A variable-dimension water network simulation method

Abstract

The application provides a variable-dimension water network simulation method and relates to the technical field of hydraulic engineering. The method comprises the following steps: locally classifying a water network topological structure; defining a cross-dimension control equation; locally representing a cross-dimension water dynamic process; quantitatively representing a gate control flow to obtain a non-constant gate control flow process; and performing numerical discrete processing and solving on the cross-dimension control equation to complete the variable-dimension water network simulation. The application solves the problem that the efficiency and the accuracy are difficult to coordinate when a single dimension is used to simulate a complex water network.

Description

Technical Field

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

[0002] The complexity of the water network is reflected in the numerous branches and curvatures of local canal sections that make up the overall network. This causes the water network to exhibit typical one- and two-dimensional mixed hydrodynamic characteristics under the physical long wave assumption. However, this mixed dimensionality makes it difficult to simulate the dynamic processes of the water network, so it is usually simplified to a one-dimensional water network dynamic process. Among them, the water distribution and water collection at the branch points only consider the mass conservation equation, but fail to consider the conservation of momentum. This is called the hierarchical simulation method of the water network, which leads to poor overall physical conservation and low overall simulation accuracy. At the same time, empirical parameters are introduced to describe the influence of local canal curvature on hydrodynamic processes, which is called the canal curvature effect. However, this makes it difficult to accurately determine the parameter values, thereby losing simulation accuracy.

[0003] In order to improve the simulation accuracy of water network dynamic processes, variable dimension simulation should be considered, but no relevant methods have emerged so far. Summary of the Invention

[0004] In response to the above-mentioned deficiencies in the prior art, the present invention provides a variable-dimensional water network simulation method, which solves the problem of difficulty in balancing efficiency and accuracy when simulating complex water networks in a single dimension.

[0005] In order to achieve the above objectives, the technical solution adopted by the present invention is: a variable-dimensional water network simulation method, comprising the following steps:

[0006] Local classification of water network topology;

[0007] Define cross-dimensional governing equations;

[0008] Local characterization of cross-dimensional hydrodynamic processes based on local classification results and the definition of cross-dimensional governing equations;

[0009] Based on the local representation of the cross-dimensional hydrodynamic process, the gate-controlled flow is quantitatively characterized and the non-constant gate-controlled flow process is obtained;

[0010] Based on the gate-controlled flow process, the cross-dimensional control equations are numerically discretized and solved to complete the simulation of the variable-dimensional water network.

[0011] The application improves the simulation accuracy of water network dynamic process, considers variable dimension simulation, and proposes a complex water network one-two dimensional mixed simulation algorithm based on a semi-Lagrange view, which can realize complete mass and momentum conservation at any point of the water network and does not contain any to-be-calibrated parameters to accurately simulate the influence of river channel bending on water flow process.

[0012] Further, the cross-dimension control equation is expressed as follows:

[0013]

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

[0015] The above further scheme has the beneficial effect that the momentum conservation equation is expressed in the form of semi-Lagrange, which can significantly increase the calculation time step and improve the efficiency.

[0016] Further, the local representation of the cross-dimension water dynamic process is specifically:

[0017] For the branch point and the inflection point, the flow Q and the flow velocity u in the cross-dimension control equation are maintained as two components: Q=(Q x Q y ), u=(u x u y ), wherein Q x and Q y represent two components of the flow Q, and u x and u y represent two components of the flow velocity u.

[0018] For the straight line segment, the flow Q and the flow velocity u are reduced to one dimension: Q=(Q x 0), u=(u x 0), to complete the local representation of the cross-dimension water dynamic process, wherein the branch point, the inflection point and the straight line segment are local grid partition node distributions based on local classification:

[0019]

[0020] Wherein, x represents spatial coordinates.

[0021] The above further scheme has the beneficial effect that the mass and momentum conservation equation is reduced to one dimension in the non-bending segment of the water network, which simplifies the calculation complexity and improves the calculation efficiency.

[0022] Further, the expression of the gate control flow process is as follows:

[0023]

[0024] wherein, denotes a gradient operator, Q denotes flow, u denotes flow velocity, t denotes time, g denotes gravitational acceleration, ζ denotes water level, n denotes roughness coefficient, and h denotes water depth.

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

[0026] Further, the numerical discretization and solving of the cross-dimension control equation are specifically as follows:

[0027] Based on the gate control flow process, the momentum conservation equation type equation in the cross-dimension control equation is processed by using the Gauss divergence theorem:

[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 time-space step ratio, k denotes the adjacent cell number of the current spatial cell i, and N denotes the number of adjacent spatial cells of the spatial cell i, denotes the adjacent cell number 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 solving result, by using the relationship between the flow increment 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 water level increment at the spatial cell i at the time iteration step n+1 and the convergence step p, and g denotes gravitational acceleration, η​j,k represents the ratio of time step to cell area and the distance between the centroid of adjacent cells, and delta represents the increment symbol of 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 single-width water flow flux through the shared boundary of spatial cell i and spatial cell k, represents the length of the shared boundary of spatial cell i and spatial cell k, represents the water level at spatial cell i at time iteration step n, and Δs i,k represents the distance between spatial cell i and the center of spatial cell k;

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

[0036]

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

[0038] The above further scheme has the beneficial effect that the unified simulation and calculation of water flow in the complex water network with and without building constraints such as water locks under different dimensions are realized in the form of water level increment. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 is a flow chart of the method of the application.

