Variable-dimension water network simulation method

Abstract

The invention provides a variable-dimension water network simulation method, and relates to the technical field of hydraulic engineering, and the method comprises the steps: carrying out the local classification of a water network topological structure; defining a cross-dimension control equation; local characterization is carried out on the cross-dimension hydrodynamic process; performing quantitative characterization on the gate control flow to obtain a non-constant gate control flow process; and numerical discrete processing and solving are carried out on the cross-dimension control equation, and variable-dimension water network simulation is completed. According to the method, the problem that efficiency and precision are difficult to coordinate when a complex water network is simulated in a single dimension at present is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of water conservancy engineering, and particularly relates to a variable-dimension water network simulation method. Background Art

[0002] The complexity of the water network is manifested in the numerous bifurcation points and the bends of local river channels that make up the overall network, which results in the water network showing typical one-two dimensional mixed-dimension hydrodynamic characteristics under the physical long-wave assumption. However, this mixed dimension makes the simulation of the water network dynamic process difficult, so it is usually simplified into a one-dimensional water network dynamic process. Among them, the water diversion and confluence at the bifurcation points only consider the mass conservation equation and cannot consider the momentum conservation, which is called the hierarchical simulation method of the water network. This leads to poor overall physical conservation and low overall simulation accuracy. At the same time, empirical parameters are introduced to describe the influence of the bends of local river channels on the hydrodynamic process, which is called the river channel bend effect. However, this will make it difficult to accurately determine the parameter values and thus reduce the simulation accuracy.

[0003] To improve the simulation accuracy of the water network dynamic process, variable-dimension simulation should be considered, but no relevant method has emerged so far. Summary of the Invention

[0004] Aiming at the above deficiencies in the prior art, the variable-dimension water network simulation method provided by the present invention solves the problem that it is difficult to coordinate efficiency and accuracy when simulating a complex water network in a single dimension.

[0005] To achieve the above purpose, the technical solution adopted by the present invention is: a variable-dimension water network simulation method, including the following steps:

[0006] Locally classify the water network topological structure;

[0007] Define the cross-dimension control equation;

[0008] Based on the local classification results and the definition results of the cross-dimension control equation, locally represent the cross-dimension hydrodynamic process;

[0009] Based on the local representation of the cross-dimension hydrodynamic process, quantitatively represent the gate control flow rate to obtain a non-constant gate control flow rate process;

[0010] Based on the gate control flow rate process, numerically discretize and solve the cross-dimension control equation to complete the simulation of the variable-dimension water network.

[0011] The beneficial effects of the present invention are as follows: The present invention improves the simulation accuracy of the hydrodynamic process of the water network. Considering variable-dimension simulation, a one-two-dimensional hybrid simulation algorithm for complex water networks based on the semi-Lagrange view is proposed, which can achieve complete mass and momentum conservation at any point in the water network and does not contain any parameters to be calibrated to accurately simulate the influence of river channel curvature on the water flow process.

[0012] Further, the expression of the cross-dimensional control equation is as follows:

[0013]

[0014] Where ζ represents the water level, t represents the time, represents the gradient operator, Q represents the flow rate, u represents the flow velocity, g represents the acceleration due to gravity, n represents the roughness coefficient, and h represents the water depth.

[0015] The beneficial effects of the above further solution are as follows: Expressing the momentum conservation equation in the semi-Lagrange form can significantly increase the computational time step and improve the efficiency.

[0016] Still further, the local characterization of the cross-dimensional hydrodynamic process is specifically as follows:

[0017] For the bifurcation points and inflection points, two components of the flow rate Q and the flow velocity u in the cross-dimensional control equation are maintained: Q = (Q x Q y ), u = (u x u y ), where Q x and Q y represent the two components of the flow rate Q, and u x and u y represent the two components of the flow velocity u;

[0018] For the straight-line segments, the flow rate Q and the flow velocity u are reduced to one dimension: Q = (Q x 0), u = (u x 0), completing the local characterization of the cross-dimensional hydrodynamic process, where the bifurcation points, inflection points, and straight-line segments are the node distributions of the local grid subdivision based on local classification:

[0019]

[0020] Where x represents the spatial coordinate.

