Method and System for Numerical Simulation of Pipeline Hydrodynamics Based on Cellular Automata

Abstract

The present invention discloses a method and system for numerical simulation of pipeline hydrodynamic based on cellular automata. The method includes: (1) constructing a one-dimensional cellular automata scenario for the pipeline, setting the size of pipeline cells, neighborhood relationship and states, and giving the boundary conditions of the upstream and downstream of the pipeline; (2) calculating the wave velocity of cell water flow, water volume flux, momentum flux and friction loss term according to the water depth and flow velocity of the current cell and the upstream cell; (3) calculating the water depth and flow velocity of each cell at the next moment according to the update rules of water depth and flow velocity, and cycling through the update rules to obtain the hydrodynamic change process of the pipeline. The present invention proposes the basic rules for the hydrodynamic change inside the pipeline based on the cellular automata theory, which can more accurately and efficiently simulate the complex hydrodynamic change process inside the pipeline, and helps to improve the hydrodynamic simulation and design related to pipelines.

Description

Technical Field

[0001] The present invention relates to the fields of hydraulics and computer numerical simulation, and particularly to a numerical simulation method and system for accurately simulating the hydrodynamic characteristics inside a pipeline. Background Art

[0002] In fields such as water conservancy projects and municipal drainage, accurately simulating the water flow characteristics in pipelines is crucial for system design and operation. In existing research on pipeline hydrodynamic models, most hydrodynamic solutions are based on the one-dimensional Saint-Venant equations, that is, a pipeline is regarded as a single computational unit, only focusing on solving the water depth and flow velocity at the two ends of the pipeline, and ignoring the hydrodynamic changes inside the pipeline. This simplified method is difficult to accurately describe the hydrodynamic change process inside the pipeline and cannot meet the needs of modern municipal and water service departments for refined simulation of the water flow characteristics inside the pipeline. Therefore, how to accurately depict the hydrodynamic change characteristics at any position inside the pipeline has become an urgent problem to be solved in the numerical simulation of urban pipeline hydrodynamics. Summary of the Invention

[0003] Object of the Invention: The object of the present invention is to provide a pipeline hydrodynamic numerical simulation method and system based on cellular automata to accurately depict the hydrodynamic change characteristics at any position inside the pipeline and provide strong technical support for the research and optimal design of pipeline hydrodynamic characteristics.

[0004] Technical Solution: A pipeline hydrodynamic numerical simulation method based on cellular automata provided by the present invention includes the following steps:

[0005] (1) Construct a one-dimensional cellular automata scenario for the pipeline, set the cell size, neighborhood relationship, and state of the pipeline cells, and specify the upstream and downstream boundary conditions of the pipeline; wherein the cell size of the pipeline includes the cell length in the pipeline length direction and the cell transverse width in the pipeline cross-section, and the cell state of the pipeline includes pipe diameter, slope, and roughness.

[0006] (2) Calculate the cell water flow wave speed, water volume flux, momentum flux, and friction loss term according to the water depth and flow velocity of the current cell and the upstream cell.

[0007] (3) Calculate the water depth and flow velocity of each cell at the next moment according to the water depth and flow velocity update rules, and cycle through the update rules to obtain the hydrodynamic change process of the pipeline; wherein after a given time step, the water depth of the pipeline cell is determined by the difference in water volume flux of the water depth of the previous moment and the cells in the neighborhood, and the flow velocity of the pipeline cell is determined by the flow velocity of the previous moment, water depth, the difference in momentum flux of the cells in the neighborhood, and the friction loss term.

