Pipeline hydrodynamic numerical simulation method and system based on cellular automaton

Abstract

The invention discloses a pipeline hydrodynamic numerical simulation method and system based on a cellular automaton, and the method comprises the steps: (1) constructing a one-dimensional cellular automaton scene of a pipeline, setting the cellular size, neighborhood relation and state of the pipeline, and giving upstream and downstream boundary conditions of the pipeline; (2) calculating a cellular water flow wave velocity, a water flux, a momentum flux and a friction loss item according to the water depth and the flow velocity of the current cellular and the upstream cellular; and (3) calculating the water depth and the flow velocity of each cell at the next moment according to a water depth and flow velocity updating rule, and circularly updating the rule to obtain the hydrodynamic force change process of the pipeline. The basic rule of the hydrodynamic change in the pipeline is provided on the basis of the cellular automaton theory, the complex hydrodynamic change process in the pipeline can be simulated more accurately and efficiently, and the hydraulic simulation and design related to the pipeline can be improved.

Description

Technical Field

[0001] The invention relates to the fields of hydraulics and computer numerical simulation, and in particular to a numerical simulation method and system for accurately simulating the dynamic characteristics of water flow inside a pipeline. Background Art

[0002] In the fields of water conservancy projects, municipal drainage, etc., accurate simulation of water flow characteristics in pipes is crucial for system design and operation. In existing pipeline hydrodynamic model research, hydrodynamic solutions are mostly based on the one-dimensional Saint-Venant equation, that is, a pipeline is considered as a calculation unit, focusing only on solving the water depth and flow rate at the nodes at both ends of the pipeline, 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 departments for refined simulation of water flow characteristics inside the pipeline. Therefore, how to accurately characterize the hydrodynamic change characteristics at any position in the pipeline has become an urgent problem to be solved in the numerical simulation of urban pipeline hydrodynamics. Summary of the invention

[0003] Purpose of the invention: The purpose of the present invention is to provide a method and system for numerical simulation of pipeline hydrodynamics based on cellular automata, so as to accurately characterize the hydrodynamic variation characteristics at any position in the pipeline, and provide strong technical support for the research and optimization design of pipeline hydrodynamic characteristics.

[0004] Technical solution: The present invention provides a pipeline hydrodynamic numerical simulation method based on cellular automata, comprising the following steps: (1) Construct a one-dimensional cellular automaton scenario for the pipeline, set the pipeline cell size, neighborhood relationship, and state, and give the upstream and downstream boundary conditions of the pipeline. The pipeline cell size includes the cell length in the pipeline length direction and the cell lateral width on the pipeline cross section. The pipeline cell state includes the pipe diameter, slope, and roughness. (2) Calculate the cell water flow wave velocity, water flux, momentum flux, and friction loss term based on the water depth and flow velocity of the current cell and the upstream cell; (3) The water depth and flow velocity of each cell at the next moment are calculated according to the water depth and flow velocity update rules, and the hydrodynamic change process of the pipeline is obtained by cyclically updating the rules. After a given time step, the water depth of the pipeline cell is determined by the water depth at the previous moment and the water flux difference of the cells in the neighborhood. The flow velocity of the pipeline cell is determined by the flow velocity at the previous moment, the water depth, the momentum flux difference of the cells in the neighborhood, and the friction loss term.

[0005] Furthermore, in step (1), the upstream boundary condition of the pipe is set by specifying the water depth of the starting cell. h , flow rate v ,flow QAny one of the indicators is used to determine the other two indicators according to the following formula, thus giving the upstream inflow boundary of the pipeline; ; ; ; in, R, D, I, n They represent the hydraulic radius, pipe diameter, slope and roughness of the cell respectively; r = D / 2; A represents the water-passing cross-sectional area of ​​the cell; It represents the wetted perimeter of the water-passing section of the cell; Indicates that the cell is at a water depth of h The corresponding sector arc angle when 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 represents the corresponding inverse function.