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

[0041] Figure 3 is a schematic diagram of the cell shape, centroid (center) and normal vector (arrow) at the branch 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 This is a schematic diagram of the canal network distribution and hydrological measurement point locations in the Pishihang Irrigation District in Anhui Province.

[0045] Figure 7 Schematic diagram for comparison between measured flow rate and simulated flow rate. DETAILED DESCRIPTION

[0046] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0047] Example

[0048] like Figure 1 As shown, the present invention provides a variable-dimensional water network simulation method, which is implemented as follows:

[0049] S1. Local classification of water network topology;

[0050] S2. Define the cross-dimensional control equations;

[0051] S3. Local characterization of cross-dimensional hydrodynamic processes based on local classification results and the definition of cross-dimensional governing equations;

[0052] In this embodiment, the explanation of local representation is as follows: the variable-dimensional equation will be maintained or reduced to the corresponding dimension in different local areas, thereby maintaining the local expression. In the local area with the gate, it is only necessary to omit the time derivative of the water level to form the control equation of the water flow process through the gate.

[0053] S4. Based on the local representation of the cross-dimensional hydrodynamic process, the gate-controlled flow is quantitatively characterized to obtain the non-constant gate-controlled flow process;

[0054] S5. Based on the gate control flow process, the cross-dimensional control equations are numerically discretized and solved to complete the simulation of the variable-dimensional water network.

[0055] In this embodiment, Figure 2The 3D distribution of a certain real river network and the local mesh partition node distribution. In the local mesh partition node distribution, the red nodes are the river network bifurcation points and the curved nodes. Figure 2 The red dots represent the turning points and bifurcation points. Figure 2 The local mesh partition node distribution in the above figure can be classified into Figure 3 , Figure 4 and Figure 5 three types of node scenarios.

[0056] In this embodiment, the water dynamic process control equation of the river network includes the mass conservation equation and the momentum conservation equation. The momentum conservation equation is Euler equation (1), and the momentum conservation equation is Lagrange equation:

[0057]

[0058] Where ζ represents the water level, t represents the time, represents the gradient operator, Q represents the flow, u represents the flow rate, g represents the acceleration of gravity, n represents the roughness coefficient, and h represents the water depth.

[0059] In this embodiment, the local representation of the cross-dimension water dynamic process is as follows:

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

[0061] For straight segments, the flow Q and flow rate u are reduced to one dimension: Q=(Q x 0), u=(u x 0), which completes the local representation of the cross-dimension water dynamic process, where the bifurcation points, inflection points and straight segments are local mesh partition node distribution based on local classification.

[0062] In this embodiment, at the bifurcation points of Figure 3 and the inflection points of Figure 4 , the flow and velocity in equations (1) and (2) are maintained as two components, i.e. Q=(Q x Q y ), u=(u x u y ), and equations (1) and (2) remain the original expressions.

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

[0064]

[0065] wherein x represents a spatial coordinate.

[0066] In this embodiment, at the gate, the water flow will change from a non-pressure flow to a pressure flow, the time derivative term in formula (1) disappears, and is changed into the expression form of formula (5), and formula (2) remains the original form, that is, formula (5) and formula (6) are used to describe the water flow process through the gate, so as to calculate the non-constant gate control flow process:

[0067]

[0068] wherein, represents a gradient operator, Q represents flow, u represents flow velocity, t represents time, g represents gravitational acceleration, ζ represents water level, n represents roughness coefficient, and h represents water depth.

[0069] In this embodiment, the cross-dimension control equation is processed and solved by numerical discretization, which is specifically:

[0070] Based on the gate control flow process, the momentum conservation equation type equation in the cross-dimension control equation is processed by using the Gauss divergence theorem;

[0071] According to the solving result, the relationship between the flow increment and the water level gradient is used to obtain the water level at the unknown time step by solving .

[0072] The momentum conservation equation in the cross-dimension control equation is discretely processed, and based on the discretely processed result and the water level at the unknown time step, the water network simulation of variable dimension is completed.

[0073] In this embodiment, formula (3), (4) and formula (5), (6) are special forms of formula (1), (2) (formula (1) and formula (2) are reduced to formula (3) and formula (4) at the straight section of the water network, and formula (1) and formula (2) are simplified to [or automatically omit the water level time derivative term formula (5), (6), so that the discrete formula of formula (1), formula (2) can be reduced in dimension and simplified in the corresponding scene]). After formula (1) is processed by using the Gauss divergence theorem, formula (1) is initially discretized into the following form: Figure 5

[0074]

[0075] wherein,​ It 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 spatial cell i at time iteration step n, λ i represents the ratio of time and space steps, k represents the number of adjacent cells to the current spatial cell i, N represents the number of spatial cells adjacent to the spatial cell i, Represents the adjacent cell number of spatial cell i, represents the length of the shared boundary between spatial cells i and k, A i represents the area of ​​cell i.

