A two-dimensional numerical simulation method and related equipment for open flow in underground spaces

Abstract

This application discloses a two-dimensional numerical simulation method and related equipment for open-flow-filled underground space. The method includes: initializing the flow field state variables of a two-dimensional unstructured grid corresponding to the underground space; reconstructing the left and right interface states of each grid cell by combining the bottom elevation and top elevation of each grid cell, and determining the interface reconstruction state variables and reconstruction water depth; calculating the equivalent wave velocity and pressure terms based on the interface reconstruction state variables and reconstruction water depth, and calculating the interface numerical flux of each grid cell; calculating the source term vector containing topographic slope source terms and friction source terms according to the bottom elevation and flow field state variables of each grid cell; and calculating the flow field state variables at the next time step using a time-stepping scheme based on the source term vector and the interface numerical flux of each grid cell. This application can achieve stable and efficient numerical simulation of open-flow-filled underground space and can be widely applied in the field of hydrodynamic numerical simulation technology.

Description

Technical Field

[0001] This application relates to the field of hydrodynamic numerical simulation technology, and in particular to a two-dimensional numerical simulation method and related equipment for open-flow underground space. Background Technology

[0002] With the large-scale development of urban underground space, the risk of flooding disasters to underground facilities (such as subway tunnels and underground shopping malls) is increasing. The evolution of floods in underground spaces has extremely unique hydraulic characteristics, and there are problems such as complex flow patterns, geometric constraints, and topological complexities.

[0003] However, the traditional two-dimensional Shallow Water Equations (SWE) model assumes that there is an atmosphere above the water surface, which cannot simulate the pressurized process after the water surface touches the top; while the three-dimensional CFD (Computational Fluid Dynamics) model can simulate it, the computational cost is too high and cannot meet the timeliness requirements of large-scale disaster prevention and early warning.

[0004] In summary, the technical problems existing in the relevant technologies need to be improved. Summary of the Invention

[0005] The embodiments of this application aim to at least partially solve one of the technical problems in the related art. Therefore, the main objective of the embodiments of this application is to propose a two-dimensional numerical simulation method and related equipment for open-circuit flow in underground spaces, which can achieve stable and efficient numerical simulation of open-circuit flow in complex underground spaces, providing reliable data support and technical basis for flood control safety, water flow management, and operational risk assessment in scenarios such as subway station-tunnel systems, underground utility tunnels, and underground parking garages.

[0006] To achieve the above objectives, one aspect of this application proposes a two-dimensional numerical simulation method for open-circuit flow in underground spaces, the method comprising the following steps:

[0007] Construct a two-dimensional unstructured grid of the target underground space, and assign the current floor elevation and the current roof elevation to each grid cell in the two-dimensional unstructured grid;

[0008] Initialize the current flow field state variables of the two-dimensional unstructured mesh; wherein, the current flow field state variables include the current water depth and the current unit width flow rate;

[0009] By combining the current bottom elevation and the current top elevation of each grid cell, the left and right states of the interface of each grid cell are reconstructed to determine the interface reconstruction state quantity, and the reconstruction water depth is determined based on the interface reconstruction state quantity; wherein, the interface reconstruction state quantity includes the reconstructed bottom elevation and the reconstructed top elevation.

[0010] Based on the reconstructed water depth and the interface reconstructed state variables, the equivalent wave velocity and pressure terms are calculated, and the current flow field state variables are updated based on the reconstructed water depth.

[0011] Using the HLL Riemann solver, the interface numerical flux of each grid cell is calculated based on the equivalent wave velocity, the pressure term, and the updated current flow field state variables.

[0012] Based on the current base elevation and the current flow field state variables of each grid cell, calculate the source term vector containing the terrain slope source term and the friction source term;

[0013] Using a time-stepping format, the flow field state variables at the next time step are calculated based on the source term vector and the interface numerical flux of each grid cell, in order to complete the numerical simulation at the current time step.

[0014] In some embodiments, after calculating the flow field state variables at the next time step using the time-stepping format, based on the source term vector and the interface numerical flux of each of the grid cells, to complete the numerical simulation at the current time step, the method further includes:

[0015] If the current moment of the numerical simulation has not reached the preset simulation end time, the flow field state variable at the next moment is used as the current flow field state variable. The process returns to the steps of combining the current bottom plate elevation and the current top cover elevation of each grid cell to reconstruct the left and right states of the interface of each grid cell, determining the interface reconstruction state quantity, and determining the reconstruction water depth based on the interface reconstruction state quantity, until the current moment of the numerical simulation reaches the preset simulation end time, and the simulation results are output.

[0016] In some embodiments, the step of reconstructing the left and right states of the interface of each grid cell by combining the current bottom elevation and the current top elevation of each grid cell, determining the interface reconstruction state quantity, and determining the reconstruction water depth based on the interface reconstruction state quantity includes:

[0017] Based on the current base plate elevation of each grid cell, determine the maximum value of the base plate elevation on the left and right sides of the interface of each grid cell to obtain the reconstructed base plate elevation;

[0018] Based on the current top cover elevation of each grid cell, the minimum top cover elevation on the left and right sides of the interface of each grid cell is determined to obtain the reconstructed top cover elevation.

[0019] Based on the reconstructed base plate elevation, the reconstructed water depth on the left and right sides of the interface of each grid cell is calculated.

[0020] In some embodiments, calculating the equivalent wave velocity and pressure term based on the reconstructed water depth and the interface reconstructed state quantity includes:

[0021] Calculate the elevation difference between the reconstructed base plate elevation and the reconstructed top cover elevation;

[0022] If the reconstructed water depth is less than or equal to the elevation difference, then the water body is determined to be in the open flow stage, the shallow water wave velocity is taken as the equivalent wave velocity of the open flow stage, and the hydrostatic pressure is taken as the pressure term of the open flow stage.

[0023] If the reconstructed water depth is greater than the elevation difference, the water body is determined to be in the full flow stage, the sound speed is taken as the equivalent wave speed of the full flow stage, and the additional pressure is taken as the pressure term of the full flow stage.

[0024] When the reconstructed water depth is within the preset critical range between the open flow stage and the full flow stage, the water body is determined to be in the transition stage. The shallow water wave velocity and the sound velocity are smoothly weighted based on normalized weights to obtain the equivalent wave velocity of the transition stage. The static pressure and the additional pressure are smoothly weighted based on normalized weights to obtain the pressure term of the transition stage.

[0025] In some embodiments, calculating the source term vector, which includes the terrain slope source term and the friction source term, based on the current base elevation and the current flow field state variables of each of the grid cells includes:

[0026] The terrain slope source term is calculated based on the current base elevation of each of the grid cells;

[0027] The friction source term is calculated based on the current water depth and the current unit width flow rate of each of the grid cells;

[0028] Based on the terrain slope source term and the friction source term, the source term vector is constructed.

[0029] In some embodiments, the method further includes:

[0030] Calculate the total outflow flux of each grid cell based on the several interface numerical fluxes corresponding to each grid cell.

[0031] Based on the total outflow flux of each grid cell, determine whether the water depth value of each grid cell is negative at the next time step;

[0032] If it is determined that there is a target grid cell with a negative water depth value in the next time step, then flux scaling technology is used to adaptively reduce the total outflow flux of the target grid cell.