[0021] The beneficial effects of the above further solution are as follows: In the non-curved sections of the water network, the mass and momentum conservation equations are reduced to one dimension, simplifying the computational complexity and improving the computational efficiency.

[0022] Furthermore, the expression for the process of the gate controlling the flow rate is as follows:

[0023]

[0024] Wherein, denotes the gradient operator, Q denotes the flow rate, u denotes the flow velocity, t denotes the time, g denotes the acceleration due to gravity, ζ denotes the water level, n denotes the roughness coefficient, and h denotes the water depth.

[0025] The beneficial effect of the above further solution is that the mass conservation equation is expressed in the form of an elliptic partial differential equation, and the process of the gate passing through the flow can be simulated without introducing any empirical parameters.

[0026] Furthermore, the numerical discretization and solution of the cross-dimensional control equation are as follows:

[0027] Based on the process of the gate controlling the flow rate, the Gaussian divergence theorem is used to process the momentum conservation equation type equation in the cross-dimensional control equation:

[0028]

[0029] λ i = Δt / A i

[0030] Wherein, denotes the water level at the spatial cell i at the time iteration step n + 1 and the convergence step p + 1, denotes the water level at the spatial cell i at the time iteration step n, λ i denotes the ratio of the space-time step size, k denotes the number of the adjacent cell of the current spatial cell i, N denotes the number of the spatial cells adjacent to the spatial cell i, denotes the number of the adjacent cell of the spatial cell i, denotes the length of the shared boundary between the spatial cell i and k, A i denotes the area of the cell i;

[0031] According to the solution result, using the relationship between the increment of the flow rate and the water level gradient, the water level at the unknown time step is obtained by solving :

[0032]

[0033] η j,k = Δt / (A i Δs i,k )

[0034] Wherein, denotes the increment of the water level at the spatial cell i at the time iteration step n + 1 and the convergence step p, g denotes the acceleration due to gravity, ηj,k represents the ratio of the time step to the cell area and the distance to the centroid of the adjacent cell, and δ represents the increment symbol of the physical variable. represents the water level at the spatial cell k at the time iteration step n + 1 and the convergence step p. represents the water level at the spatial cell i at the time iteration step n + 1 and the convergence step p. represents the unit-width water flow flux through the shared boundary between the spatial cell i and the spatial cell k. represents the length of the shared boundary between the spatial cell i and the spatial cell k. represents the water level at the spatial cell i at the time iteration step n, Δs i,k represents the distance between the origin points of the spatial cell i and the spatial cell k;

[0035] The momentum conservation equation in the cross-dimensional control equation is discretized using the following formula, and based on the discretization result and the water level at the unknown time step, the simulation of the variable-dimensional water network is completed:

[0036]

[0037] where, represents the flow velocity at the spatial cell i at the time iteration step n + 1, u * represents the velocity of the spatial point when moving a distance of Δt in the reverse direction along the characteristic line, represents the water level at the boundary i + 1 / 2 of the spatial cell at the time iteration step n + 1, represents the water level at the boundary i - 1 / 2 of the spatial cell at the time iteration step n + 1, n represents the roughness coefficient, and t represents the time. represents the gradient operator, represents the water level at the spatial cell i at the time iteration step n + 1.

[0038] The beneficial effect of the above further solution is: in the form of water level increment, it realizes the unified simulation calculation of the water flow in the complex water network with and without the constraints of buildings such as sluices under different dimensions. Description of the Drawings

[0039] Figure 1 is the flowchart of the method of the present invention.

[0040] Figure 2 is the schematic diagram of the overall and local topological structures of the water network.

[0041] Figure 3 is the schematic diagram of the cell shape, centroid (dot), and normal vector (arrow) at the bifurcation point.

[0042] Figure 4Schematic diagram of the cell shape, centroid (dot), and normal vector (arrow) at the turning point.

[0043] Figure 5 Schematic diagram of the cell shape, centroid (dot), and normal vector (arrow) at the straight line segment.