[0008] Further, in step (1), the upstream boundary condition of the pipeline is specified by specifying the water depth h , flow velocity v , and flow rateQ For any one of the following indicators, determine the other two indicators according to the following formula to obtain the upstream inflow boundary of a given pipeline; ;

[0009] ;

[0010] ;

[0011] where, R, D, I, n respectively represent the hydraulic radius, pipe diameter, slope, and roughness of the cell; r = D / 2; A represents the cross-sectional area of flow of the cell; represents the wetted perimeter of the cross-sectional area of flow of the cell; represents the sector radian angle corresponding to the cell at a water depth of h ; f represents the water depth - flow velocity relationship of the cell, F represents the water depth - flow rate relationship of the cell, f -1 and F -1 represent the corresponding inverse functions.

[0012] Furthermore, in step (1), the downstream boundary condition of the pipeline is set as a free outflow boundary.

[0013] Furthermore, in step (2), for the pipeline cell i , at t the water wave velocity , water flux , momentum flux , and frictional loss term are calculated according to the following formula:

[0014] ;

[0015] ;

[0016] ;

[0017] ;

[0018] where, , respectively represent t the flow velocity and water depth of the pipeline cell i at , respectively represent t the flow velocity and water depth of the upstream cell i -1 atg is the gravitational acceleration; is the gravitational action coefficient affected by the pipeline slope, with a value range of 0 to 1; represents the upstream cell i -1's hydraulic radius.

[0019] Furthermore, in step (3), the water depth update rule is: after a given time step, the water depth of the pipeline cell i at t +1 moment is determined by t the water depth at moment and the difference in water volume flux of the cells in the neighborhood, and is calculated according to the following formula:

[0020] ;

[0021] wherein, d x represents the cell length; represents t the water volume flux of the upstream cell i -1 at

[0022] Furthermore, in step (3), the flow velocity update rule is: after a given time step, the flow velocity of the pipeline cell i at t +1 moment is determined by t the flow velocity at moment, the water depth the difference in momentum flux of the cells in the neighborhood, and the friction loss term and is calculated according to the following formula:

[0023] ;

[0024] wherein, represents t the momentum flux of the downstream cell i +1 at

[0025] Based on the same inventive concept, the present invention also provides a pipeline hydrodynamic numerical simulation system based on cellular automata, including:

[0026] A pipeline cell scenario construction module, used to construct a one-dimensional cellular automata scenario of the pipeline, set the pipeline cell size, neighborhood relationship, and state, and given the upstream and downstream boundary conditions of the pipeline; wherein the pipeline cell size includes the cell length in the pipeline length direction and the cell transverse width in the pipeline cross-section, and the pipeline cell state includes pipe diameter, slope, and roughness;

[0027] A pipeline flux calculation module, which is used to calculate the water wave velocity, water volume flux, momentum flux and friction loss term of the cell according to the water depth and flow velocity of the current cell and the upstream cell;

[0028] A pipeline hydrodynamic calculation module, which is used to update the water depth and flow velocity of each cell at the next moment according to the water depth and flow velocity update rules, and obtain the hydrodynamic change process of the pipeline by looping the update rules; among them, after a given time step, the water depth of the pipeline cell is determined by the difference between the water depth at the previous moment and the water volume flux of the cells in the neighborhood, and the flow velocity of the pipeline cell is determined by the flow velocity, water depth, the difference in momentum flux of the cells in the neighborhood and the friction loss term at the previous moment.

[0029] The present invention also provides a computer system, including a memory, a processor, and a computer program / instruction stored on the memory and executable on the processor. When the computer program / instruction is executed by the processor, the steps of the pipeline hydrodynamic numerical simulation method based on cellular automata are implemented.

[0030] The present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by the processor, the steps of the pipeline hydrodynamic numerical simulation method based on cellular automata are implemented.

[0031] The present invention also provides a computer program product, including a computer program / instruction. When the computer program / instruction is executed by the processor, the steps of the pipeline hydrodynamic numerical simulation method based on cellular automata are implemented.