[0006] Furthermore, in step (1), the downstream boundary condition of the pipeline is set to a free outflow boundary.

[0007] Furthermore, in step (2), for the pipeline cell i ,exist t Water velocity at a given moment , water flux , momentum flux , friction loss term Calculated as follows: ; ; ; ; in, , Respectively t Time Pipeline Cell i flow velocity and water depth; , Respectively t Upstream cell at time i -1 for flow velocity and water depth; g is the acceleration due to gravity; It is the gravity coefficient affected by the pipeline slope, with a value of 0~1; Represents the upstream cell i -1 hydraulic radius.

[0008] Furthermore, in step (3), the water depth update rule is: after a given After a time step, the pipeline cell i exist t +1 moment of water depth Depend on t The depth of time It is determined by the difference in water flux between the cells in the neighborhood and is calculated as follows: ; in, d x represents the cell length; express t Upstream cell at time i -1 water flux.

[0009] Furthermore, in step (3), the flow rate update rule is: after a given After a time step, the pipeline cell i exist t +1 flow rate Depend on t The flow rate of time , water depth , the momentum flux difference of cells in the neighborhood and the friction loss term Determine, calculated according to the following formula: ; in, express t Downstream cells at time i +1 Momentum Flux.

[0010] Based on the same inventive concept, the present invention also provides a pipeline hydrodynamic numerical simulation system based on cellular automata, comprising: The pipeline cell scene construction module is used to construct a one-dimensional cellular automaton scene of the pipeline, set the pipeline cell size, neighborhood relationship and state, and give the upstream and downstream boundary conditions of the pipeline; the pipeline cell size includes the cell length in the pipeline length direction and the cell lateral width on the pipeline cross section, and the pipeline cell state includes the pipe diameter, slope and roughness; The pipeline flux calculation module is used to calculate the cell water flow wave velocity, water flux, momentum flux and friction loss term according to the water depth and flow velocity of the current cell and the upstream cell; 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 cyclically updating the rules; wherein after a given time step, the water depth of the pipeline cell is determined by the water depth at the previous moment and the water flux difference of the cells in the neighborhood, and the flow velocity of the pipeline cell is determined by the flow velocity at the previous moment, the water depth, the momentum flux difference of the cells in the neighborhood, and the friction loss term.

[0011] The present invention also provides a computer system, comprising a memory, a processor, and a computer program / instruction stored in the memory and executable on the processor, wherein the computer program / instruction, when executed by the processor, implements the steps of the cellular automaton-based pipeline hydrodynamic numerical simulation method.

[0012] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores 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.

[0013] The present invention also provides a computer program product, comprising a computer program / instruction, which, when executed by a processor, implements the steps of the cellular automaton-based pipeline hydrodynamic numerical simulation method.

[0014] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: (1) Previous related studies only focused on solving the water depth and flow rate at the two nodes of the pipeline, ignoring the hydrodynamic changes inside the pipeline. Based on the cellular automaton theory, this paper proposes the basic rules for the hydrodynamic changes inside the pipeline, forming an innovative hydrodynamic simulation method that can more accurately and efficiently simulate the complex hydrodynamic changes inside the pipeline, including flow and wave characteristics, thereby improving the efficiency and accuracy of the simulation.

[0015] (2) Compared with the traditional global partial differential equation solution, the present invention can more accurately describe the local hydrodynamic changes through flexible cell size settings (including length direction and cross-sectional direction), precise neighborhood relationship definition and comprehensive cell state description (including pipe diameter, slope, roughness, etc.), and capture the microscopic effects that may be ignored by traditional methods. At the same time, the water depth and flow velocity update rules established based on the principles of conservation of mass and momentum ensure the physical rationality of the simulation results and overcome the problem of non-compliance with physical laws that may be caused by some simplified numerical methods.

[0016] (3) The present invention provides reliable technical support for decision makers related to municipal and water engineering projects, enabling more accurate prediction of pipeline water flow behavior during hydraulic simulation and design stages, thereby improving the feasibility and pertinence of engineering design, and is widely applicable to a variety of practical application scenarios such as urban drainage, water supply, and river systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flowchart of an embodiment of the present invention.