[0033] To achieve the above objectives, another aspect of this application proposes a two-dimensional numerical simulation device for open-circuit flow in underground spaces, the device comprising the following modules:

[0034] An unstructured mesh construction module is used to construct a two-dimensional unstructured mesh of the target underground space and assign the current bottom elevation and the current top elevation to each mesh cell in the two-dimensional unstructured mesh;

[0035] The flow field state variable initialization module is used to initialize the current flow field state variables of the two-dimensional unstructured mesh; wherein, the current flow field state variables include the current water depth and the current unit width flow rate;

[0036] The unit interface state reconstruction module is used to reconstruct the left and right states of the interface of each grid unit by combining the current bottom plate elevation and the current top cover elevation of each grid unit, determine the interface reconstruction state quantity, and determine the reconstruction water depth based on the interface reconstruction state quantity; wherein, the interface reconstruction state quantity includes the reconstructed bottom plate elevation and the reconstructed top cover elevation.

[0037] The flow regime and state update module is used to calculate the equivalent wave velocity and pressure terms based on the reconstructed water depth and the interface reconstructed state variables, and update the current flow field state variables based on the reconstructed water depth.

[0038] The interface numerical flux calculation module is used to calculate the interface numerical flux of each grid cell using the HLL Riemann solver, based on the equivalent wave velocity, the pressure term, and the updated current flow field state variables.

[0039] The source term vector calculation module is used to calculate a source term vector containing topographic slope source term and friction source term based on the current base elevation and the current flow field state variables of each grid cell.

[0040] The flow field state variable update module is used to calculate the flow field state variables at the next time step using the time step format, based on the source term vector and the interface numerical flux of each grid cell, so as to complete the numerical simulation at the current time step.

[0041] To achieve the above objectives, another aspect of this application provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-described method.

[0042] To achieve the above objectives, another aspect of the embodiments of this application proposes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0043] To achieve the above objectives, another aspect of this application provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0044] The embodiments of this application include at least the following beneficial effects: This application provides a two-dimensional numerical simulation method and related equipment for open-circuit flow in underground space. This method constructs a two-dimensional unstructured grid of the target underground space and assigns the current floor elevation and current roof elevation to each grid cell in the two-dimensional unstructured grid; initializes the current flow field state variables of the two-dimensional unstructured grid; wherein, the current flow field state variables include the current water depth and the current unit width flow rate; combining the current floor elevation and current roof elevation of each grid cell, reconstructs the left and right interface states of each grid cell, determines the interface reconstruction state variables, and determines the reconstruction water depth based on the interface reconstruction state variables; wherein, the boundary... The reconstructed state variables include the reconstructed bottom elevation and the reconstructed top elevation. Based on the reconstructed water depth and interface reconstructed state variables, the equivalent wave velocity and pressure terms are calculated, and the current flow field state variables are updated based on the reconstructed water depth. Using the HLL Riemann solver, the interface numerical flux of each grid cell is calculated based on the equivalent wave velocity, pressure terms, and the updated current flow field state variables. Based on the current bottom elevation and current flow field state variables of each grid cell, the source term vector, which includes the topographic slope source term and the frictional source term, is calculated. Using a time-stepping scheme, the flow field state variables at the next time step are calculated based on the source term vector and the interface numerical flux of each grid cell to complete the numerical simulation of the current time step. This application's embodiments construct a two-dimensional unstructured grid for underground space and assign elevations to the bottom plate and top cover, which can adapt to complex underground space geometry and improve model applicability. By reconstructing the left and right states of the grid cell interfaces, the reconstructed water depth, equivalent wave velocity, and pressure terms can be reasonably determined, ensuring the physical rationality and numerical stability of interface variables. The use of the HLL Riemann solver to calculate the interface numerical flux can improve the flux calculation accuracy and adapt to complex flow states of open and full flow transitions. By calculating the topographic slope source term and friction source term separately, the combined effects of gravity and resistance in underground space flow can be accurately reflected. By using a time-stepping scheme combined with the source term vector and interface numerical flux to update the flow field state, stable and efficient numerical simulation of open and full flow in complex underground spaces can be achieved. Attached Figure Description

[0045] Figure 1 This is a flowchart illustrating the steps of a two-dimensional numerical simulation method for open-circuit flow in underground space provided in an embodiment of this application;

[0046] Figure 2 This is a schematic diagram of the overall process of a two-dimensional numerical simulation method for open flow in underground space provided in an embodiment of this application;

[0047] Figure 3This is a schematic diagram illustrating the principle of a smooth transition mechanism for full-flow flow provided in an embodiment of this application;

[0048] Figure 4 This is a schematic diagram of a static water reconstruction considering the roof elevation provided in an embodiment of this application;

[0049] Figure 5 This is a schematic diagram of the interface flux exchange principle of the finite volume method provided in an embodiment of this application;

[0050] Figure 6 This is a schematic diagram of the wave structure of an HLL approximate Riemann solver provided in an embodiment of this application;

[0051] Figure 7 This is a schematic diagram of the flooding calculation results for a U-shaped tunnel provided in an embodiment of this application;

[0052] Figure 8 This is a schematic diagram illustrating the water head changes at different locations during the submersion of a U-shaped tunnel, provided in an embodiment of this application.

[0053] Figure 9 This is a schematic diagram of the structure of a two-dimensional numerical simulation device for open flow in underground space provided in an embodiment of this application;

[0054] Figure 10 This is a schematic diagram of the hardware structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit it. In the following description, when referring to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with those of this application; they are merely examples of apparatuses and methods consistent with some aspects of the embodiments of this application as detailed in the appended claims.

[0056] It is understood that the terms “first,” “second,” etc., used in this application may be used herein to describe various concepts, but unless otherwise stated, these concepts are not limited by these terms. These terms are only used to distinguish one concept from another. For example, without departing from the scope of the embodiments of this application, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the words “if,” “when,” or “in response to a determination” as used herein may be interpreted as “when…” or “when…” or “in response to a determination.”

[0057] As used in this application, the terms "at least one", "multiple", "each", "any", etc., "at least one" includes one, two or more, "multiple" includes two or more, "each" refers to each of the corresponding multiples, and "any" refers to any one of the multiples.

[0058] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0059] With the large-scale development of urban underground space, the risk of flooding in underground facilities (such as subway tunnels and underground shopping malls) is increasing. The evolution of floods in underground spaces exhibits extremely unique hydraulic characteristics:

[0060] (1) Complex flow patterns: Water flow may switch rapidly between "open flow" with a free surface and "full flow" (pressurized flow) that fills the entire cross section;

[0061] (2) Geometric constraints: It is not only affected by the terrain of the base plate, but also by the height of the top plate (top cover);

[0062] (3) Topological complexity: Underground structures are often irregular and require unstructured meshes for body-fitting.

[0063] Traditional two-dimensional shallow water equation (SWE) models assume that the atmosphere is above the water surface and cannot simulate the pressurized process after the water surface touches the top; while three-dimensional CFD models can simulate this, the computational cost is too high and cannot meet the timeliness requirements of large-scale disaster prevention and early warning.

[0064] In view of this, this application provides a two-dimensional numerical simulation method and related equipment for open and full flow in underground spaces. This scheme constructs a two-dimensional unstructured grid of the underground space and assigns elevations to the bottom plate and top cover, which can adapt to complex underground space geometry and improve the applicability of the model. By reconstructing the left and right states of the grid cell interface, the reconstructed water depth, equivalent wave velocity, and pressure terms can be reasonably determined, ensuring the physical rationality and numerical stability of the interface variables. The HLL Riemann solver is used to calculate the interface numerical flux, which can improve the flux calculation accuracy and adapt to the complex flow regime of open and full flow conversion. By calculating the topographic slope source term and friction source term respectively, the combined effect of gravity and resistance in the underground space flow can be accurately reflected. By using a time-stepping scheme combined with the source term vector and the interface numerical flux to update the flow field state, stable and efficient numerical simulation of open and full flow in complex underground spaces can be achieved.