[0032] Advantageous effects: Compared with the prior art, the remarkable advantages of the present invention are:

[0033] (1) In previous related studies, only the water depth and flow velocity at the two ends of the pipeline were focused on, ignoring the hydrodynamic changes inside the pipeline. Based on the cellular automata theory, the present invention proposes the basic rules of the hydrodynamic changes inside the pipeline, forming an innovative hydrodynamic simulation method, which can more accurately and efficiently simulate the complex hydrodynamic change process inside the pipeline, including flow and wave characteristics, thereby improving the simulation efficiency and accuracy.

[0034] (2) Compared with the traditional global partial differential equation solving, the present invention can more accurately depict the local hydrodynamic changes, capture the microscopic effects that may be ignored by traditional methods, through flexible cell size settings (including the length direction and the cross-sectional direction), fine neighborhood relationship definitions, and comprehensive cell state descriptions (including pipe diameter, slope, roughness, etc.). At the same time, the water depth and flow velocity update rules established based on the principles of mass conservation and momentum conservation ensure the physical rationality of the simulation results, overcoming the problems that may not conform to physical laws brought by some simplified numerical methods.

[0035] (3) The present invention provides reliable technical support for decision-makers related to municipal and water conservancy projects, enabling more accurate prediction of pipeline water flow behavior during the hydraulic simulation and design stages, enhancing the feasibility and pertinence of engineering designs, and being widely applicable to various practical application scenarios such as urban drainage, water supply, and river systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a schematic flowchart of an embodiment of the present invention.

[0037] Figure 2 is a schematic diagram of a one-dimensional cellular automaton scenario in an embodiment of the present invention.

[0038] Figure 3 is an algorithm flowchart for calculating the change of pipeline hydrodynamic force in an embodiment of the present invention.

[0039] Figure 4 is a comparison chart of the simulation and measurement of the pipeline hydrodynamic process under constant boundary conditions in an embodiment of the present invention; among them, (a), (b), (c), and (d) respectively correspond to the water depth and flow velocity at 1 second, 10 seconds, 30 seconds, and 300 seconds.

[0040] Figure 5 is a comparison chart of the simulation and measurement of the pipeline hydrodynamic process under fluctuating boundary conditions in an embodiment of the present invention; among them, (a), (b), (c), and (d) respectively correspond to the water depth and flow velocity at 1 second, 10 seconds, 30 seconds, and 300 seconds. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0041] The technical solution of the present invention will be further described below in conjunction with the drawings and specific embodiments.

[0042] As Figure 1 shown, a numerical simulation method for pipeline hydrodynamic force based on cellular automaton disclosed in an embodiment of the present invention includes the following steps:

[0043] (1) Construction of the pipeline cell scenario: Construct a one-dimensional cellular automaton scenario for the pipeline, set the pipeline cell size, neighborhood relationship, and state, and given the upstream and downstream boundary conditions of the pipeline. Specifically, step (1) includes:

[0044] (1-1) Set the pipeline cell size: Set the cell length d x in the pipeline length direction, and set the cell transverse width d y in the pipeline cross-section, d y from the water depth h and the pipe diameter D (radius r = D / 2) Decision , d y The variation range is 0 ≤ d y ≤ D .

[0045] (1 - 2) Set the neighborhood relationship of pipeline cells: Number each cell starting from the first pipeline cell upstream i ( i = 1, 2, 3, …, k - 1, k), k is the number of cells, and the neighborhood of the pipeline cell i is the upstream cell of the cell i -1 and the downstream cell i +1.

[0046] (1 - 3) Set the cell state: Obtain the basic state attributes of each cell according to the pipe diameter, slope, and roughness parameters of the pipeline, that is, the pipe diameter D , slope I , roughness n .

[0047] (1 - 4) Set the upstream boundary condition of the pipeline: The cell numbered 1 at the most upstream of the pipeline is the starting cell. By specifying any one of the water depth h , flow velocity v , and flow rate Q of the starting cell, the other two indicators can be determined according to the following formula, thereby specifying the upstream inflow boundary of the pipeline.

