the grid cells of the adjacent river segments.
In step 4, a Godunov format finite volume method is adopted to disperse a one-dimensional Saint-Wei equation, and the equation form is as follows:
wherein, the first and the second end of the pipe are connected with each other,
in the formula, D, U, F and S are vector forms of river section, basic variable, flux and source term respectively; t is time; x is the length of the river reach; b is the water surface width; z is the height of the water surface of the river channel; q is the section flow; g is the acceleration of gravity; s f Is the riverbed resistance with the expression S f ＝n 2 Q|Q|/A 2 R 4/3 (ii) a In the formula, n is a Manning coefficient, and R is the hydraulic radius of a section.
In step 5, the time step Δ t is calculated by:
in the formula, i is a grid unit number; dx (x) i Is the length of the grid cell; u. of i Flow rate for grid cells; g is the acceleration of gravity, m/s 2 ；h i Is the water depth in grid cell i; the value range of CFL is 0-1, and the value of CFL is 0.5 in the invention.
In step 6, the approximate Riemann solver computational interface flux expression in the HLL format is as follows:
in the formula, S L And S R The wave velocities of the left side and the right side of the grid unit are obtained; f L Flux of the left hand grid, F R Flux of the right hand grid, F (U) L ) Flux, F (U), calculated to take grid basis variables on the left side of the interface R ) Flux, U, calculated to take grid basis variables on the right side of the interface R Is a basic variable on the right side of the interface, U L Is the basic variable on the left side of the interface.
In step 7, the water surface gradient source item and the friction resistance source item are solved by adopting a bottom slope flux method and a explicit-implicit method respectively so as to ensure the simulation precision and the calculation efficiency.
The invention has the beneficial effects that: the invention provides a complex open channel water flow numerical model suitable for the simultaneous existence of slow flow, rapid flow and critical flow based on a Godunov format finite volume method, and a river reach flux is calculated by adopting an HLL Riemann solver. The branch points are processed by a generalization method, and the water level of the branch points is calculated by constructing the water level volume relation of the branch points and applying a water conservation equation. The method is a river network hydrodynamic process simulation method based on branch point water conservation, so that accurate and efficient simulation of a complex open channel hydrodynamic process is realized. By accurately calculating the complex flow of the complex open channel river reach, the branch point solving method is simple and efficient, iterative calculation is not needed, the calculation process is clear, simple and fast, the calculation amount is greatly reduced, the calculation resource consumption is low, and the method has important application value.
Drawings
Fig. 1 is a flow chart of a river network hydrodynamic process simulation method based on branch point water conservation according to the present invention;
fig. 2 is a schematic diagram of a branch point of a river network hydrodynamic process simulation method based on branch point water conservation;
FIG. 3 is a diagram illustrating the terrain change and the comparison between the simulation result and the accurate result in the steep slope channel calculation example with the rapid and slow flow state alternation according to the embodiment 1 of the present invention;
FIG. 4 is a schematic view of a simple river network example layout including three river reach according to example 2 of the present invention;
fig. 5 is a comparison graph of water level processes of a river reach 3 from a branch point 4000m in a simple river network calculation example containing three river reaches in example 2 of the present invention.
Detailed Description
The invention is described in detail below with reference to the drawings and the detailed description.
The invention relates to a river network hydrodynamic process simulation method based on branch point water conservation, which is implemented by the following steps in a flow chart shown in figure 1:
step 1, collecting basic data of each river section and each branch point of a river network, and determining roughness, wherein the basic data comprises geometric shapes, section lengths, section materials and the like;
when establishing the water level volume relation V-Z of branch punishment department, generalize branch punishment for the grid node that has the retaining effect, establish the water level volume relation of branch punishment department according to adjacent grid, branch punishment department volume is half the sum of the grid volume of adjacent grid unit, and the computational expression is as follows:
in the formula, j is a branch point number; i is the number of the river section grid unit adjacent to the branch point; k is the number of grid cells adjacent to the branch point j; v is the volume at the branch point; b is the water surface width; z is the water surface elevation at the branch point; h is a total of i The water depth of the grid cells; dx is the length of the grid cell of the adjacent river reach.
in step 4, a Godunov format finite volume method discrete one-dimensional Saint-Venn equation is adopted, and the equation form is as follows:
wherein the content of the first and second substances,
in the formula, D, U, F and S are vector forms of river section, basic variable, flux and source term respectively; t is time; x is the length of the river reach; b is the water surface width; z is the height of the water surface of the river channel; q is the section flow; g is the acceleration of gravity; s. the f Is the riverbed resistance with the expression S f ＝n 2 Q|Q|/A 2 R 4/3 (ii) a In the formula, n is a Manning coefficient, and R is the hydraulic radius of a section.
in step 5, the time step Δ t is calculated by:
in the formula, i is a grid unit number; dx i Is the length of the grid cell; u. of i Flow rate for grid cells; g is the acceleration of gravity, m/s 2 ；h i Is the water depth in grid cell i; the value range of CFL is 0-1, and the value of CFL is 0.5 in the invention.