[0044] Figure 6 Schematic diagram of the canal network distribution and hydrological measurement point locations in the Pi-Shi-Hang Irrigation District, Anhui.

[0045] Figure 7 Schematic diagram of the comparison between the measured and simulated flow rates. Detailed implementation manners

[0046] The following describes the detailed implementation manners of the present invention to facilitate those skilled in the art of this technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the detailed implementation manners. For those of ordinary skill in the art of this technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are within the scope of protection.

[0047] Embodiment

[0048] As Figure 1 shown, the present invention provides a variable-dimension water network simulation method, and its implementation method is as follows:

[0049] S1. Locally classify the water network topological structure;

[0050] S2. Define the cross-dimension control equation;

[0051] S3. Based on the local classification results and the definition results of the cross-dimension control equation, locally characterize the cross-dimension hydrodynamic process;

[0052] In this embodiment, the explanation of local characterization: The variable-dimension equation will maintain or reduce to the corresponding dimension in different local regions, so as to maintain the local expression. In the local region with a gate, only the time derivative term of the water level needs to be omitted to form the control equation for the water flow process through the gate.

[0053] S4. Based on the local characterization of the cross-dimension hydrodynamic process, quantitatively characterize the gate control flow rate to obtain the unsteady gate control flow rate process;

[0054] S5. Based on the gate control flow rate process, perform numerical discretization and solution on the cross-dimension control equation to complete the simulation of the variable-dimension water network.

[0055] In this embodiment, as Figure 2The 3D distribution of a certain real water network and the distribution of local grid division nodes are shown. Among them, in the distribution of local grid division nodes, the red nodes are the river network fork points and bending nodes. Figure 2 The red dots represent turning points and fork points. Figure 2 In the distribution of local grid division nodes in Figure 3 , Figure 4 and Figure 5 can be classified into three types of node scenarios.

[0056] In this embodiment, the hydrodynamic process control equations of the water network include the mass conservation equation and the momentum conservation equation. Among them, the momentum conservation equation is the Euler-type equation (1), and the momentum conservation equation is the Lagrange-type equation:

[0057]

[0058] Among them, ζ represents the water level, t represents the time, represents the gradient operator, Q represents the flow rate, u represents the flow velocity, g represents the acceleration due to gravity, n represents the roughness coefficient, and h represents the water depth.

[0059] In this embodiment, the local characterization of the cross-dimensional hydrodynamic process is specifically:

[0060] For the fork points and inflection points, two components of the flow rate and velocity in the cross-dimensional control equation, namely the flow rate Q and the flow velocity u, are maintained: Q = (Q x Q y ), u = (u x u y ), where Q x and Q y represent two components of the flow rate Q, and u x and u y represent two components of the flow velocity u;

[0061] For the straight line segment, the flow rate Q and the flow velocity u are reduced to one dimension: Q = (Q x 0), u = (u x 0), completing the local characterization of the cross-dimensional hydrodynamic process, where the fork points, inflection points, and straight line segments are the local grid division node distributions based on local classification.

[0062] In this embodiment, at the fork points in Figure 3 and the inflection points in Figure 4 , the flow rate and velocity in equations (1) and (2) maintain two components, that is, Q = (Q x Q y ), u = (u x u y ), and equations (1) and (2) maintain the original expressions.

[0063] At Figure 5 the straight section of, the flow rate and flow velocity are reduced to one dimension, that is, only the component in the x - coordinate direction is retained: Q=(Q x 0), u=(u x 0):

[0064]

[0065] where x represents the spatial coordinate.

[0066] In this embodiment, at the gate, the open - channel flow will become pressurized flow, and the time - derivative term in Equation (1) disappears and becomes the expression form of Equation (5). Equation (2) still retains its original form. That is, Equation (5) and Equation (6) are used to describe the flow process through the gate, so as to calculate the unsteady gate - controlled flow rate process:

[0067]

[0068] where represents the gradient operator, Q represents the flow rate, u represents the flow velocity, t represents the time, g represents the acceleration due to gravity, ζ represents the water level, n represents the roughness coefficient, and h represents the water depth.