[0065] This application provides a two-dimensional numerical simulation method for open-flow underground space, relating to the field of hydrodynamic numerical simulation technology. This method can be applied to a terminal, a server, or software running on either a terminal or a server. In some embodiments, the terminal can be a smartphone, tablet, laptop, desktop computer, smart speaker, smartwatch, or vehicle terminal, but is not limited to these. The server can be configured as an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms. The server can also be a node server in a blockchain network. The software can be an application implementing the two-dimensional numerical simulation method for open-flow underground space, but is not limited to the above forms.

[0066] This application can be used in a wide variety of general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics devices, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices. This application can be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform specific tasks or implement specific abstract data types. This application can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0067] Please see Figure 1 , Figure 1 This is an optional flowchart of a two-dimensional numerical simulation method for open-circuit flow in underground space provided in an embodiment of this application. Figure 1 The method may include, but is not limited to, steps S101 to S107.

[0068] Step S101: Construct a two-dimensional unstructured grid of the target underground space, and assign the current bottom elevation and the current top elevation to each grid cell in the two-dimensional unstructured grid;

[0069] The target underground space refers to the specific underground water flow or fluid scene area that needs to be simulated in two-dimensional numerical simulation, such as underground pipe networks, tunnels, underground rivers, reservoirs, etc., which is the physical space range of the entire numerical simulation.

[0070] The term "open flow" refers to both open flow and full flow. Open flow means that the groundwater or fluid does not fill the entire cross-section, leaving a free water surface that is directly in contact with air (or a vacuum), and the water level can rise and fall freely. Full flow means that the groundwater or fluid fills the entire pipe, tunnel, or space, with no free water surface; the top, bottom, left, and right sides are all filled with water and are constrained by a top cover.

[0071] Two-dimensional unstructured meshes are sets of two-dimensional cells of arbitrary shapes and irregular arrangements that discretize the target underground space within a plane. The cell types are usually triangular or polygonal. They can flexibly fit complex boundaries and refine local areas, and can be used for numerical calculations in irregular areas such as underground spaces, tunnels, and rivers. The two-dimensional unstructured mesh includes node coordinates and cell topological relationships.

[0072] A grid cell is the smallest computational unit (such as a triangular cell) after a two-dimensional unstructured grid has been divided. Each cell is an independent storage and computational carrier for physical quantities.

[0073] Among them, the bottom plate elevation This refers to the elevation / base value at the bottom of each grid cell (i.e., the z-coordinate of the cell's lower boundary), representing the bottom topography of the underground space. Top Cover Elevation This refers to the elevation / base value at the top of each grid cell (i.e., the z-coordinate of the cell's upper boundary), representing the top constraint of underground space (such as the top of a tunnel or pipe).

[0074] In this embodiment of the application, a base plate elevation is assigned to each node or cell in the two-dimensional unstructured mesh. and roof elevation Attributes. Subsequent steps will involve spatial discretization and numerical solution of the governing equations describing fluid motion in underground spaces based on a two-dimensional unstructured grid. This will yield the flow field state variables of each grid cell at different times, enabling high-precision simulation of open and full-flow processes in underground spaces. This will provide reliable numerical support for underground fluid disaster prevention and control, engineering design optimization, and flow process regulation.

[0075] In step S101, by constructing an unstructured mesh model that includes the elevation attributes of the base plate and the top cover, it is possible to adapt to the irregular geometric shape of complex underground spaces and accurately describe the spatial constraints and boundary conditions of underground structures.

[0076] Step S102: Initialize the current flow field state variables of the two-dimensional unstructured mesh; wherein, the current flow field state variables include the current water depth and the current unit width flow rate;

[0077] Here, the flow field state variables are a set of core physical quantities describing the instantaneous state of the fluid within each grid cell. The flow field state variables are defined as follows: .in, Because of the water depth, Let be the velocity component of the fluid in the x-direction. Let be the velocity component of the fluid in the y-direction. For the unit width flow rate in the x direction, For the unit width flow rate in the y direction, This is a transpose.

[0078] Step S103: Combine the current bottom plate elevation and the current top cover elevation of each grid cell to reconstruct the left and right states of the interface of each grid cell, determine the interface reconstruction state quantity, and determine the reconstruction water depth based on the interface reconstruction state quantity; wherein, the interface reconstruction state quantity includes the reconstruction bottom plate elevation and the reconstruction top cover elevation.

[0079] In some embodiments, step S103 may include: determining the maximum value of the bottom plate elevation on the left and right sides of the interface of each grid cell based on the current bottom plate elevation of each grid cell, so as to obtain the reconstructed bottom plate elevation; determining the minimum value of the top plate elevation on the left and right sides of the interface of each grid cell based on the current top plate elevation of each grid cell, so as to obtain the reconstructed top plate elevation; and calculating the reconstructed water depth on the left and right sides of the interface of each grid cell based on the reconstructed bottom plate elevation.

[0080] Among them, the interface reconstruction state quantities include the reconstruction base plate elevation and the reconstruction top cover elevation.

[0081] Before calculating the numerical flux at the interface, a hydrostatic reconstruction method considering the bottleneck effect of the top cover is used to preprocess the interface state to prepare for the subsequent calculation of the numerical flux at the interface. Specifically: First, the maximum elevation of the bottom plate on the left and right sides of the interface of each grid cell is taken. This yields the reconstructed base elevation. Simultaneously, the minimum elevation of the top cover on the left and right sides of the interface of each grid cell is taken. This yields the reconstructed top elevation; then, based on the reconstructed bottom elevation, the reconstructed water depth on both sides of the interface of each grid cell is calculated. .

[0082] in, This refers to the elevation of the base plate of the unit on the left side of the interface. This refers to the elevation of the base plate of the unit on the right side of the interface. This refers to the elevation of the top cover of the unit on the left side of the interface. The elevation of the top cover of the unit on the right side of the interface. This represents the original water depth (water depth value before reconstruction) of the left / right cells of the interface. This represents the original base plate elevation of the left / right side units of the interface.

[0083] Step S104: Based on the reconstructed water depth and the interface reconstruction state variables, calculate the equivalent wave velocity and pressure terms, and update the current flow field state variables based on the reconstructed water depth;

[0084] In some embodiments, the step of calculating the equivalent wave velocity and pressure term based on the reconstructed water depth and interface reconstruction state quantity may include: calculating the elevation difference between the reconstructed bottom plate elevation and the reconstructed top cover elevation; if the reconstructed water depth is less than or equal to the elevation difference, the water body is determined to be in the open flow stage, the shallow water wave velocity is taken as the equivalent wave velocity of the open flow stage, and the hydrostatic pressure is taken as the pressure term of the open flow stage; if the reconstructed water depth is greater than the elevation difference, the water body is determined to be in the full flow stage, the sound velocity is taken as the equivalent wave velocity of the full flow stage, and the additional pressure is taken as the pressure term of the full flow stage; when the reconstructed water depth is within a preset critical range between the open flow stage and the full flow stage, the water body is determined to be in the transition stage, the shallow water wave velocity and sound velocity are smoothly weighted based on normalized weights to obtain the equivalent wave velocity of the transition stage, and the hydrostatic pressure and additional pressure are smoothly weighted based on normalized weights to obtain the pressure term of the transition stage.

[0085] Among them, elevation difference =Top cover elevation - Bottom plate elevation The elevation difference is used to characterize the height of the flow channel.