[0018] Figure 2 Schematic diagram of a one-dimensional cellular automation scene in an embodiment of the present invention.

[0019] Figure 3 It is a flow chart of the algorithm for calculating pipeline hydrodynamic changes in an embodiment of the present invention.

[0020] Figure 4 1 is a comparison diagram of the simulation and actual measurement of the pipeline hydrodynamic process under constant boundary conditions in an embodiment of the present invention; wherein (a), (b), (c), and (d) correspond to the water depth and flow rate of 1 second, 10 seconds, 30 seconds, and 300 seconds, respectively.

[0021] Figure 5 1 is a comparison diagram between the simulation and actual measurement of pipeline hydrodynamic process under fluctuating boundary conditions in an embodiment of the present invention; wherein (a), (b), (c), and (d) correspond to the water depth and flow rate of 1 second, 10 seconds, 30 seconds, and 300 seconds, respectively. DETAILED DESCRIPTION

[0022] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0023] like Figure 1 As shown, a pipeline hydrodynamic numerical simulation method based on cellular automata disclosed in an embodiment of the present invention comprises the following steps: (1) Pipeline cell scene construction: Construct a one-dimensional pipeline cellular automaton scene, set the pipeline cell size, neighborhood relationship and state, and give the upstream and downstream boundary conditions of the pipeline. Specifically, step (1) includes: (1-1) Set the pipeline cell size: Set the cell length in the pipeline length direction d x , set the cell lateral width on the pipe cross section d y , d y By water depth h and pipe diameter D (radius r = D / 2) Decision, , dy The range of variation is 0≤ d y ≤ D .

[0024] (1-2) Set the neighborhood relationship of pipeline cells: number each cell starting from the first upstream pipeline cell i ( i =1, 2, 3, …, k-1, k), k is the number of cells, pipeline cells i The neighborhood of the cell is the upstream cell of the cell i -1 and downstream cells i +1.

[0025] (1-3) Set the cell state: According to the pipe diameter, slope, and roughness parameters of the pipeline, the basic state attributes of each cell are obtained, that is, the pipe diameter D ,slope I Roughness n .

[0026] (1-4) Set the upstream boundary conditions of the pipeline: The cell numbered 1 at the most upstream end of the pipeline is the starting cell. h , flow rate v ,flow Q By taking any one of the indicators, the other two indicators can be determined according to the following formula, thus giving the upstream inflow boundary of the pipeline.

[0027] ; ; ; in, R represents the hydraulic radius of the cell, m; A Represents the water-passing cross-sectional area of ​​the cell, m 2 ; Indicates the wetted perimeter of the water-passing section of the current cell, m; Indicates that the cell is at a water depth of h The corresponding sector arc angle when 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 represents the corresponding inverse function.

[0028] (1-5) Set the downstream boundary conditions of the pipeline: The downstream number of the pipeline is k The cell with is the terminal cell, which allows water to leave the pipe system. The water depth and flow rate of the outflow can be adjusted according to the actual simulation requirements. Usually, it can be set as the free outflow boundary, that is, the terminal cellk The velocity and depth of the flow cell are equal to the upstream cell. k -1 velocity depth ( h k , v k ) = ( h k-1 , v k-1 ).

[0029] In this embodiment, combined with the pipeline experimental device, the total length of the pipeline is 10m and the diameter D =0.3m, radius r =0.15m, slope I =0.006, roughness n =0.014. In order to monitor the water depth and flow rate at different locations of the pipeline, the upper half of the pipeline is divided and only the lower half is retained for pipeline hydrodynamic experiments. Constructing a one-dimensional pipeline cellular automation scenario Figure 2 As shown, the cell length is set in the direction of the pipe length d x= 0.01m, divided into k=1000 pipeline cells.