Step 6, regarding the branched points as boundary water level conditions, performing numerical reconstruction by adopting an MUSCL format, calculating interface flux by using an approximate Riemann solver of an HLL format, and acquiring flux of the branched points adjacent to the grids;
in step 6, the approximate Riemann solver computational interface flux expression in the HLL format is as follows:
in the formula, S L And S R The wave velocities of the left side and the right side of the grid unit are obtained; f L Flux of the left hand grid, F R Flux of the right hand grid, F (U) L ) Flux, F (U), calculated to take grid basis variables on the left side of the interface R ) Flux, U, calculated to take grid basis variables on the right side of the interface R Is a basic variable on the right side of the interface, U L Is the basic variable on the left side of the interface.
Step 7, solving water surface gradient source items and friction source items of each grid unit of the independent river reach, and updating hydraulic elements of each unit to t + delta t moment;
in the step 7, the water surface gradient source item and the friction resistance source item are solved by adopting a bottom slope flux method and a explicit-implicit method respectively, and the simulation precision and the calculation efficiency are guaranteed.
Step 8, updating the water quantity at the branch point according to a water quantity conservation equation through the flux obtained in the step 6, and further obtaining the water level value of the branch point at the next moment t + delta t;
step 9, updating the time by enabling t = t + delta t, and repeating the steps 5-8 until the simulation time reaches the total time length in the step 4;
and step 10, outputting results, obtaining the hydraulic element values of each grid unit at each moment, and outputting the flow of the overflow section and a water depth map.
Example 1
This embodiment 1 is a river network hydrodynamic process simulation method based on conservation of branch point water volume, and this embodiment 1 is a process for comparing a terrain change condition in a steep slope channel example with alternation of a fast and slow flow state and a simulation result with an accurate result, as shown in fig. 3, where the steep slope channel example with alternation of a fast and slow flow state in fig. 3 has a total length of 1000m and a channel bottom width of 10m. Its upstream boundary fixed flow rate is 20m 3 And/s, the fixed water depth of the lower boundary is 1.35m, the Manning coefficient n =0.02, and the inflow and outflow of the channel are slow flows. The river reach flow state belongs to a gradual transition flow state, the slow flow is firstly transited to the rapid flow, and then the rapid flow is transited to the slow flow, so that a rapid and slow flow alternating flow state with water drop and water jump is formed.
The simulation comparison result is shown in fig. 3, and it can be seen from the water surface process that the simulation result of the model is basically consistent with the accurate solution, obvious discontinuity exists at the hydraulic jump, and other areas are smooth transitions, so that the model is proved to have better accuracy in the aspect of the river reach numerical model.
Example 2
This embodiment 2 is a river network hydrodynamic process simulation method based on branch point water conservation, and this embodiment 2 includes a simple river network calculation example layout diagram of three river reach segments, as shown in fig. 4, which is a simple river network calculation example composed of three river reach segments, and is referred to in the literature (Zhang y]Communications in Nonlinear Science and Numerical Simulation,2005, 10 (5): 467-478) used this example to validate the river network model. The river network distribution is shown in fig. 4, each river reach of the example is 5000m long, the cross section is rectangular, the bottom slope is 0.0002, and the Manning coefficient is 0.025; the upstream of the river reach 1 and 2 has inflow process, the bottom width is 50m, and the initial flow is 50m 3 S; the tail end of the river reach 3 is in constant water depth, the bottom width is 100m, and the initial flow is 100m 3 /s。
Fig. 5 shows a comparison of water level processes of the river section 3 from the branch point 4000m, where fig. 5 is a comparison graph of water level processes of the river section 3 from the branch point 4000m in the simple river network calculation example including three river sections according to this embodiment 2. The figure shows that the simulation result of the invention is better in total coincidence with the water depth process of the literature result, the maximum value of the water depth calculated by Zhang adopting an implicit finite element is 1.660m, the maximum value of the water depth is 1.658m, the maximum value is basically consistent, and the calculation precision and the stability of the model are verified again.
The invention relates to a river network hydrodynamic process simulation method based on branch point water conservation. The branch point calculation adopts a simple and efficient water conservation method, and the complex river network hydrodynamic process simulation can be realized without iterative calculation.
Claims (6)
1. A river network hydrodynamic process simulation method based on branch point water conservation is characterized by comprising the following steps:
step 1, collecting basic data of each river section and each branch point of the river network, and determining the roughness;
step 2, determining the quantity and numbering of branch points, and establishing a topological relation between the branch points and adjacent river sections;
step 3, assigning initial values to each calculation unit, setting initial conditions of a river reach, and determining an initial water level and an initial water amount at a branch point according to the initial conditions of adjacent units of the branch point;
step 4, setting the total simulation operation duration, recording the current time as the time t, and dispersing each independent river reach by adopting a Godunov format finite volume method one-dimensional Saint-Venen equation;
step 5, determining the time step delta t by adopting a Runge-Kutta method, and limiting the time step by using a CFL condition to ensure the calculation stability;
step 6, regarding the branched points as boundary water level conditions, performing numerical reconstruction by adopting an MUSCL format, calculating interface flux by using an approximate Riemann solver of an HLL format, and acquiring flux of the branched points adjacent to the grids;
step 7, solving water surface gradient source items and friction source items of each grid unit of the independent river reach, and updating hydraulic elements of each unit to t + delta t moment;
step 8, updating the water volume at the branch point according to a water conservation equation by using the flux obtained in the step 6, and further acquiring a water level value of the branch point at the t + delta t moment;
step 9, updating the time by enabling t = t + delta t, and repeating the steps 5-8 until the simulation time reaches the total time length in the step 4;
and step 10, outputting results, obtaining the hydraulic element values of each grid unit at each moment, and outputting the flow of the overflow section and a water depth map.