[0086] In the embodiments of this application, the pressure item With equivalent wave velocity The calculation method is defined as follows:

[0087] Specifically, based on the current water depth Elevation of the roof Relationship, calculate equivalent wave velocity and pressure items Among them, pressure item With equivalent wave velocity Satisfying consistency ;

[0088] Among them, equivalent wave velocity and pressure items The calculation methods are divided into two categories: piecewise or smooth transition. Specifically:

[0089] when (Open flow) use shallow water wave velocity and hydrostatic pressure ;

[0090] when (At full flow) speed of sound and additional pressure ;

[0091] Specifically, to ensure a unified solution for open flow and pressurized flow (full flow), the pressure term... The pressure law is calculated using the Preissmann slit equivalent equation of state to ensure consistency with wave velocity, where the pressure term... satisfy:

[0092] when At that time, pressure item Using hydrostatic pressure, specifically ;

[0093] when At that time, pressure item Additional pressure is used, specifically: ;

[0094] Among them, the flow channel height , It represents the acceleration due to gravity.

[0095] In the transition zone, a normalized weight-based approach is adopted. Smoothing is applied to suppress numerical oscillations during flow regime transitions. The transition region ranges from h ∈ [ ), 1.05×( Normalized weights =(h- )) / (0.05× The pressure in the transition zone is P(h) = (1-w)× + w× .

[0096] Optionally, segmented equivalent wave velocity It can be represented as:

[0097] ;

[0098] in, The numerical sound velocity (which can be a "reduced wave velocity" much smaller than the actual water hammer wave velocity, in order to obtain an acceptable time step while maintaining the pressurized characteristics).

[0099] In the specific implementation, the water depth will be reconstructed. The pressure term is input as the water depth h. With equivalent wave velocity The corresponding pressure term is obtained from the calculation formula. With equivalent wave velocity Furthermore, the water depth will be reconstructed. As the water depth h, update the flow field state variable. Among them, the pressure item Equivalent wave velocity and the updated flow field state variables Used as input to the subsequent HLL Riemann solver to solve for the interface numerical flux of the mesh element.

[0100] In this embodiment, a consistent pressure law is adopted by introducing the Preissmann slit equivalent state equation for pressurized-open channel unification. With wave speed It can uniformly describe the flow states of free surface flow and pressurized flow, and can naturally complete the conversion between open and full surface flow without switching models.

[0101] Step S105: Using the HLL Riemann solver, calculate the interface numerical flux of each grid cell based on the equivalent wave velocity, the pressure term, and the updated current flow field state variables.

[0102] The HLL Riemann solver is a standard numerical method for calculating the numerical flux of an interface. The specific implementation principle can be found in the relevant technical content, and the embodiments of this application will not be described in detail here.

[0103] In the specific implementation, the pressure term, equivalent wave velocity, and flow field state variables updated based on reconstructed water depth are input into the HLL Riemann solver, and the interface numerical flux of each grid cell is calculated through the HLL Riemann solver.

[0104] Step S106: Calculate the source term vector containing the terrain slope source term and the friction source term based on the current base elevation and the current flow field state variable of each grid cell;

[0105] In some embodiments, step S106 may include: calculating the terrain slope source term based on the current base elevation of each grid cell; calculating the friction source term based on the current water depth and current unit width flow rate of each grid cell; and constructing a source term vector based on the terrain slope source term and the friction source term.

[0106] The topographic slope source term represents the water flow driving force generated by the difference in elevation. The frictional resistance source term represents the flow resistance term formed by the friction between the water flow and the bottom plate. The source term vector is the total external force term formed by combining the topographic driving force and the frictional resistance.

[0107] In this embodiment of the application, by employing a Riemann solver that combines hydrostatic reconstruction with source term balancing in flux calculation, the bottleneck effect of the top cover can be accurately captured, numerical oscillations at abrupt flow changes can be suppressed, and consistency between hydrostatic balance and flux calculation can be ensured.

[0108] Step S107: Using a time-stepping format, calculate the flow field state variables at the next time step based on the source term vector and the interface numerical flux of each grid cell, so as to complete the numerical simulation at the current time step.

[0109] In some embodiments, the method may further include: calculating the total outflow flux of each grid cell based on a plurality of interface numerical fluxes corresponding to each grid cell; determining whether the water depth value of each grid cell is negative at the next time step based on the total outflow flux of each grid cell; and if it is determined that there is a target grid cell with a negative water depth value at the next time step, then using flux scaling techniques to adaptively reduce the total outflow flux of the target grid cell.

[0110] In this grid cell, there are multiple interfaces. By summing the numerical fluxes of the multiple interfaces of a cell, the total outflow flux of that grid cell can be obtained.

[0111] This application also includes a flux scaling step: calculating the total outflow flux corresponding to each grid cell. If the total outflow flux of a certain cell causes the water depth of that cell to be negative, the total outflow flux of that cell is adaptively reduced to ensure the positive definiteness of the water depth.

[0112] In the specific implementation, a non-negative flux scaling mechanism and semi-implicit friction processing are adopted in the time progression to ensure that the water depth is non-negative during the simulation process, avoid numerical anomalies in the wet-dry alternation process, improve the robustness of the algorithm, and improve the stability and efficiency of time progression while ensuring the accuracy of calculation. It is suitable for long-term, large-scale flood evolution simulation.

[0113] In some embodiments, after step S107, the method may further include: if the current time of the numerical simulation has not reached the preset simulation end time, then the flow field state variable at the next time moment is taken as the current flow field state variable, and the method returns to execute the steps of combining the current bottom plate elevation and the current top cover elevation of each grid cell to reconstruct the left and right states of the interface of each grid cell, determine the interface reconstruction state quantity, and determine the reconstruction water depth based on the interface reconstruction state quantity, until the current time of the numerical simulation reaches the preset simulation end time, and the simulation results are output.

[0114] In this embodiment, the completion of the numerical simulation is primarily determined based on a preset simulation end time. In specific implementations, the conditions for determining the completion of the numerical simulation may include, but are not limited to, the preset simulation end time. For example, the completion may also be determined based on a preset number of iterations, or on flow field convergence conditions, etc. These can be set according to actual applications, and this embodiment does not impose any limitations on them. Furthermore, this embodiment outputs the total simulation results for all desired time steps at once. However, in actual operation, single simulation results can also be output at each time step, and this embodiment does not impose any limitations on this either.

[0115] Steps S101 to S107 as shown in the embodiments of this application, by constructing a two-dimensional unstructured grid of underground space and assigning elevations to the bottom plate and top cover, can adapt to complex underground space geometry and improve the applicability of the model; by reconstructing the left and right states of the grid cell interface, the reconstructed water depth, equivalent wave velocity, and pressure terms can be reasonably determined, ensuring the physical rationality and numerical stability of the interface variables; using the HLL Riemann solver to calculate the interface numerical flux can improve the flux calculation accuracy and adapt to the complex flow regime of open and full flow conversion; by calculating the topographic slope source term and friction source term respectively, the combined effect of gravity and resistance in underground space flow can be accurately reflected; by using the time step format combined with the source term vector and interface numerical flux to update the flow field state, stable and efficient numerical simulation of open and full flow in complex underground spaces can be achieved.

[0116] To explain in detail the principles of the technical solution of this application, the overall process of this application will be described below with reference to some specific embodiments. It is easy to understand that the following is an explanation of the technical principles of this application and should not be regarded as a limitation of this application.