[0048] ;

[0049] ;

[0050] ;

[0051] Among them, R represents the hydraulic radius of the cell, m; A represents the cross-sectional area of the cell, m 2 ; represents the wetted perimeter of the cross-section of the current cell, m; represents the sector radian angle corresponding to the cell when the water depth is h ; f represents the water depth - flow velocity relationship of the cell, F represents the water depth - flow rate relationship of the cell, f -1 and F -1 represent the corresponding inverse functions.

[0052] (1 - 5) Set the downstream boundary condition of the pipeline: The number of the cell at the most downstream of the pipeline isk The cell is the end cell, which allows water to flow out of the pipeline system. The water depth and flow velocity of its outflow can be adjusted according to actual simulation requirements. It can usually be set as a free outflow boundary, that is, the flow velocity and water depth of the end cell k are equal to those of its upstream cell k -1 ( h k , v k ) = ( h k-1 , v k-1 ).

[0053] In this embodiment, combined with the pipeline experimental device, the total length of the pipeline is 10 m, the pipe diameter D = 0.3 m, the radius r = 0.15 m, the slope I = 0.006, and the roughness coefficient n = 0.014. To monitor the water depth and flow velocity at different positions of the pipeline, the upper half of the pipeline is segmented, and only the lower half of the pipeline is reserved for the pipeline hydrodynamic experiment. A one-dimensional cellular automaton scenario of the pipeline is constructed as Figure 2 shown. The cell length d x= 0.01 m is set in the pipeline length direction, and a total of k = 1000 pipeline cells are divided.

[0054] The cell numbered 1 is the upstream inflow boundary. The upstream boundary conditions consider the simulation of two working conditions: ① The constant flow velocity v 1 = 0.3 m / s, and the upstream constant water depth h 1 = 0.0195 m can be calculated, and the water passing simulation duration is 5 minutes; ② The water depth changes sinusoidally with time at the boundary , and the initial upstream flow velocity , and the water passing simulation duration is 5 minutes.

[0055] The initial values of the water depth and flow velocity of the remaining cells under both working conditions are 0; the cell numbered 1000 is the downstream outflow boundary, and the free outflow boundary is adopted, that is, ( h 1000 , v 1000 ) = ( h 999 , v 999 ).

[0056] (2) Pipeline flux calculation: According to the water depth and flow velocity of the current cell and its upstream cell, calculate the cell water wave velocity, water volume flux, momentum flux, and friction loss term.

[0057] Specifically, step (2) includes:

[0058] (2-1) Water flow wave velocity: For the pipeline cell i , at t the wave velocity at time is calculated according to the following formula:

[0059] ;

[0060] wherein, , respectively represent t the flow velocity and water depth of the pipeline cell i at time; , respectively represent t the flow velocity and water depth of the upstream cell i -1 at time; g is the acceleration due to gravity, approximately 9.8 m / s 2 .

[0061] (2-2) Calculation of water volume flux, momentum flux, and friction loss term: For the pipeline cell i , its water volume flux t , momentum flux , and friction loss term at time are calculated according to the following formula: ;

[0062] ;

[0063] ;

[0064] ;

[0065] wherein, is the gravity action coefficient affected by the pipeline slope, with a value range of 0 to 1; represents the hydraulic radius of the upstream cell i -1.

[0066] In this embodiment, taking condition ① as an example, the initialization calculations of the water flow wave velocity, water volume flux, momentum flux, and friction loss term are carried out. The initial values of the water depth and flow velocity with the initial time number i = 2 to 1000 are all 0. Therefore, when starting the calculation, only the water flow wave velocity, water volume flux, momentum flux, and friction loss term of the cell with the number i = 2 need to be calculated first.

