A river network hydrodynamic process simulation method based on bifurcation point water quantity conservation

Abstract

The application discloses a river network hydrodynamic process simulation method based on branch point water quantity conservation, and specifically comprises the following steps: collecting basic data of each river section and each branch point of a river network; establishing a topological relationship between the branch point and adjacent river sections; discretizing one-dimensional Saint-Venant equations by using a finite volume method, and carrying out grid division on the river network; determining a time step and limiting by using a Runge-Kutta method; calculating an interface flux, and solving water surface slope source terms and friction source terms of each grid unit of an independent river section; calculating water quantity and water level at the branch point based on a water quantity conservation equation according to flux values of adjacent river sections of the branch point; updating the river network calculation grid, and outputting simulation results after simulation time reaches a set total time. The method can simulate complex river network hydrodynamic processes, can accurately simulate complex water flow movement processes of complex river sections, and has a simple and efficient branch point calculation method without iterative calculation.

Description

Technical Field

[0001] This invention belongs to the field of water conservancy engineering technology, specifically relating to a method for simulating the hydrodynamic process of a river network based on the conservation of water volume at distributaries. Background Technology

[0002] A river network is a system formed by a series of interconnected river segments. The connection points between river segments are called distributaries. River networks are typically classified into dendritic and ring-shaped networks based on their layout. River network systems are extremely common in practical engineering projects, such as urban drainage networks, irrigation and drainage channels, and natural river systems. Numerical simulation of the hydrodynamic processes of river network systems is crucial for understanding river hydraulic conditions, and it has become both a hot topic and a challenging area of ​​research.

[0003] Current mathematical models of unsteady flow in one-dimensional river networks are typically solved using the Saint-Venant equations, with two main types of difference schemes: implicit and explicit. Existing models often employ implicit difference to solve the entire river network and obtain key hydraulic information to ensure simulation stability. However, this method performs poorly when dealing with rapid currents or shock waves in river sections. Explicit difference methods are easier to understand and program, and with the improvement of numerical simulation methods, they are widely used to solve the hydrodynamic processes of river networks. In particular, the use of the Godunov-type finite volume method for river floods, surface runoff, and dam breaks has become a research hotspot and challenge. In solving river network systems, each river section is usually solved independently, and the distributaries connecting river sections are treated as internal boundary conditions. Currently, commonly used methods include predictive correction algorithms and the method of characteristics. However, these methods all require iterative calculations, resulting in complex calculations, high computational load, low efficiency, and low accuracy. Summary of the Invention

[0004] The purpose of this invention is to provide a method for simulating the hydrodynamic process of a river network based on the conservation of water volume at the distributary points, which solves the problems of complex calculation process, low operating efficiency and low accuracy in existing simulations of complex river network hydrodynamic processes.

[0005] The technical solution adopted in this invention is a method for simulating the hydrodynamic process of a river network based on the conservation of water volume at distributaries, which is implemented according to the following steps:

[0006] Step 1: Collect and organize basic cross-sectional data such as the geometric shape and cross-sectional length of the river network grid, as well as the cross-sectional material to facilitate the determination of roughness.

[0007] Step 2: Determine the number and number of distributaries, establish the topological relationship between distributaries and adjacent river segments, and determine the external boundary conditions or distributary numbers corresponding to the beginning and end of each river segment; establish the water level-volume relationship VZ at the distributaries based on the cross-sectional shape and length of adjacent river segments.

[0008] Step 3: Assign initial values ​​to each calculation unit and set the initial conditions of the river section, such as water level and flow rate; determine the initial water level and initial water volume at the distributary based on the initial conditions of the adjacent units.

[0009] Step 4: Set the total simulation duration, record the current time as time t, and use the Godunov scheme finite volume method to discretize the one-dimensional Saint-Venant equations to discretize each independent river segment;

[0010] Step 5: Determine the time step Δt using the Runge-Kutta method, and use the CFL condition to constrain the time step to ensure computational stability;

[0011] Step 6: Treat the distributary as a boundary water level condition, perform numerical reconstruction using the MUSCL scheme, calculate the interface flux using the approximate Riemann solver of the HLL scheme, and obtain the flux of the grid adjacent to the distributary.