[0117] Please see Figure 2 , Figure 2 This is a schematic diagram of the overall process of a two-dimensional numerical simulation method for open-circuit flow in underground space provided in an embodiment of this application, as shown below. Figure 2 As shown, Figure 2 This application demonstrates the complete lifecycle of a two-dimensional numerical simulation method for open-circuit flow in underground space, as provided in this embodiment: starting with reading the unstructured mesh and initializing properties, a time loop is entered. Within each time step, static water reconstruction, pressure / wave velocity smoothing calculation, HLL flux solution, and source term update are performed sequentially, forming a closed loop. For example... Figure 2 As shown, the specific implementation process of a two-dimensional numerical simulation method for open-circuit flow in underground space provided in this application embodiment includes the following steps S201-S206:

[0118] Step S201: Construct a two-dimensional unstructured mesh for the underground space. The two-dimensional unstructured mesh includes node coordinates and element topological relationships, and assigns a floor elevation to each node or element. and roof elevation The properties are then used to spatially discretize the subsequent governing equations based on this two-dimensional unstructured mesh, and then numerically solve them.

[0119] Specifically, mesh construction and attribute definition are as follows:

[0120] The embodiments of this application first construct a geometric model of the underground space. Unlike the surface model, the underground model must be closed.

[0121] (1) Data loading: Use meshio to read the .msh file generated by Gmsh.

[0122] (2) Core attributes, taking the unit as an example:

[0123] 1) self.z_bottom: Elevation of the unit's bottom plate (simulating ground undulations);

[0124] 2) self.z_crown: Elevation of the unit top cover (simulating the top of the tunnel). The default value is the maximum value (9999.0) representing the open area. For underground areas, it can be set in batches according to the area ID using the set_crown_by_tag method.

[0125] 3) boundary_edges: Identifies boundary edges and is used to set inflow, outflow, or solid wall boundaries.

[0126] It should be noted that, in the embodiments of this application, the elevation of the base plate is mainly assigned to the unit. and roof elevation The attributes are explained. Additionally, a base elevation can be assigned to the node. and roof elevation If a value is assigned to a node, the weight from the center of a unit to the node is calculated using the inverse distance interpolation algorithm, and then the unit value (base elevation, top elevation) is calculated based on the weight. The embodiments of this application will not be described in detail here.

[0127] Step S202: Initialize the flow field state variables of the two-dimensional unstructured mesh. This assigns parameters such as water depth and flow velocity to a two-dimensional unstructured grid to reflect the water flow state. Because of the water depth, and For unit width flow;

[0128] Step S203, Define the pressure term With equivalent wave velocity The calculation method;

[0129] Specifically, based on the current water depth Elevation of the roof Relationship, calculate equivalent wave velocity and pressure items Among them, pressure item With equivalent wave velocity Satisfying consistency ;

[0130] Among them, equivalent wave velocity and pressure items The calculation methods are divided into two categories: piecewise or smooth transition. Specifically:

[0131] when (Open flow) use shallow water wave velocity and hydrostatic pressure ;

[0132] when (At full flow) speed of sound and additional pressure ;

[0133] Specifically, to ensure a unified solution for open flow and pressurized flow (full flow), the pressure term... The pressure law is calculated using the Preissmann slit equivalent equation of state to ensure consistency with wave velocity, where the pressure term... satisfy:

[0134] when At that time, pressure item Using hydrostatic pressure, specifically ;

[0135] when At that time, pressure item Additional pressure is used, specifically: ;

[0136] Among them, the flow channel height , It represents the acceleration due to gravity.

[0137] In the transition zone, a normalized weight-based approach is adopted. Smoothing is applied to suppress numerical oscillations during flow regime transitions. The transition region ranges from h ∈ [ ), 1.05×( Normalized weights =(h- )) / (0.05× The pressure in the transition zone is P(h) = (1-w)× + w× .

[0138] Optionally, segmented equivalent wave velocity It can be represented as:

[0139] ;

[0140] in, The numerical sound velocity (which can be a "reduced wave velocity" much smaller than the actual water hammer wave velocity, in order to obtain an acceptable time step while maintaining the pressurized characteristics).

[0141] It should be noted that step S203 is to define the pressure term. With equivalent wave velocity The calculation method can be pre-set; that is, step S203 can be set before step S201, step S202, or step S204, and is not limited to the flow order of step S203. It can be understood that the pressure item defined in step S203... With equivalent wave velocity The calculation method is the same as the method used in step S204 to calculate the pressure term and the equivalent wave velocity.

[0142] Step S204: Based on the finite volume method, the left and right states of the mesh cell interface are reconstructed to obtain the reconstructed water depth. The calculation method in step S203 is called to calculate the pressure term and equivalent wave velocity based on the reconstructed water depth. Finally, the pressure term, equivalent wave velocity and the flow field state variables updated based on the reconstructed water depth are input into the HLL Riemann solver to calculate the numerical flux at the interface.

[0143] Before calculating the numerical flux at the interface, the interface state is reconstructed using a hydrostatic reconstruction method that considers the bottleneck effect of the top cover. Then, the numerical flux at the interface is calculated based on the reconstructed data. Specifically, first, the maximum elevation of the bottom plate on the left and right sides of the interface is taken. At the same time, the minimum elevation of the top cover on the left and right sides of the interface is taken. Then, based on the reconstructed bottom elevation, the reconstructed water depth on both sides of the interface is calculated. Next, based on the reconstructed top elevation and reconstructed water depth, the equivalent wave velocity and pressure terms are calculated using the method described in step S203. At the same time, the flow field state variables in step S202 are updated based on the reconstructed water depth. Finally, the updated flow field state variables and the equivalent wave velocity and pressure terms calculated based on the reconstructed water depth are substituted into the HLL Riemann solver to calculate the interface numerical flux of each element.

[0144] It should be noted that when calculating the pressure term and equivalent wave velocity based on the reconstructed water depth, and when updating the flow field state variables based on the reconstructed water depth, the reconstructed water depth will be used as a reference. As the original formula Perform the calculation.

[0145] in, This refers to the elevation of the base plate of the unit on the left side of the interface. This refers to the elevation of the base plate of the unit on the right side of the interface. This refers to the elevation of the top cover of the unit on the left side of the interface. The elevation of the top cover of the unit on the right side of the interface. This represents the original water depth (water depth value before reconstruction) of the left / right cells of the interface. This represents the original base plate elevation of the left / right side units of the interface.

[0146] Step S205: Calculate the source term vector containing the terrain slope source term and the friction source term, and use the time stepping scheme to solve for the flow field state variables at the next time step.

[0147] In this grid cell, there are multiple interfaces. By summing the numerical fluxes of the multiple interfaces of a cell, the total outflow flux of that grid cell can be obtained.

[0148] This application also includes a flux scaling step: calculating the total outflow flux corresponding to each cell. If the total outflow flux of a cell causes the water depth of that cell to be negative, the total outflow flux of that cell is adaptively reduced to ensure the positive definiteness of the water depth.

[0149] Step S206: Repeat steps S204 to S205 until the simulation end time is reached, and output the simulation results.

[0150] The purpose of this application is to provide a two-dimensional simulation method for open-circuit flow in underground space that is computationally efficient and numerically stable. The core technical solution of this application is as follows:

[0151] (1) Data structure: Based on the traditional hydrodynamic grid, the following was added (Cover Elevation) Attribute. Different underground areas (such as low-lying drainage ditches and tall subway stations) are assigned different cover heights using physical tags.

[0152] (2) Physical Model: Based on the Preissmann slot generalization concept, an equivalent state equation is introduced at the flux calculation level of two-dimensional underground space. Instead of directly modifying the geometric width, a consistent pressure law is used. With wave speed To achieve a unified solution for the full flow, making the pressure increment in the pressurized region correlate with the sound velocity. Matching.

[0153] (3) Pressure Law With wave speed Supports two implementation types: segmented and smooth transition. While ensuring... Under the premise that, A transition band width parameter is introduced nearby to reduce numerical oscillations at the switching point.