[0030] The cell numbered 1 is the upstream inflow boundary. The upstream boundary condition considers the simulation of two working conditions: ① constant flow rate v 1 =0.3m / s, constant water depth upstream can be calculated h 1 =0.0195m, water flow simulation duration is 5 minutes; ② The water depth changes sinusoidally with time periodicity. , initial upstream flow velocity The water flow simulation lasts for 5 minutes.

[0031] The initial values ​​of water depth and flow velocity of the remaining cells under both 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 ).

[0032] (2) Pipeline flux calculation: Based on the water depth and flow velocity of the current cell and the upstream cell, the cell water flow wave velocity, water flux, momentum flux and friction loss term are calculated.

[0033] Specifically, step (2) includes: (2-1) Water flow velocity: For pipe cells i ,existt The speed of time Calculated as follows: ; in, , Respectively t Time Pipeline Cell i flow velocity and water depth; , Respectively t Upstream cell at time i -1 for velocity and water depth; g is the acceleration due to gravity, which is about 9.8 m / s 2 .

[0034] (2-2) Calculation of water flux, momentum flux, and friction loss: For the pipeline cell i , which is t Water flux at time , momentum flux , friction loss term Calculated as follows: ; ; ; in, It is the gravity coefficient affected by the pipeline slope, with a value of 0~1; Represents the upstream cell i -1 hydraulic radius.

[0035] In this embodiment, the initialization calculation of water flow velocity, water flux, momentum flux and friction loss term is carried out by taking working condition ① as an example. i =2~1000, the initial values ​​of water depth and flow velocity are both 0. Therefore, when starting the calculation, you only need to calculate the number i =2, the water flow wave velocity, water flux, momentum flux and friction loss term of the cell.

[0036] Water flow velocity: For pipe cell 2, it can be calculated t= Wave speed at time 0 : ; At this time, the wave speed The velocity is greater than the velocity of the inflow boundary, 0.3 m / s, because there is no water in cell 2, and the water flowing from cell 1 is also significantly accelerated by gravity. You can first take 0.5 to reflect the degree to which the water flow is affected by gravity.

[0037] Calculation of water flux, momentum flux, and friction loss: For pipeline cell 2, it can be calculated in t= Water flux at time 0 , momentum flux , friction loss term : ; ; ; ; ; ; ; (3) Pipeline hydrodynamic calculation: The water depth and flow velocity of each cell at the next moment are calculated according to the water depth and flow velocity update rules, and the hydrodynamic change process of the pipeline is obtained by cyclically updating the rules.

[0038] After a given time step, the water depth of the pipe cell is determined by the water depth at the previous moment and the difference in water flux of the cells in the neighborhood. The flow rate of the pipe cell is determined by the flow rate at the previous moment, the water depth, the difference in momentum flux of the cells in the neighborhood, and the friction loss term. Specifically, step (3) includes: (3-1) Water depth update rule: After a given After a time step, the pipeline cell i The water depth of the previous moment ( t ) water depth The water flux difference between the cells in the neighborhood is determined by the following formula to update the cell i At the next moment ( t +1) Water Depth : ; (3-2) Flow rate update rule: After a given After a time step, the pipeline cell i The flow rate is determined by the previous moment ( t ) flow rate , water depth , the momentum flux difference of cells in the neighborhood and the friction loss term Determine, the cell can be updated according to the following formula i At the next moment ( t +1) Flow rate : ; In this embodiment, the algorithm flow for solving the pipeline hydrodynamic change process is as follows: Figure 3After completing the construction of the pipeline one-dimensional cellular automaton scene and the flux initialization calculation in steps (1) and (2), the water depth, flow rate update rules and water volume transfer rules in step (3) can be executed cyclically to obtain the spatiotemporal change process of the pipeline hydrodynamics until the required simulation time is reached. t end In this embodiment, the simulation duration t end = 5 min, time step d t = 0.002 s. During the experiment, the flow velocity and water depth changes at different positions (2m, 4m, 6m, 8m) in the pipeline were measured using a Doppler flowmeter and a water gauge recorder.