[0012] Step 7: Solve for the water surface slope source term and friction source term of each grid cell in the independent river segment, and update the hydraulic elements of each cell to time t+Δt.

[0013] Step 8: Using the flux obtained in Step 6, update the water volume at the inlet according to the water conservation equation, and then obtain the water level value at the inlet at time t+Δt.

[0014] Step 9: Update the time by setting t = t + Δt, and repeat steps 5 to 8 until the simulation time reaches the total duration.

[0015] Step 10: Output the results. Obtain the hydraulic element values ​​of each grid cell at each time point, and output the flow rate and water depth map of the cross-section.

[0016] The invention is further characterized in that,

[0017] In step 2, the inlets are generalized as grid nodes with water storage function. The water level-volume relationship at the inlets is established based on adjacent grids. The volume at the inlet is the sum of half the grid volumes of the adjacent grid cells. The calculation expression is as follows:

[0018]

[0019] In the formula, j is the branch point number; i is the grid cell number of the river segment adjacent to the branch point; k is the number of grid cells adjacent to branch point j; V is the volume at the branch point; B is the width of the water surface; Z is the water surface elevation at the branch point; h i dx represents the water depth of the grid cell; dx represents the length of the grid cell in the adjacent river segment.

[0020] In step 4, the one-dimensional Saint-Venant equations are discretized using the finite volume method of the Godunov scheme. The equations are in the following form:

[0021]

[0022] in,

[0023]

[0024] In the formula, D, U, F, and S are the vector forms of the river cross-section, basic variables, flux, and source term, respectively; t is time; x is the length of the river segment; B is the width of the water surface; Z is the height of the river surface; Q is the cross-sectional discharge; g is the acceleration due to gravity; S f The riverbed resistance is expressed as S. f =n 2 Q|Q| / A 2 R 4 / 3 In the formula, n is the Manning coefficient and R is the hydraulic radius of the cross section.

[0025] In step 5, the time step Δt is calculated as follows:

[0026]

[0027] In the formula, i is the grid cell number; dx i The length of the grid cell; u i The velocity of the grid cell is g; g is the acceleration due to gravity, m / s². 2 h i The water depth in grid cell i; the CFL value ranges from 0 to 1, and is 0.5 in this invention.

[0028] In step 6, the expression for the flux of the approximate Riemann solver in HLL format is:

[0029]

[0030] In the formula, S L and S R F represents the wave velocity on the left and right sides of the grid cell; L F represents the flux of the left grid. R F(U) represents the flux of the right grid. L F(U) represents the flux calculated using the basic variables of the grid on the left side of the interface. R U represents the flux calculated using the basic variables of the grid on the right side of the interface. R U is a basic variable on the right side of the interface. L These are the basic variables on the left side of the interface.

[0031] In step 7, the water surface slope source term and friction source term are solved using the bottom slope flux method and the explicit / implicit method, respectively, to ensure the accuracy of the simulation and the computational efficiency.

[0032] The beneficial effects of this invention are as follows: Based on the Godunov scheme finite volume method, this invention proposes a numerical model for complex open channel flow where slow flow, rapid flow, and critical flow coexist. The HLL Riemann solver is used to calculate the flux in the river reach. A generalized method is employed to handle the distributaries, constructing the water level-volume relationship at the distributaries and applying the water conservation equation to calculate the water level at the distributaries. This invention provides a method for simulating river network hydrodynamic processes based on the water conservation at distributaries, enabling accurate and efficient simulation of complex open channel hydrodynamic processes. By accurately calculating the complex flows in complex open channel river reaches, the distributary solution method is simple and efficient, requiring no iterative calculations. The calculation process is clear, simple, and fast, greatly reducing the computational load and consuming few computational resources, thus possessing significant application value. Attached Figure Description

[0033] Figure 1 This is a flowchart of a method for simulating the hydrodynamic process of a river network based on the conservation of water volume at the distributary points, according to the present invention.

[0034] Figure 2 This is a schematic diagram of a river network in a method for simulating the hydrodynamic process of a river network based on the conservation of water volume at the inlets, as described in this invention.