[0154] (4) Adaptation of numerical format: A well-balanced design was adopted. When calculating the numerical flux of the interface, not only the elevation of the base plate was reconstructed, but also the elevation of the top cover was reconstructed (taking the minimum value), so as to correctly simulate the flow resistance at the point of sudden contraction of cross section (such as gate, variable diameter pipe).

[0155] The numerical model and governing equations in this embodiment are as follows:

[0156] (1) Governing Equations: This application adopts the conservation-type two-dimensional shallow water equations (2D Shallow Water Equations) as the governing equations for the two-dimensional unstructured grid, and introduces the Preissmann slit theory to modify the pressure term, so as to uniformly describe open channel flow and pressurized flow (full flow). The vector form of the conservation-type two-dimensional shallow water equations is defined as:

[0157] ;

[0158] in, The vector of conserved variables (i.e., flow field state variables). For numerical flux, Let be the source term vector, and t be the time variable. Conserved variable vector. Numerical flux and source term vector The definition is as follows:

[0159] ;

[0160] ;

[0161] ;

[0162] in, For water depth; and For unit width flow; Let x be the velocity component of the fluid in the x-direction; Let be the velocity component of the fluid in the y-direction; For stress terms; For terrain slope source term; For friction source term; This is the roughness coefficient; It is the acceleration due to gravity; This is the elevation of the base plate.

[0163] (2) Unified Equation of State for Underground Flow: In order to handle pressurized flow in underground space, this application improves the pressure equation. and wave speed The calculation method. Let the elevation of the roof be... The elevation of the base plate is The flow channel height is This application employs the Preissmann slit equivalent state equation and supports the introduction of transition variables. ( Smoothly connect the open flow area and the full flow area (pressurized area).

[0164] To ensure a unified solution for open channel and pressurized flow, the Preissmann slit equivalent equation of state is adopted, making the pressure law consistent with the wave velocity. It is understandable that the pressure term... With the equivalent wave velocity Satisfying consistency .

[0165] 1) Correcting hydrostatic pressure :

[0166] Specifically, to ensure a unified solution for open flow and pressurized flow (full flow), the pressure term... The pressure law is calculated using the Preissmann slit equivalent equation of state to ensure consistency with wave velocity, where the pressure term... satisfy:

[0167] when At that time, pressure item Using hydrostatic pressure, specifically ;

[0168] when At that time, pressure item Additional pressure is used, specifically: ;

[0169] Among them, the flow channel height , It represents the acceleration due to gravity.

[0170] In the transition zone, a normalized weight-based approach is adopted. Smoothing is applied to suppress numerical oscillations during flow regime transitions. The transition region ranges from h ∈ [ ), 1.05×( Normalized weights =(h- )) / (0.05× The pressure in the transition zone is P(h) = (1-w)× + w× .

[0171] When further suppression of switching oscillations (i.e., numerical oscillations near the peak) is required, it is possible to... Introduce transition weights nearby For segmented form and Perform continuous processing.

[0172] 2) Equivalent wave velocity :

[0173] Segmented equivalent wave velocity It can be represented as:

[0174] ;

[0175] in, The numerical sound velocity (which can be a "reduced wave velocity" much smaller than the actual water hammer wave velocity, in order to obtain an acceptable time step while maintaining the pressurized characteristics).

[0176] Please see Figure 3 , Figure 3 This is a schematic diagram illustrating the principle of a smooth transition mechanism for full-flow under normal conditions provided in this application embodiment. Figure 3 As shown, Figure 3 Showing pressure With water depth The curve showing the change. In Near the orange-yellow area, the curve transitions from a quadratic parabola (hydrostatic pressure) to an approximately linear increase (contribution of the pressurized overpressure term), and the slope of this linear segment is... Consistent with wave velocity models, thus maintaining consistency and suppressing switching oscillations.

[0177] (3) Numerical discretization scheme:

[0178] This application employs the finite volume method (FVM) based on unstructured meshes. For any control unit... The discrete equation is:

[0179] ;

[0180] in, The vector of conserved variables within element i The rate of change over time, where i is the number of the current control unit and j is the number of a control unit adjacent to unit i; Let i be the set of all adjacent interfaces of element i; Let i be the area of ​​cell i; For the interface numerical flux; The interface normal unit vector; The length of the interface; For terrain slope source term; This is the friction source term.

[0181] 1) HLL Riemann Solver: Interface Numerical Flux The HLL format was used for calculation, which has good shock wave capture capability and interface numerical flux. The calculation formula is:

[0182] ;

[0183] in, and The states on the left side of the interface are respectively The corresponding original flux vector and the state on the right side of the interface The corresponding original flux vector; The normal velocity on the left side of the interface; The normal velocity on the right side of the interface; and These are the wave velocity estimates on the left and right sides of the interface, respectively. and The calculation formula is as follows:

[0184] ;

[0185] ;

[0186] in, The wave speed is shown on the left side of the interface. The wave speed is shown on the right side of the interface. Let be the unit vector normal to the interface.

[0187] 3) Well-balanced Reconstruction and Source Term Balancing: To eliminate spurious flow caused by the slope of the bottom plate, a well-balanced reconstruction method is used to reconstruct the bottom plate, top cover, and water depth. Specifically:

[0188] Base plate reconstruction: Maximum elevation of the base plate on the left and right sides of the interface. It is used to handle terrain steps.

[0189] Top cover reconstruction: ;

[0190] Reconstruct water depth at the interface : ;

[0191] in, This refers to the elevation of the base plate of the unit on the left side of the interface. This refers to the elevation of the base plate of the unit on the right side of the interface. This refers to the elevation of the top cover of the unit on the left side of the interface. The elevation of the top cover of the unit on the right side of the interface. This represents the original water depth (water depth value before reconstruction) of the left / right cells of the interface. This represents the original base plate elevation of the left / right side units of the interface.

[0192] This ensures that the flow obstruction effect is correctly generated when the fluid enters the low-profile pipe. Understandably, when the water flows from the high-cover area to the low-cover area, the effective cover height at the interface is smaller, which limits the flow rate and generates the correct backflow effect. This is the key to the simulation of underground variable cross-section tunnels.

[0193] Please see Figure 4 , Figure 4 This is a schematic diagram of a static water remodeling method considering the roof elevation, provided in an embodiment of this application. Figure 4 This demonstrates the refactoring logic at the unit interface. For example... Figure 4 As shown, the left unit's top cover is high, and the right unit's top cover is low. During reconstruction, the effective flow height at the interface is limited by the lower top cover on the right (Bottleneck Effect), which is crucial for accurately calculating the flow rate into the confined space. Please refer to... Figure 5 , Figure 5 This is a schematic diagram illustrating the principle of interface flux exchange using a finite volume method, as provided in an embodiment of this application. Figure 5 As shown, Figure 5 This demonstrates two adjacent control volumes in the finite volume method. They exchange numerical flux through a public interface. The geometric relationship, where the normal vector Pointing outwards, state variables ( Defined at the center of the unit.

[0194] 4) HLL flux and source terms:

[0195] Flux calculation: The HLL (Harten-Lax-van Leer) format is used to automatically capture shock waves (such as hydraulic jumps) and rarefaction waves. See also... Figure 6 , Figure 6 This is a schematic diagram of the wave structure of an HLL approximate Riemann solver provided in an embodiment of this application, as shown below. Figure 6 As shown, Figure 6 This demonstrates the wave system structure of the HLL (Harten-Lax-van Leer) approximate Riemann solver, a model that assumes two waves and Starting from the interface, the spatiotemporal region is divided into three constant states: the left state Right side state and the average state in the middle In subsonic flow ( In this case, along shaft (i.e.) The numerical flux of the characteristic line is from Decide.