[0067] Water flow wave velocity: For pipeline cell 2, the wave velocity t= at 0 time can be calculated :

[0068] ;

[0069] At this time, the wave velocity is greater than the flow velocity of 0.3 m / s at the inflow boundary. This is because there is no water in cell 2, and the water flowing from cell 1 is still accelerated by the obvious gravitational force. Therefore, 0.5 can be taken first to reflect the influence degree of the gravitational force on the water flow.

[0070] Calculation of water volume flux, momentum flux, and friction loss term: For pipeline cell 2, the water volume flux t= at time 0 , momentum flux , and friction loss term can be calculated as follows:

[0071] ;

[0072] ;

[0073] ;

[0074] ;

[0075] ;

[0076] ;

[0077] ;

[0078] (3) Pipeline hydrodynamic calculation: Calculate the water depth and flow velocity of each cell at the next moment according to the water depth and flow velocity update rules, and cycle through the update rules to obtain the hydrodynamic change process of the pipeline.

[0079] After a given time step, the water depth of the pipeline cell is determined by the water depth at the previous moment and the difference in water volume flux of the cells in the neighborhood. The flow velocity of the pipeline cell is determined by the flow velocity, water depth, difference in momentum flux of the cells in the neighborhood, and friction loss term at the previous moment. Specifically, step (3) includes:

[0080] (3-1) Water depth update rule: After a given time step, the water depth of pipeline cell i is determined by the water depth t at the previous moment ( ) and the difference in water volume flux of the cells in the neighborhood. The water depth i of cell t at the next moment ( +1) can be updated according to the following formula:

[0081] ;

[0082] (3 - 2) Flow velocity update rule: After a given time step, the flow velocity of the pipeline cell i is determined by the flow velocity at the previous moment ( t ), water depth , the difference in momentum flux of cells in the neighborhood, and the friction loss term . The flow velocity of the cell at the next moment ( i ( + 1)) can be updated according to the following formula: t :

[0083] ;

[0084] In this embodiment, the algorithm flow for solving the pipeline hydrodynamic change process is as Figure 3 shown. When the construction of the one - dimensional pipeline cellular automaton scenario and the calculation of flux initialization in steps (1) and (2) are completed, the water depth, flow velocity update rules, and water volume transfer rules in step (3) can be looped to obtain the spatio - temporal hydrodynamic change process of the pipeline until the required simulation duration t end is reached. In this embodiment, the simulation duration t end = is 5 min, and the time step d t = 0.002 s. During the experiment, a Doppler flowmeter and a water level recorder are used to measure the flow velocity and water depth change processes at different positions (2m, 4m, 6m, 8m) of the pipeline.

[0085] The comparison between the hydrodynamic simulation and the measured values of the pipeline at different times under two working conditions is as Figure 4 and Figure 5 shown. Since the pipeline is in a water - free state at the initial moment, after the water starts flowing ( Time = 1 s), an effective head difference is formed between the water - filled and water - free cells, and the gravitational potential energy is converted into the kinetic energy of the water body, so the flow velocity is significantly greater than the upstream - given 0.3 m / s. While the flow velocity increases, due to the continuity of the water flow, the water depth shows a decreasing trend along the way. When the pipeline is full of water ( Time ≥ 30 s), it can be seen that the head difference gradually disappears, the pipeline flow velocity gradually decreases to a stable value, and the water depth gradually increases to a stable value. Generally speaking, the simulated water depth and flow velocity values are close to the measured values, and the average error is less than 5%. At the same time, it can be seen that the present invention can not only accurately simulate the whole process of hydrodynamic changes from the start of water flow to the stable stage in the pipeline, but also finely depict the pipeline hydrodynamic process under the condition of periodic boundary fluctuations ( Figure 5 ​), indicating that the pipeline hydrodynamic numerical simulation technology proposed by the present invention has good reliability and applicability.