[0035] Figure 3 This is a diagram showing the terrain changes in a steep-slope channel with alternating rapid and slow flow patterns in Embodiment 1 of the present invention, as well as the comparison between the simulation results and the accurate results.

[0036] Figure 4 This is a simplified river network layout diagram of Embodiment 2 of the present invention, which includes three river sections;

[0037] Figure 5 This is a comparison diagram of the water level process at a point 4000m from a distributary in river segment 3 in a simplified river network example containing three river segments in Embodiment 2 of the present invention. Detailed Implementation

[0038] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0039] This invention discloses a method for simulating river network hydrodynamic processes based on the conservation of water volume at distributaries, the flowchart of which is shown below. Figure 1 As shown, please follow these steps:

[0040] Step 1: Collect basic data of each river section and distributary in the river network and determine the roughness. The basic data includes geometric shape, cross-sectional length and cross-sectional material, etc.

[0041] Step 2: Determine the number of distributaries and number them, and establish the topological relationship between the distributaries and adjacent river segments;

[0042] Step 2 involves establishing the water level-volume relationship at the distributary points based on the geometry and cross-sectional length of adjacent river segments from Step 1, determining the outer boundary conditions or distributary numbers corresponding to the beginning and end of each river segment, and establishing the water level-volume relationship VZ at the distributary points based on the cross-sectional shape and length of adjacent river segments, such as... Figure 2 As shown;

[0043] When establishing the water level-volume relationship VZ at a distributary, the distributary is generalized as a grid node with water storage function. The water level-volume relationship at the distributary is established based on adjacent grids. The volume at the distributary is the sum of half the grid volumes of adjacent grid cells. The calculation expression is as follows:

[0044]

[0045] In the formula, j is the branch point number; i is the grid cell number of the river segment adjacent to the branch point; k is the number of grid cells adjacent to branch point j; V is the volume at the branch point; B is the width of the water surface; Z is the water surface elevation at the branch point; h i dx represents the water depth of the grid cell; dx represents the length of the grid cell in the adjacent river segment.

[0046] Step 3: Initialize the grid cells of the distributary and each river segment, assign initial values ​​to each calculation cell, and set the initial conditions of the river segment, such as water level and flow rate; determine the initial water level and initial water volume at the distributary based on the initial conditions of the adjacent cells.

[0047] Step 4: Set the total simulation duration, record the current time as time t, and use the Godunov scheme finite volume method to discretize the one-dimensional Saint-Venant equations to discretize each independent river segment;

[0048] In step 4, the one-dimensional Saint-Venant equations are discretized using the finite volume method of the Godunov scheme. The equations are in the following form:

[0049]

[0050] in,

[0051]

[0052] In the formula, D, U, F, and S are the vector forms of the river cross-section, basic variables, flux, and source term, respectively; t is time; x is the length of the river segment; B is the width of the water surface; Z is the height of the river surface; Q is the cross-sectional discharge; g is the acceleration due to gravity; S f The riverbed resistance is expressed as S. f =n 2 Q|Q| / A 2 R 4 / 3In the formula, n is the Manning coefficient and R is the hydraulic radius of the cross section.

[0053] Step 5: Determine the time step Δt using the Runge-Kutta method, and use the CFL condition to constrain the time step to ensure computational stability;

[0054] In step 5, the time step Δt is calculated as follows:

[0055]

[0056] In the formula, i is the grid cell number; dx i The length of the grid cell; u i The velocity of the grid cell is g; g is the acceleration due to gravity, m / s². 2 h i The water depth in grid cell i; the CFL value ranges from 0 to 1, and is 0.5 in this invention.

[0057] Step 6: Treat the distributary as a boundary water level condition, perform numerical reconstruction using the MUSCL scheme, calculate the interface flux using the approximate Riemann solver of the HLL scheme, and obtain the flux of the grid adjacent to the distributary.