[0196] Source term balance: Since static water reconstruction is used, the pressure flux uses the reconstructed water depth. The pressure difference caused by reconstruction needs to be compensated in the source term to ensure accurate balance in static water (i.e., the velocity remains 0 when the water surface is flat).

[0197] 5) Time Stepping and Positivity Preservation: An explicit Euler scheme is used for time advancement, and flux scaling is introduced into the iterative time method. Specifically, the net outflow flux of each cell is calculated; if this results in a negative water depth, a flux scaling factor is introduced. The outflow flux of this unit is adaptively reduced to ensure the positive definiteness of the water depth. The calculation formula for the adaptive reduction is as follows:

[0198] ;

[0199] ;

[0200] in, The numerical flux before correction. This is the corrected numerical flux. For correction factor, This is the sum of the outflow flux from each unit. For time step.

[0201] This ensures that, at the wet-dry stage, numerical errors will not lead to the extraction of more water than actually present, thus guaranteeing the water depth. This greatly improves the robustness of the model.

[0202] Please see Figure 7 , Figure 7 This is a schematic diagram of the flooding calculation results for a U-shaped tunnel provided in an embodiment of this application, as shown below. Figure 7 As shown, Figure 7 The image shows a U-shaped tunnel divided into a triangular unstructured grid, depicting the tunnel gradually being completely submerged as water flows in from the left.

[0203] Please see Figure 8 , Figure 8 This is a schematic diagram illustrating the water head changes at different locations during the submersion of a U-shaped tunnel, as provided in an embodiment of this application. Figure 8 As shown, Figure 8 Showing Figure 7 The changes in water head at the inlet (left side), middle, and outlet (right side) locations during the tunnel flooding process are shown by... Figure 8As can be seen, the simulation results are smooth and there are no oscillations that do not conform to the laws of physics, which can meet the requirements of high-precision underground space inundation simulation.

[0204] It should be noted that this embodiment is only a brief illustrative description of the overall process of a two-dimensional numerical simulation method for open flow in underground space. Detailed descriptions of each step can be found in the relevant content of the foregoing embodiments, and will not be repeated here. It is understood that this application does not impose any limitations on this.

[0205] In summary, the two-dimensional numerical simulation method for open-water flooding in underground spaces provided in this application is a method for simulating flood inundation processes in underground spaces such as subways, tunnels, and underground utility tunnels. It relates to the fields of water conservancy engineering and urban safety and disaster prevention technology, specifically belonging to the field of hydrodynamic numerical simulation and disaster prevention and mitigation technology. This application constructs an unstructured mesh model containing the elevation attributes of the bottom slab and the top cover, which can adapt to the irregular geometry of complex underground spaces and accurately describe the spatial constraints and boundary conditions of underground structures. It uses the finite volume method to discretize the numerical flux at the interface of the two-dimensional shallow water equations, ensuring the conservation of the flow control equations and improving the computational stability and accuracy of large-scale flow simulation. It introduces the Preissmann slot equivalent state equation for pressurized-open channel unification and adopts a consistent pressure law. With wave speed This method can uniformly describe the flow regimes of free surface flow and pressurized flow, and can naturally complete the transition between open and full flow without switching models. In flux calculation, it employs a Riemann solver combined with hydrostatic reconstruction and source term balancing, which can accurately capture the bottleneck effect of the overhead cover, suppress numerical oscillations at abrupt flow changes, and ensure consistency between hydrostatic balance and flux calculation. In time progression, it uses a non-negativity-preserving flux scaling mechanism and semi-implicit friction handling to ensure non-negative water depth during simulation, avoid numerical anomalies during wet-dry transitions, improve algorithm robustness, and enhance the stability and efficiency of time progression while maintaining computational accuracy. It is suitable for long-term, large-scale flood evolution simulation. This application can stably simulate the transition between open and full flow, the bottleneck effect of the overhead cover, and the wet-dry transition process of flood intrusion under complex underground geometries, and is applicable to scenarios such as subway station-tunnel systems, underground utility tunnels, and underground parking garages.

[0206] Please see Figure 9 This application also provides a two-dimensional numerical simulation device 900 for open-circuit flow in underground space, which can implement the above-mentioned method. The device includes the following modules:

[0207] The unstructured mesh construction module 901 is used to construct a two-dimensional unstructured mesh of the target underground space and assign the current bottom elevation and the current top elevation to each mesh cell in the two-dimensional unstructured mesh.

[0208] The flow field state variable initialization module 902 is used to initialize the current flow field state variables of the two-dimensional unstructured grid; wherein, the current flow field state variables include the current water depth and the current unit width flow rate;

[0209] The unit interface state reconstruction module 903 is used to reconstruct the left and right states of the interface of each grid unit by combining the current bottom plate elevation and the current top cover elevation of each grid unit, determine the interface reconstruction state quantity, and determine the reconstruction water depth based on the interface reconstruction state quantity; wherein, the interface reconstruction state quantity includes the reconstructed bottom plate elevation and the reconstructed top cover elevation.

[0210] The flow regime and state update module 904 is used to calculate the equivalent wave velocity and pressure terms based on the reconstructed water depth and the interface reconstructed state variables, and update the current flow field state variables based on the reconstructed water depth.

[0211] The interface numerical flux calculation module 905 is used to calculate the interface numerical flux of each grid cell using the HLL Riemann solver, based on the equivalent wave velocity, the pressure term, and the updated current flow field state variables.

[0212] The source term vector calculation module 906 is used to calculate a source term vector containing topographic slope source term and friction source term based on the current base elevation and the current flow field state variable of each grid cell.

[0213] The flow field state variable update module 907 is used to calculate the flow field state variables at the next moment using a time step format, based on the source term vector and the interface numerical flux of each grid cell, so as to complete the numerical simulation at the current moment.

[0214] It is understood that the content of the above method embodiments is applicable to the present device embodiments. The specific functions implemented by the present device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0215] This application also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-described method. This electronic device can be any smart terminal, including tablet computers, in-vehicle computers, etc.

[0216] It is understood that the content of the above method embodiments is applicable to this device embodiment. The specific functions implemented by this device embodiment are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0217] Please see Figure 10 , Figure 10 The hardware structure of an electronic device according to another embodiment is illustrated. The electronic device includes:

[0218] The processor 1001 can be implemented using a general-purpose CPU (Central Processing Unit), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this application.

[0219] The memory 1002 can be implemented as a read-only memory (ROM), static storage device, dynamic storage device, or random access memory (RAM). The memory 1002 can store the operating system and other applications. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 1002 and is called and executed by the processor 1001 using the methods described in the embodiments of this application.

[0220] Input / output interface 1003 is used to implement information input and output;

[0221] The communication interface 1004 is used to enable communication and interaction between this device and other devices. Communication can be achieved through wired means (such as USB, network cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.).

[0222] Bus 1005 transmits information between various components of the device (e.g., processor 1001, memory 1002, input / output interface 1003, and communication interface 1004);

[0223] The processor 1001, memory 1002, input / output interface 1003 and communication interface 1004 are connected to each other within the device via bus 1005.

[0224] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0225] It is understood that the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0226] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0227] It is understood that the content of the above method embodiments is applicable to the embodiments of this program product. The specific functions implemented by the embodiments of this program product are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0228] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0229] This application provides a two-dimensional numerical simulation method and related equipment for open and full flow in underground spaces. By constructing a two-dimensional unstructured grid of the underground space and assigning elevations to the bottom plate and top cover, it can adapt to complex underground space geometries and improve model applicability. By reconstructing the left and right states of the grid cell interfaces, it can reasonably determine the reconstructed water depth, equivalent wave velocity, and pressure terms, ensuring the physical rationality and numerical stability of the interface variables. The use of the HLL Riemann solver to calculate the interface numerical flux can improve the flux calculation accuracy and adapt to the complex flow regimes of open and full flow transitions. By calculating the topographic slope source term and friction source term separately, it can accurately reflect the combined effect of gravity and resistance in underground space flow. By using a time-stepping scheme combined with the source term vector and interface numerical flux to update the flow field state, it can achieve stable and efficient numerical simulation of open and full flow in complex underground spaces.