[0086] In summary, the present invention simulates the behavior of fluids by defining the local rules of cellular automata, thereby capturing the dynamic changes in water flow in the local pipeline. Compared with solving traditional partial differential equations, the cellular automata model does not require complex mathematical descriptions, making the model setup and implementation simpler. At the same time, since the state of each cell depends only on its neighbors, it is very suitable for parallel computing, which can significantly improve the computing efficiency for large-scale pipeline system simulations.

[0087] Based on the same inventive concept, an embodiment of the present invention also discloses a pipeline hydrodynamic numerical simulation system based on cellular automata, including:

[0088] A pipeline cell scenario construction module for constructing a one-dimensional cellular automata scenario of the pipeline, setting the cell size of the pipeline, the neighborhood relationship, and the state, and giving the upstream and downstream boundary conditions of the pipeline; wherein the cell size of the pipeline includes the cell length in the pipeline length direction and the cell lateral width in the pipeline cross-section, and the cell state of the pipeline includes the pipe diameter, slope, and roughness.

[0089] A pipeline flux calculation module for calculating the cell water wave velocity, water volume flux, momentum flux, and friction loss term according to the water depth and flow velocity of the current cell and the upstream cell.

[0090] A pipeline hydrodynamic calculation module for calculating the water depth and flow velocity of each cell at the next moment according to the water depth and flow velocity update rules, and obtaining the hydrodynamic change process of the pipeline by cycling the update rules; wherein after a given time step, the water depth of the pipeline cell is determined by the difference between the water depth at the previous moment and the water volume flux of the cells in the neighborhood, and the flow velocity of the pipeline cell is determined by the flow velocity at the previous moment, water depth, the difference in momentum flux of the cells in the neighborhood, and the friction loss term.

[0091] An embodiment of the present invention also discloses a computer system, including a memory, a processor, and a computer program / instructions stored on the memory and executable on the processor. When the computer program / instructions are executed by the processor, the steps of the pipeline hydrodynamic numerical simulation method based on cellular automata are implemented.

[0092] An embodiment of the present invention also discloses a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the steps of the pipeline hydrodynamic numerical simulation method based on cellular automata are implemented.

[0093] An embodiment of the present invention also discloses a computer program product, including computer programs / instructions, which, when executed by a processor, implement the steps of the pipeline hydrodynamic numerical simulation method based on cellular automata as described above.

[0094] The above-disclosed are only preferred embodiments of the present invention, and thus cannot be used to limit the scope of rights of the present invention. Therefore, equivalent changes made according to the claims of the present invention still fall within the scope covered by the present invention.

Claims

1. A numerical simulation method for pipeline hydrodynamic based on cellular automata, characterized in that, The method includes the following steps: (1)Construct a one-dimensional cellular automaton scenario for the pipeline, set the cell size, neighborhood relationship, and state of the pipeline cells, and specify the upstream and downstream boundary conditions of the pipeline; among them, the pipeline cell size includes the cell length in the pipeline length direction d x and the cell transverse width in the pipeline cross-section, and the pipeline cell state includes pipe diameter, slope, and roughness coefficient; (2) Calculate the cell water flow wave velocity based on the water depth and flow velocity of the current cell and the upstream cell and water volume flux and momentum flux as well as the friction loss term; wherein ； ； , respectively represent t the flow velocity and water depth of the pipeline cell i at a certain moment; , respectively represent t the flow velocity and water depth of the upstream cell i at a certain moment; g is the gravitational acceleration; is the gravitational action coefficient affected by the pipeline slope, with a value range of 0 to 1; (3) Calculate the water depth and flow velocity of each cell at the next moment according to the water depth and flow velocity update rules, and obtain the hydrodynamic change process of the pipeline by looping the update rules; among them, after a given time step, the water depth of the pipeline cell at t +1 moment is determined by the water depth at t moment and the difference in water volume flux of the cells in the neighborhood. , and respectively represent t the water volume flux of the pipeline cell at i moment i and the upstream cell t -1; the flow velocity of the pipeline cell at +1 moment t is determined by the flow velocity at moment, water depth , the difference in momentum flux of the cells in the neighborhood, and the friction loss term . , and respectively represent t the momentum flux of the pipeline cell at i moment i and the downstream cell +1.