[0069] In this embodiment, numerical discretization and solution are performed on the cross - dimensional control equations. Specifically:

[0070] Based on the gate - controlled flow rate process, the Gaussian divergence theorem is used to process the momentum - conservation - equation - type equations in the cross - dimensional control equations;

[0071] According to the solution results, using the relationship between the increment of the flow rate and the water - level gradient, by solving the water level at the unknown time step is obtained;

[0072] The momentum - conservation equation in the cross - dimensional control equations is discretized, and based on the discretization results and the water level at the unknown time step, the simulation of the variable - dimension water network is completed.

[0073] In this embodiment, Equations (3), (4) and Equations (5), (6) are special forms of Equations (1), (2) (Equations (1) and (2) are reduced to Equations (3) and (4) at the straight section of the water network in Figure 5 , and Equations (1) and (2) are simplified (or the water - level time - derivative terms in Equations (5), (6) are automatically omitted) at the gate. Therefore, the discrete forms of Equations (1) and (2) can be dimension - reduced and simplified in the corresponding scenarios). After processing Equation (1) using the Gaussian divergence theorem, Equation (1) is preliminarily discretized into the following form:

[0074]

[0075] where Denotes the water level at spatial cell i at time iteration step n+1 and convergence step p+1, Denotes the water level at spatial cell i at time iteration step n, λ i Denotes the ratio of the spatio-temporal step size, k denotes the number of the adjacent cell to the current spatial cell i, N denotes the number of spatial cells adjacent to spatial cell i, Denotes the number of the adjacent cell to spatial cell i, Denotes the length of the shared boundary between spatial cell i and k, A i Denotes the area of cell i.

[0076] In the formula, λ i =Δt / A i .

[0077] The increment of flow is proportional to the water level gradient:

[0078]

[0079] After substituting formula (8) into formula (7), the following formula to be solved is obtained, by solving And solving for the water level at the unknown time step according to formula (10):

[0080]

[0081] In the formula, η j,k =Δt / (A i Δs i,k )

[0082] Among them, Denotes the water level increment at spatial cell i at time iteration step n+1 and convergence step p, g denotes the acceleration due to gravity, η j,k Denotes the ratio of the time step to the cell area and the distance between the centroids of adjacent cells, δ denotes the increment symbol of physical variables, Denotes the water level at spatial cell k at time iteration step n+1 and convergence step p, Denotes the water level at spatial cell i at time iteration step n+1 and convergence step p, Denotes the unit-width water flow flux through the shared boundary between spatial cell i and spatial cell k, Denotes the length of the shared boundary between spatial cell i and spatial cell k, Denotes the water level at spatial cell i at time iteration step n, Δs i,k Denotes the distance between the dots of spatial cell i and spatial cell k.

[0083] The discretization of formula (2) is as follows:

[0084]

[0085] Among them, represents the flow velocity at spatial cell i at time iteration step n + 1, u * represents the velocity of the spatial point when moving a distance of Δt in the reverse direction along the characteristic line, represents the water level at the boundary i + 1 / 2 of the spatial cell at time iteration step n + 1, represents the water level at the boundary i - 1 / 2 of the spatial cell at time iteration step n + 1, n represents the roughness coefficient, and t represents the moment, represents the gradient operator, represents the water level at spatial cell i at time iteration step n + 1.

[0086] In this embodiment, the simulation effect is verified as follows. At the hydrological observation point on the main canal of the Pi - Shi - Hang Irrigation District in Anhui ( Figure 6 ), a rainfall process and its flow process in July 2020 were observed. Through numerical calculations of equations (9) to (11), Figure 5 the water flow process of the entire canal network was simulated. From Figure 7 it can be seen that there is a good degree of fit between the simulation results and the measured values, indicating that the method proposed by the present invention is feasible.