[0039] Comparison of the simulated and measured values ​​of the hydrodynamics of the pipeline at different times under two working conditions Figure 4 and Figure 5 As shown. Since the pipeline is initially dry, after water is first passed ( Time =1s) forms an effective head difference between the cells with water and without water, and the gravitational potential energy is converted into the kinetic energy of the water body, so the flow rate is significantly greater than the 0.3m / s given upstream. As the flow rate increases, the water depth tends to decrease along the way due to the continuity of the water flow. When the pipeline is completed with water ( Time ≥30s), it can be seen that the head difference gradually disappears, the pipeline flow rate gradually decreases to a stable value, and the water depth gradually increases to a stable value. Overall, the simulated water depth and flow rate values ​​are close to the measured values, with an average error of less than 5%. At the same time, it can be seen that the present invention can not only accurately simulate the entire process of hydrodynamic changes from the pipeline water flow to the stable stage, but also finely depict the pipeline hydrodynamic process under the condition of periodic fluctuations at the boundary ( Figure 5 ), indicating that the pipeline hydrodynamic numerical simulation technology proposed in this invention has good reliability and applicability.

[0040] In summary, the present invention simulates the behavior of the fluid by defining the local rules of the cellular automaton, thereby capturing the dynamic change process of the water flow in the local pipeline. Compared with solving traditional partial differential equations, the cellular automaton model does not require complex mathematical descriptions, which makes the model setting 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 simulation.

[0041] Based on the same inventive concept, an embodiment of the present invention further discloses a pipeline hydrodynamic numerical simulation system based on cellular automata, comprising: The pipeline cell scene construction module is used to construct a one-dimensional cellular automaton scene of the pipeline, set the pipeline cell size, neighborhood relationship and state, and give the upstream and downstream boundary conditions of the pipeline; the pipeline cell size includes the cell length in the pipeline length direction and the cell lateral width on the pipeline cross section, and the pipeline cell state includes the pipe diameter, slope and roughness; The pipeline flux calculation module is used to calculate the cell water flow wave velocity, water flux, momentum flux and friction loss term according to the water depth and flow velocity of the current cell and the upstream cell; 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 cyclically updating the rules; wherein after a given time step, the water depth of the pipeline cell is determined by the water depth at the previous moment and the water flux difference of the cells in the neighborhood, and the flow velocity of the pipeline cell is determined by the flow velocity at the previous moment, the water depth, the momentum flux difference of the cells in the neighborhood, and the friction loss term.

[0042] An embodiment of the present invention also discloses a computer system, including a memory, a processor, and a computer program / instruction stored in the memory and executable on the processor, wherein the computer program / instruction, when executed by the processor, implements the steps of the cellular automaton-based pipeline hydrodynamic numerical simulation method.

[0043] The embodiment of the present invention further discloses a computer-readable storage medium, wherein the computer-readable storage medium stores 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.

[0044] The embodiment of the present invention further discloses a computer program product, including a computer program / instruction, which implements the steps of the pipeline hydrodynamic numerical simulation method based on cellular automata when executed by a processor.

[0045] The above disclosure is only the preferred embodiment of the present invention, which cannot be used to limit the scope of the present invention. Therefore, equivalent changes made according to the claims of the present invention are still within the scope of the present invention.

Claims

1. A numerical simulation method of pipeline hydrodynamics based on cellular automata, characterized in that: The method comprises the following steps: (1) Construct a one-dimensional cellular automaton scenario for the pipeline, set the pipeline cell size, neighborhood relationship, and state, and give the upstream and downstream boundary conditions of the pipeline. The pipeline cell size includes the cell length in the pipeline length direction and the cell lateral width on the pipeline cross section. The pipeline cell state includes the pipe diameter, slope, and roughness. (2) Calculate the cell water flow wave velocity, water flux, momentum flux, and friction loss term based on the water depth and flow velocity of the current cell and the upstream cell; (3) The water depth and flow velocity of each cell at the next moment are calculated according to the water depth and flow velocity update rules, and the hydrodynamic change process of the pipeline is obtained by cyclically updating the rules. After a given time step, the water depth of the pipeline cell is determined by the water depth at the previous moment and the water flux difference of the cells in the neighborhood. The flow velocity of the pipeline cell is determined by the flow velocity at the previous moment, the water depth, the momentum flux difference of the cells in the neighborhood, and the friction loss term.