2. The river network hydrodynamic process simulation method based on branch point water conservation according to claim 1, wherein the outer boundary conditions or branch point numbers corresponding to the head and the tail ends of each river section are determined in the step 2, and a water level volume relationship V-Z at the branch point is established according to the section shape and the section length of the adjacent river sections;
when establishing the water level volume relation V-Z of branch punishment department, generalize branch punishment for the grid node that has the retaining effect, establish the water level volume relation of branch punishment department according to adjacent grid, branch punishment department volume is half the sum of the grid volume of adjacent grid unit, and the computational expression is as follows:
in the formula, j is a branch point number; i is the number of the river section grid unit adjacent to the branch point; k is the number of grid units adjacent to the branch point j; v is the volume at the branch point; b is the water surface width; z is the water surface elevation at the branch point; h is i The water depth of the grid cells; dx is the length of the grid cell of the adjacent river reach.
3. The branched point water conservation-based river network hydrodynamic process simulation method according to claim 2, wherein in the step 4, a finite volume method discrete one-dimensional saint-wien equation in the Godunov format is adopted, and the equation is in the form of:
wherein, the first and the second end of the pipe are connected with each other,
in the formula, D, U, F and S are vector forms of river cross section, basic variable, flux and source term respectively; t is time; x is the length of the river reach; b is the water surface width; z is the height of the river water surface; q is the section flow; g is the acceleration of gravity; s f Is the riverbed resistance with the expression S f ＝n 2 Q|Q|/A 2 R 4/3 (ii) a In the formula, n is a Manning coefficient, and R is the hydraulic radius of a section.
4. The branch point water conservation-based river network hydrodynamic process simulation method according to claim 3, wherein in the step 5, the time step Δ t is calculated by:
in the formula, i is a grid unit number; dx i Is the length of the grid cell; u. u i Is the flow velocity of the grid cell; g is the acceleration of gravity, m/s 2 ；h i Is the water depth in grid cell i; the value range of CFL is 0-1, and the value of CFL is 0.5 in the invention.
5. The branch point water conservation-based river network hydrodynamic process simulation method according to claim 4, wherein in the step 6, an approximate Riemann solver computational interface flux expression of the HLL format is as follows:
in the formula, S L And S R The wave velocities of the left side and the right side of the grid unit are obtained; f L Flux of the left hand grid, F R Flux of the right hand grid, F (U) L ) Flux calculated to take the grid base variable on the left side of the interface, F (U) R ) Flux calculated for taking grid basic variables on the right side of the interface, UR is the basic variable on the right side of the interface, U L Is the basic variable on the left side of the interface.
6. The river network hydrodynamic process simulation method based on water conservation of branch points according to claim 5, wherein the water surface gradient source term and the friction resistance source term in the step 7 are solved by a bottom slope flux method and an explicit-implicit method respectively, so that the simulation precision and the calculation efficiency are guaranteed.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116757003A (en) * | 2023-08-18 | 2023-09-15 | 长江三峡集团实业发展(北京)有限公司 | Plain river network simulation method, plain river network simulation device, computer equipment and medium |
| CN116822400A (en) * | 2023-05-30 | 2023-09-29 | 长江勘测规划设计研究有限责任公司 | One-dimensional unsteady flow simulation method suitable for large-scale plain river network |
| CN116663146B (en) * | 2023-05-30 | 2023-11-17 | 西安理工大学 | Calculation method of non-circular pipeline on-way resistance |
| CN117669408A (en) * | 2023-11-13 | 2024-03-08 | 广东省水利水电科学研究院 | River network safety assessment method and system based on hydrodynamic force simulation |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116822400A (en) * | 2023-05-30 | 2023-09-29 | 长江勘测规划设计研究有限责任公司 | One-dimensional unsteady flow simulation method suitable for large-scale plain river network |
| CN116663146B (en) * | 2023-05-30 | 2023-11-17 | 西安理工大学 | Calculation method of non-circular pipeline on-way resistance |
| CN116757003A (en) * | 2023-08-18 | 2023-09-15 | 长江三峡集团实业发展(北京)有限公司 | Plain river network simulation method, plain river network simulation device, computer equipment and medium |
| CN116757003B (en) * | 2023-08-18 | 2024-01-05 | 长江三峡集团实业发展(北京)有限公司 | Plain river network simulation method, plain river network simulation device, computer equipment and medium |
| CN117669408A (en) * | 2023-11-13 | 2024-03-08 | 广东省水利水电科学研究院 | River network safety assessment method and system based on hydrodynamic force simulation |
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