[0230] The embodiments described in this application are for the purpose of more clearly illustrating the technical solutions of the embodiments of this application, and do not constitute a limitation on the technical solutions provided by the embodiments of this application. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by the embodiments of this application are also applicable to similar technical problems.

[0231] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of this application, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0232] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0233] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or suitable combinations thereof.

[0234] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0235] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0236] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of the units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0237] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0238] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0239] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes multiple instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing programs, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0240] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. A two-dimensional numerical simulation method for open-circuit flow in underground spaces, characterized in that, The method includes the following steps: Construct a two-dimensional unstructured grid of the target underground space, and assign the current floor elevation and the current roof elevation to each grid cell in the two-dimensional unstructured grid; Initialize the current flow field state variables of the two-dimensional unstructured mesh; wherein, the current flow field state variables include the current water depth and the current unit width flow rate; By combining the current bottom elevation and the current top elevation of each grid cell, the left and right states of the interface of each grid cell are reconstructed to determine the interface reconstruction state quantity, and the reconstruction water depth is determined based on the interface reconstruction state quantity; wherein, the interface reconstruction state quantity includes the reconstructed bottom elevation and the reconstructed top elevation. Based on the reconstructed water depth and the interface reconstructed state variables, the equivalent wave velocity and pressure terms are calculated, and the current flow field state variables are updated based on the reconstructed water depth. Using the HLL Riemann solver, the interface numerical flux of each grid cell is calculated based on the equivalent wave velocity, the pressure term, and the updated current flow field state variables. Based on the current base elevation and the current flow field state variables of each grid cell, calculate the source term vector containing the terrain slope source term and the friction source term; Using a time-stepping format, the flow field state variables at the next moment are calculated based on the source term vector and the interface numerical flux of each grid cell, so as to complete the numerical simulation at the current moment. The process of reconstructing the left and right states of the interface of each grid cell by combining the current bottom elevation and the current top elevation of each grid cell, determining the interface reconstruction state quantity, and determining the reconstruction water depth based on the interface reconstruction state quantity includes: Based on the current base plate elevation of each grid cell, determine the maximum value of the base plate elevation on the left and right sides of the interface of each grid cell to obtain the reconstructed base plate elevation; Based on the current top cover elevation of each grid cell, the minimum top cover elevation on the left and right sides of the interface of each grid cell is determined to obtain the reconstructed top cover elevation. Based on the reconstructed base plate elevation, the reconstructed water depth on the left and right sides of the interface of each grid cell is calculated.

2. The method according to claim 1, characterized in that, After calculating the flow field state variables at the next time step using the time-stepping format, based on the source term vector and the interface numerical flux of each grid cell, to complete the numerical simulation at the current time step, the method further includes: If the current moment of the numerical simulation has not reached the preset simulation end time, the flow field state variable at the next moment is used as the current flow field state variable. The process returns to the steps of combining the current bottom plate elevation and the current top cover elevation of each grid cell to reconstruct the left and right states of the interface of each grid cell, determining the interface reconstruction state quantity, and determining the reconstruction water depth based on the interface reconstruction state quantity, until the current moment of the numerical simulation reaches the preset simulation end time, and the simulation results are output.

3. The method according to claim 1, characterized in that, The calculation of the equivalent wave velocity and pressure term based on the reconstructed water depth and the interface reconstructed state quantity includes: Calculate the elevation difference between the reconstructed base plate elevation and the reconstructed top cover elevation; If the reconstructed water depth is less than or equal to the elevation difference, then the water body is determined to be in the open flow stage, the shallow water wave velocity is taken as the equivalent wave velocity of the open flow stage, and the hydrostatic pressure is taken as the pressure term of the open flow stage. If the reconstructed water depth is greater than the elevation difference, the water body is determined to be in the full flow stage, the sound speed is taken as the equivalent wave speed of the full flow stage, and the additional pressure is taken as the pressure term of the full flow stage. When the reconstructed water depth is within the preset critical range between the open flow stage and the full flow stage, the water body is determined to be in the transition stage. The shallow water wave velocity and the sound velocity are smoothly weighted based on normalized weights to obtain the equivalent wave velocity of the transition stage. The static pressure and the additional pressure are smoothly weighted based on normalized weights to obtain the pressure term of the transition stage.

4. The method according to claim 1, characterized in that, The step of calculating the source term vector, which includes the terrain slope source term and the friction source term, based on the current base elevation and the current flow field state variables of each grid cell, includes: The terrain slope source term is calculated based on the current base elevation of each of the grid cells; The friction source term is calculated based on the current water depth and the current unit width flow rate of each of the grid cells; Based on the terrain slope source term and the friction source term, the source term vector is constructed.

5. The method according to claim 1, characterized in that, The method further includes: Calculate the total outflow flux of each grid cell based on the several interface numerical fluxes corresponding to each grid cell. Based on the total outflow flux of each grid cell, determine whether the water depth value of each grid cell is negative at the next time step; If it is determined that there is a target grid cell with a negative water depth value in the next time step, then flux scaling technology is used to adaptively reduce the total outflow flux of the target grid cell.

6. A two-dimensional numerical simulation device for open flow in underground space, characterized in that, The device includes the following modules: An unstructured mesh construction module is used to construct a two-dimensional unstructured mesh of the target underground space and assign the current bottom elevation and the current top elevation to each mesh cell in the two-dimensional unstructured mesh; The flow field state variable initialization module is used to initialize the current flow field state variables of the two-dimensional unstructured mesh; wherein, the current flow field state variables include the current water depth and the current unit width flow rate; The unit interface state reconstruction module is used to reconstruct the left and right states of the interface of each grid unit by combining the current bottom plate elevation and the current top cover elevation of each grid unit, determine the interface reconstruction state quantity, and determine the reconstruction water depth based on the interface reconstruction state quantity; wherein, the interface reconstruction state quantity includes the reconstructed bottom plate elevation and the reconstructed top cover elevation. The flow regime and state update module is used to calculate the equivalent wave velocity and pressure terms based on the reconstructed water depth and the interface reconstructed state variables, and update the current flow field state variables based on the reconstructed water depth. The interface numerical flux calculation module is used to calculate the interface numerical flux of each grid cell using the HLL Riemann solver, based on the equivalent wave velocity, the pressure term, and the updated current flow field state variables. The source term vector calculation module is used to calculate a source term vector containing topographic slope source term and friction source term based on the current base elevation and the current flow field state variables of each grid cell. The flow field state variable update module is used to calculate the flow field state variables at the next moment using a time step format, based on the source term vector and the interface numerical flux of each grid cell, so as to complete the numerical simulation at the current moment. The unit interface state reconstruction module is specifically used for: Based on the current base plate elevation of each grid cell, determine the maximum value of the base plate elevation on the left and right sides of the interface of each grid cell to obtain the reconstructed base plate elevation; Based on the current top cover elevation of each grid cell, the minimum top cover elevation on the left and right sides of the interface of each grid cell is determined to obtain the reconstructed top cover elevation. Based on the reconstructed base plate elevation, the reconstructed water depth on the left and right sides of the interface of each grid cell is calculated.

7. An electronic device, characterized in that, The electronic device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the method according to any one of claims 1 to 5.

8. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 5.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 5.

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