2. The pipeline hydrodynamic numerical simulation method based on cellular automata according to claim 1, characterized in that: In step (1), the upstream boundary condition of the pipe is determined by specifying the water depth of the starting cell. h , flow rate v ,flow Q Any one of the indicators is used to determine the other two indicators according to the following formula, thus giving the upstream inflow boundary of the pipeline; ； ； ； in, R, D, I, n They represent the hydraulic radius, pipe diameter, slope and roughness of the cell respectively; r = D / 2; A represents the water-passing cross-sectional area of ​​the cell; It represents the wetted perimeter of the water-passing section of the cell; Indicates that the cell is at a water depth of h The corresponding sector arc angle when 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 represents the corresponding inverse function.

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

4. The pipeline hydrodynamic numerical simulation method based on cellular automata according to claim 1, characterized in that: In step (2), for the pipeline cell i ,exist t Water velocity at a given moment , water flux , momentum flux , friction loss term Calculated as follows: ； ； ； ； in, , Respectively t Time Pipeline Cell i flow velocity and water depth; , Respectively t Upstream cell at time i -1 for flow velocity and water depth; g is the acceleration due to gravity; It is the gravity coefficient affected by the pipeline slope, with a value of 0~1; Represents the upstream cell i -1 hydraulic radius; n Indicates roughness.

5. The pipeline hydrodynamic numerical simulation method based on cellular automata according to claim 1, characterized in that: In step (3), the water depth update rule is: after a given After a time step, the pipeline cell i exist t +1 moment of water depth Depend on t The depth of time It is determined by the difference in water flux between the cells in the neighborhood and is calculated as follows: ； in, d x represents the cell length; and Respectively t Time Pipeline Cell i and upstream cells i -1 water flux.

6. The pipeline hydrodynamic numerical simulation method based on cellular automata according to claim 1, characterized in that: In step (3), the flow rate update rule is: after passing the given After a time step, the pipeline cell i exist t +1 flow rate Depend on t The flow rate of time , water depth , the momentum flux difference of cells in the neighborhood and the friction loss term Determine, calculated according to the following formula: ； in, d x represents the cell length; and Respectively t Time Pipeline Cell i and downstream cells i +1 momentum flux; express t Time Pipeline Cell i The friction loss term; express t +1 time pipeline cell i The depth of water.

7. A numerical simulation system of pipeline hydrodynamics based on cellular automata, characterized in that: include: The pipeline cell scene construction module is used to construct a one-dimensional cellular automaton scene of the pipeline, set the pipeline cell size, neighborhood relationship and state, and give the upstream and downstream boundary conditions of the pipeline; the pipeline cell size includes the cell length in the pipeline length direction and the cell lateral width on the pipeline cross section, and the pipeline cell state includes the pipe diameter, slope and roughness; The pipeline flux calculation module is used to calculate the cell water flow wave velocity, water flux, momentum flux and friction loss term according to the water depth and flow velocity of the current cell and the upstream cell; 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 cyclically updating the rules; wherein after a given time step, the water depth of the pipeline cell is determined by the water depth at the previous moment and the water flux difference of the cells in the neighborhood, and the flow velocity of the pipeline cell is determined by the flow velocity at the previous moment, the water depth, the momentum flux difference of the cells in the neighborhood, and the friction loss term.

8. A computer system comprising a memory, a processor, and a computer program / instruction 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 to 6 are implemented.

9. 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 automaton according to any one of claims 1 to 6 are implemented.

10. 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 to 6 are implemented.

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