Claims

1. A variable-dimension water network simulation method, characterized in that It includes the following steps: Perform local classification on the water network topological structure; Define the cross-dimensional control equations; Based on the local classification results and the definition results of the cross-dimensional control equations, perform local characterization of the cross-dimensional hydrodynamic process; Based on the local characterization of the cross-dimensional hydrodynamic process, quantitatively characterize the gate control flow rate to obtain a non-constant gate control flow rate process; Based on the gate control flow rate process, perform numerical discretization and solution of the cross-dimensional control equations to complete the simulation of the variable-dimensional water network.

2. The variable-dimension water network simulation method according to claim 1, wherein The expression of the cross-dimensional control equations is as follows: Among them, ζ represents the water level, and t represents the time. represents the gradient operator, Q represents the flow rate, u represents the flow velocity, g represents the acceleration due to gravity, n represents the roughness coefficient, and h represents the water depth.

3. The variable-dimension water network simulation method according to claim 2, characterized in that The local characterization of the cross-dimensional hydrodynamic process is specifically: For the bifurcation points and inflection points, two components of flow rate and velocity in the cross-dimensional control equations, namely flow rate Q and flow velocity u, are maintained: Q = (Q x Q y ), u = (u x u y ), where Q x and Q y represent two components of the flow rate Q, and u x and u y represent two components of the flow velocity u; For the straight-line segment, the flow rate Q and the flow velocity u are reduced to one dimension: Q = (Q x 0), u = (u x 0), to complete the local characterization of the cross-dimensional hydrodynamic process. Among them, the bifurcation points, inflection points, and straight-line segments are the node distributions of the local grid subdivision based on local classification: Where x represents the spatial coordinate.

4. The variable-dimension water network simulation method according to claim 1, wherein, The expression of the gate control flow rate process is as follows: Among them, represents the gradient operator, Q represents the flow rate, u represents the flow velocity, t represents the time, g represents the acceleration due to gravity, ζ represents the water level, n represents the roughness coefficient, and h represents the water depth.

5. The variable-dimension water network simulation method according to claim 1, characterized in that The numerical discretization and solution of the cross-dimensional control equations are specifically: Based on the gate control flow rate process, use the Gauss divergence theorem to process the momentum conservation equation type in the cross-dimensional control equations: λ i = Δt / A i wherein, represents the water level at the spatial cell i at the time iteration step n + 1 and the convergence step p + 1, represents the water level at the spatial cell i at the time iteration step n, and λ i represents the ratio of the spatio-temporal step sizes, k represents the number of the adjacent cell of the current spatial cell i, and N represents the number of the spatial cells adjacent to the spatial cell i, represents the number of the adjacent cell of the spatial cell i, represents the length of the shared boundary between the spatial cell i and k, and A i represents the area of the cell i; Based on the solution results, using the relationship between the increment of flow rate and the water level gradient, by solving the water level at the unknown time step is obtained: η j,k = Δt / (A i Δs i,k ) wherein, represents the water level increment at spatial cell i at time iteration step n+1 and convergence step p, g represents the acceleration due to gravity, η j,k represents the ratio of the time step to the cell area and the distance to the centroid of the adjacent cell, δ represents the increment symbol of the physical variable, represents the water level at spatial cell k at time iteration step n+1 and convergence step p, represents the water level at spatial cell i at time iteration step n+1 and convergence step p, represents the unit-width water flow flux through the shared boundary between spatial cell i and spatial cell k, represents the length of the shared boundary between spatial cell i and spatial cell k, represents the water level at spatial cell i at time iteration step n, Δs i,k represents the distance between the origin points of spatial cell i and spatial cell k; Use the following formula to discretize the momentum conservation equation in the cross-dimensional control equations, and based on the discretization results and the water levels at unknown time steps, complete the simulation of the variable-dimensional water network: Among them, represents the flow velocity at spatial cell i at time iteration step n + 1, u * represents the velocity of the spatial point when moving a distance of Δt in the reverse direction along the characteristic line, represents the water level at the boundary i + 1 / 2 of the spatial cell at time iteration step n + 1, represents the water level at the boundary i - 1 / 2 of the spatial cell at time iteration step n + 1, n represents the roughness coefficient, t represents the moment, represents the gradient operator, represents the water level at spatial cell i at time iteration step n + 1.

Images