[0076] Where λ i =Δt / A i .

[0077] The increase in flow is proportional to the water level gradient:

[0078]

[0079] After substituting equation (8) into equation (7), we get the following equation to be solved. And solve the water level at the unknown time step according to formula (10):

[0080]

[0081] Where η j,k =Δt / (A i Δs i,k )

[0082] in, represents the water level increment at the spatial cell i during the time iteration step n+1 and the convergence step p, g represents the gravitational acceleration, η j,k It represents the ratio of the time step to the cell area and the distance between the adjacent cell centroids, δ represents the incremental sign 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 single-width water flux through the shared boundary between space cell i and space 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 points of spatial cell i and spatial cell k.

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

[0084]

[0085] in, represents the flow velocity at spatial cell i at time iteration step n+1, u * express The speed of a point in space when it moves a distance Δt in the opposite direction along the characteristic line, represents the water level at the spatial cell boundary i+1 / 2 at time iteration step n+1, represents the water level at the space cell boundary i-1 / 2 at the time iteration step n+1, n represents the roughness coefficient, t represents the time, represents the gradient operator, Represents the water level at spatial cell i at time iteration step n+1.

[0086] In this embodiment, the following simulation effect verification is carried out. At the hydrological observation point of the main canal of the Pishihang Irrigation District in Anhui Province ( Figure 6 ), observed a rainfall process and its flow process in July 2020. By numerically calculating Equations (9) to (11), we simulated Figure 5 The water flow process of the entire canal network. Figure 7 It can be seen that there is a good fit between the simulation results and the measured values, which shows that the method proposed in the present invention is feasible.

Claims

1. A variable-dimensional water network simulation method, characterized in that: The following steps are involved: Local classification of water network topology; Define cross-dimensional governing equations; The expression of the cross-dimensional control equation is as follows: ； ； in, Indicates the water level, Indicates the moment, represents the gradient operator, Indicates flow rate, Indicates flow rate, represents the acceleration due to gravity, represents the roughness coefficient, Indicates water depth; Local characterization of cross-dimensional hydrodynamic processes based on local classification results and the definition of cross-dimensional governing equations; Based on the local representation of cross-dimensional hydrodynamic processes, the gate-controlled flow is quantitatively characterized, and the non-constant gate-controlled flow process is obtained; Based on the gate control flow process, the cross-dimensional control equations are numerically discretized and solved to complete the simulation of the variable-dimensional water network; The numerical discretization and solution of the cross-dimensional control equations are specifically as follows: Based on the gate control flow process, the Gaussian divergence theorem is used to process the momentum conservation equation in the cross-dimensional control equation: ； ； in, represents the time iteration step n +1 and convergence step p +1 Space-Time Cell i At water level, represents the time iteration step n Space-time cell i At water level, represents the ratio of time and space steps, k Indicates the current space cell i The adjacent cell numbers of N Representation and spatial cells i The number of adjacent spatial cells, Representation and spatial cells i The adjacent cell numbers of Represents a spatial cell i and k The length of the shared boundary between Represents a cell i area; According to the solution results, using the relationship between flow increment and water level gradient, by solving Get the water level at an unknown time step: ； ； ； in, represents the time iteration step n +1 and convergence step p Space-time cell i The water level increment at It represents the ratio of the time step to the cell area and the distance between the centroids of adjacent cells. Indicates the increment symbol of the physical variable, represents the time iteration step n +1 and convergence step p Space-time cell k The water level at represents the time iteration step n +1 and convergence step p Space-time cell i The water level at Represents the space cell i With space cells k The single-width water flux of the shared boundary, Represents a spatial cell i With space cells k The length of the shared boundary, represents the time iteration step n Space-time cell i The water level at Represents a spatial cell i With space cells k the distance between the dots; The momentum conservation equation in the cross-dimensional control equation is discretized using the following formula. Based on the discretization results and the water level at the unknown time step, the variable-dimensional water network simulation is completed: ； in, represents the time iteration step n +1 Space-Time Cell i The flow rate at express Move in the opposite direction along the feature line The speed of a point in space at distance, represents the time iteration step n +1 time space cell border i +1 / 2 water level, represents the time iteration step n +1 time space cell border i -1 / 2 water level, represents the time iteration step n +1 Space-Time Cell i The water level at.

2. The variable dimension water network simulation method according to claim 1, characterized in that: The local characterization of the cross-dimensional hydrodynamic process is specifically as follows: For the branch points and inflection points, the flow and velocity in the cross-dimensional control equations are maintained. and flow rate Two components: , ,in, and Indicates traffic flow The two components of and Indicates flow rate The two components of For the straight line segment, the flow and flow rate Dimensionality reduction to one dimension: , , completing the local characterization of the cross-dimensional hydrodynamic process, where the branch points, inflection points, and straight line segments are the local meshing node distribution based on local classification: ； ； in, Represents spatial coordinates.

3. The variable dimension water network simulation method according to claim 1, characterized in that: The expression of the gate control flow process is as follows: ； 。

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