2. The method for numerically simulating the hydrodynamic of pipelines based on cellular automata according to claim 1, wherein: In step (1), for the upstream boundary condition of the pipeline, by specifying the water depth h , flow velocity v , or flow rate Q of any one of the indicators, the other two indicators are determined according to the following formula, so as to specify the upstream inflow boundary of the pipeline; ； ； ； Among them, R, D, I, n respectively represent the hydraulic radius, pipe diameter, slope and roughness of the cell; r = D / 2; A represents the cross-sectional area of flow of the cell; represents the wetted perimeter of the cross-sectional area of flow of the cell; represents when the water depth of the cell is h the corresponding sector radian angle; f represents the water depth-velocity relationship of the cell, F represents the water depth-discharge relationship of the cell, f -1 and F -1 represent the corresponding inverse functions.

3. The numerical simulation method of pipeline hydrodynamic based on cellular automata according to claim 1, characterized in that: In step (1), the downstream boundary condition of the pipeline is set as a free outflow boundary.

4. The numerical simulation method for pipeline hydrodynamic based on cellular automata according to claim 1, characterized in that: In step (2), for the pipeline unit cell i , at t the water flow wave velocity , the friction loss term is calculated according to the following formula: ； ； Among them, represents the hydraulic radius of the upstream cell i with a value of -1; n represents the roughness coefficient.

5. A pipeline hydrodynamic numerical simulation system based on cellular automata, characterized in that, including: A pipeline cell scenario construction module for constructing a one-dimensional cellular automaton scenario of the pipeline, setting the cell size, neighborhood relationship and state of the pipeline cells, and giving the upstream and downstream boundary conditions of the pipeline; wherein the cell size of the pipeline cells includes the cell length in the pipeline length direction and the cell transverse width in the pipeline cross section, and the cell state of the pipeline cells includes pipe diameter, slope and roughness; A pipeline flux calculation module, which is used to calculate the cell water flow wave velocity, water volume flux, momentum flux and friction loss term according to the water depth and flow velocity of the current cell and the upstream cell , water volume flux , momentum flux and friction loss term; wherein ； ； , respectively represent t the flow velocity and water depth of the pipeline cell i at time , respectively represent t the flow velocity and water depth of the upstream cell i -1 at time g is the gravitational acceleration; is the gravitational action coefficient affected by the pipeline slope, with a value range of 0 to 1; The pipeline hydrodynamic calculation module is used to calculate the water depth and flow velocity of each cell at the next moment according to the water depth and flow velocity update rules, and the hydrodynamic change process of the pipeline is obtained by cycling the update rules; among them, after a given time step, the water depth of the pipeline cell at t the +1 moment is determined by t the water depth at the moment and the difference in water volume flux of the cells in the neighborhood. , and respectively represent t the water volume flux of the pipeline cell at i the moment and the upstream cell i -1; the flow velocity of the pipeline cell at t the +1 moment is determined by t the flow velocity at the moment, the water depth , the difference in momentum flux of the cells in the neighborhood, and the friction loss term . , and respectively represent t the momentum flux of the pipeline cell at i the moment and the downstream cell i +1.

6. A computer system, comprising a memory, a processor, and a computer program / instructions stored in the memory and executable on the processor, characterized in that, When the computer program / instructions are executed by a processor, the steps of the pipeline hydrodynamic numerical simulation method based on cellular automata according to any one of claims 1-4 are implemented.

7. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, the steps of the pipeline hydrodynamic numerical simulation method based on cellular automata according to any one of claims 1-4 are implemented.

8. A computer program product, comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by a processor, the steps of the pipeline hydrodynamic numerical simulation method based on cellular automata according to any one of claims 1-4 are implemented.

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