[0058] In step 6, the expression for the flux of the approximate Riemann solver in HLL format is:

[0059]

[0060] In the formula, S L and S R F represents the wave velocity on the left and right sides of the grid cell; L F represents the flux of the left grid. R F(U) represents the flux of the right grid. L F(U) represents the flux calculated using the basic variables of the grid on the left side of the interface. R U represents the flux calculated using the basic variables of the grid on the right side of the interface. R U is a basic variable on the right side of the interface. L These are the basic variables on the left side of the interface.

[0061] Step 7: Solve for the water surface slope source term and friction source term of each grid cell in the independent river segment, and update the hydraulic elements of each cell to time t+Δt.

[0062] In step 7, the water surface slope source term and friction source term are solved using the bottom slope flux method and the explicit / implicit method, respectively, to ensure the accuracy of the simulation and the computational efficiency.

[0063] Step 8: Using the flux obtained in Step 6, update the water volume at the inlet according to the water conservation equation, and then obtain the water level value at the inlet at the next time t+Δt.

[0064] Step 9: Update the time by setting t = t + Δt, and repeat steps 5 to 8 until the simulation time reaches the total duration in step 4.

[0065] Step 10: Output the results. Obtain the hydraulic element values ​​of each grid cell at each time point, and output the flow rate and water depth map of the cross-section.

[0066] Example 1

[0067] This embodiment 1 presents a method for simulating river network hydrodynamic processes based on the conservation of water volume at distributaries. It details the topographical changes in a steep-slope channel with alternating rapid and slow flow patterns, and the comparison between the simulation results and the accurate results. Figure 3 As shown, Figure 3 A case study of a steep-slope channel with alternating rapid and slow flow patterns is presented. The channel is 1000m long and 10m wide at the bottom. The fixed flow rate at the upstream boundary is 20m³ / s. 3 / s, with a fixed water depth of 1.35m at the lower boundary, and a Manning coefficient n = 0.02, both the inflow and outflow from the channel are slow-moving. The flow pattern in this river section is a gradually transitioning flow pattern, first transitioning from slow flow to rapid flow, and then from rapid flow back to slow flow, forming an alternating flow pattern of rapid and slow flow with water drops and jumps.

[0068] Simulation comparison results are as follows Figure 3 As shown in the figure, the simulation results of this model are basically consistent with the exact solution. There is a clear discontinuity at the hydraulic jump, while other areas are smooth transitions, which proves that this model has good accuracy in the numerical model of river sections.

[0069] Example 2

[0070] This embodiment 2 presents a method for simulating the hydrodynamic processes of a river network based on the conservation of water volume at river distributaries. This embodiment 2 includes a simplified river network layout diagram for three river segments, as shown below. Figure 4 As shown, this is a simplified river network example consisting of three river segments. The river network model has been validated using this example in the reference (Zhang Y. Simulation of open channel network flows using finite element approach[J]. Communications in Nonlinear Science and Numerical Simulation, 2005, 10(5):467-478). The river network distribution is as follows. Figure 4 As shown, each river segment in this example is 5000m long, with a rectangular cross-section, a bottom slope of 0.0002, and a Manning coefficient of 0.025. Both segments 1 and 2 have upstream inflow processes, a bottom width of 50m, and an initial flow rate of 50m³. 3 / s; the end of section 3 has a constant water depth, a bottom width of 100m, and an initial flow rate of 100m³ / s. 3 / s.

[0071] A comparison of water level processes at a point 4000m from the distributary in section 3 of the river, as follows: Figure 5 As shown, Figure 5 This is a comparison diagram of the water level process at a distance of 4000m from the distributary in river segment 3 of the simplified river network example containing three river segments in Example 2 of this invention. The diagram shows that the simulation results of this invention generally agree well with the results in the literature. The maximum water depth calculated by Zhang using implicit finite element method is 1.660m, while the maximum water depth calculated by this invention is 1.658m, which is basically consistent, further confirming the calculation accuracy and stability of the model.

[0072] This invention presents a method for simulating river network hydrodynamic processes based on water conservation at distributaries. The one-dimensional Saint-Venant equations are solved using the finite volume method with Godunov scheme for each river segment, and the mesh interface flux is solved using the Riemann solver with HLL scheme. This method can accurately simulate complex flow processes in complex river segments. The distributary calculation employs a simple and efficient water conservation method, enabling the simulation of complex river network hydrodynamic processes without iterative calculations.

Claims

1. A river network hydrodynamic process simulation method based on junction water mass conservation, characterized in that, The method is implemented according to 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 number of branch points and numbering, and establishing the topological relationship between the branch points and adjacent river sections; Step 3, assigning initial values to each calculation unit, setting the initial conditions of the river section, and determining the initial water level and initial water volume at the branch point according to the initial conditions of the adjacent units of the branch point; Step 4, set the total length of the simulation, the current time as At the time, the finite volume method of Godunov format is used to disperse one-dimensional Saint-Venant equation to each independent river section. Step 5, determine time step using Runge-Kutta method and limit the time step using CFL condition to ensure stability of the calculation; Step 6, regarding the branch point as a boundary water level condition, using the MUSCL format for numerical reconstruction, using the approximate Riemann solver of the HLL format to calculate the interface flux, and obtaining the flux of the adjacent grid of the branch point; Step 7, solve the water surface slope source term and the friction source term of each grid cell of the independent river section, and update the hydraulic elements of each cell to moment; Step 8, update the water quantity at the branch point according to the water quantity conservation equation through the flux obtained in step 6, and then obtain the water level value of the branch point at the moment the water level value of the branch point at the moment Step 9, causing The time is updated, and steps 5-8 are repeated until the simulation time reaches the total duration in step 4. Step 10, outputting the results to obtain the hydraulic element value of each grid unit at each time, and outputting the water section flow and water depth diagram.

2. The river network hydrodynamic process simulation method based on the junction water mass conservation of claim 1, wherein, The step 2 determines the outer boundary condition or branch point number corresponding to the first and last ends of each river section, and establishes the water level-volume relationship at the branch point according to the cross section shape and length of the adjacent river section ; Establishing water level-volume relationship at branch point At this time, the branch point is generalized as a grid node with water storage function, and the water level-volume relationship at the branch point is established according to adjacent grids. The volume at the branch point is half of the sum of the grid volumes of adjacent grid cells, and the calculation expression is as follows: where, is the junction number; is the number of the grid cell adjacent to the junction; is the number of the grid cell adjacent to the junction is the number of the grid cells adjacent to the junction; is the volume at the junction; is the water surface width; is the water surface elevation at the junction; is the water depth of the grid cell; is the length of the adjacent grid cell.

3. The river network hydrodynamic process simulation method based on bifurcation point water quantity conservation according to claim 2, characterized in that, In step 4, the one-dimensional Saint-Venant equation is discretized by using the finite volume method of Godunov format, and the equation form is: Wherein, wherein, , , and are the vector forms of the river section, the basic variable, the flux and the source term, respectively; is the time; is the length of the river section; is the water surface width; is the water surface height of the river section; is the section flow rate; is the gravitational acceleration; is the river bed resistance, expressed as ; wherein, is the Manning coefficient, is the hydraulic radius of the section.

4. The river network hydrodynamic process simulation method based on bifurcation point water quantity conservation according to claim 3, characterized in that, In step 5, the time step is calculated as follows: where, i is the grid cell number; is the length of the grid cell; is the flow velocity of the grid cell; g is the gravitational acceleration, m / s 2 ; h i is the water depth in the grid cell i CFL is taken as 0.

5.

5. The river network hydrodynamic process simulation method based on bifurcation point water quantity conservation according to claim 4, characterized in that, In step 6, the approximate Riemann solver of the HLL format calculates the interface flux expression as: where and are the wave speeds on the left and right sides of the grid cell; is the flux of the left grid, is the flux of the right grid, is the flux calculated using the left grid primitive variables at the interface, is the flux calculated using the right grid primitive variables at the interface, is the right interface primitive variable, is the left interface primitive variable.

6. The river network hydrodynamic process simulation method based on bifurcation point water quantity conservation according to claim 5, characterized in that, In step 7, the water surface slope source term and the friction source term are solved by using the bottom slope flux method and the explicit-implicit method respectively, so as to ensure the accuracy and calculation efficiency of the simulation.

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