A one- and two-dimensional hydrodynamic coupling and solution method based on virtual water storage unit

Abstract

The present invention discloses a one- and two-dimensional hydrodynamic coupling and solution method based on a virtual water storage unit, comprising: S1, accurately identifying the one- and two-dimensional coupling interface by introducing a judgment method for flow gradient screening; S2, embedding the virtual water storage unit into the one- and two-dimensional coupling interface based on the determination of the one- and two-dimensional coupling interface, and constructing the initialization conditions of the virtual water storage unit using the CHM hydrological model; S3, calculating the water flux at the one- and two-dimensional coupling interface using the HLL solver; S4, combining the water flux and the source-sink term at the one- and two-dimensional coupling interface to update the state of the virtual water storage unit using the time integration method; S5, constructing a hybrid solution strategy for one- and two-dimensional hydrodynamic coupling based on a one-dimensional semi-implicit iterative method and a two-dimensional fully implicit method. The advantages are: achieving high-precision coupling and efficient solution of one- and two-dimensional models, and improving the accuracy and computational efficiency of hydrodynamic simulation of complex river and lake systems.

Description

Technical Field

[0001] The present invention relates to the technical field of hydrological forecasting, and in particular to a one- and two-dimensional hydrodynamic coupling and solution method based on a virtual water storage unit. Background Art

[0002] Hydrodynamic simulation of rivers, lakes, and floodplains is an important technical means for flood prevention and disaster reduction, water resources management, and ecological restoration. Traditional methods usually simplify the river channel into a one-dimensional model (such as the Manning formula) and treat the lake or floodplain as a two-dimensional model (such as the shallow water equation), and couple the two through interfacial flux transfer. However, the differences in physical scale, numerical discretization, and time step between one-dimensional and two-dimensional models lead to challenges such as mass-momentum conservation imbalance and insufficient numerical stability in the coupling process, which directly affects the accuracy and reliability of key business scenarios such as runoff evolution simulation and flood inundation analysis.

[0003] First, existing methods often use direct interpolation or average flux matching to transfer one- and two-dimensional data, ignoring the hydraulic continuity characteristics at the interface, resulting in non-strict conservation of mass and momentum fluxes. In long-term simulations, accumulated errors can cause abnormal water level fluctuations, especially when the dry-wet boundary dynamically changes, which can easily generate false mass sources and sinks. Second, existing one- and two-dimensional hydrodynamic coupling models often use a fully implicit sparse linear equation system for global solution. This results in high complexity in solving the global matrix and is difficult to scale to large-scale grids. Summary of the Invention

[0004] The object of the present invention is to provide a one- and two-dimensional hydrodynamic coupling and solution method based on a virtual water storage unit, thereby solving the above-mentioned problems existing in the prior art.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0006] A one- and two-dimensional hydrodynamic coupling and solution method based on a virtual water storage unit includes the following steps:

[0007] S1. Accurately identify one- and two-dimensional coupling interfaces by introducing a velocity gradient screening method;

[0008] S2. On the basis of determining the one- and two-dimensional coupling interface, the virtual water storage unit is embedded in the one- and two-dimensional coupling interface, and the initialization conditions of the virtual water storage unit are constructed using the CHM hydrological model;

[0009] S3, using the HLL solver to calculate the water flux at the one- and two-dimensional coupling interface;

[0010] S4, combining the water flux and sink-source terms at the one- and two-dimensional coupling interface, and using the time integration method to update the state of the virtual water storage unit;

[0011] S5. Based on the one-dimensional semi-implicit iterative method and the two-dimensional fully implicit method, a hybrid solution strategy for one- and two-dimensional hydrodynamic coupling is constructed.

[0012] Preferably, the flow velocity gradient screening method calculates the spatial gradient of the flow velocity to achieve accurate screening of the one- and two-dimensional coupling interface; the formula is,

[0013]

[0014] Where, Γ is the coupling interface; is the spatial gradient; x, y is a two-dimensional grid; u thresh is the flow rate threshold.

[0015] Preferably, in step S2, based on the water depth and flow in the one-dimensional and two-dimensional hydrodynamic models, the CHM hydrological model is used to calculate the initial field of water depth and flow velocity to construct the initialization condition of the virtual water storage unit. The formula is:

[0016]

[0017] Where h is the water depth; w is the width of the water body; u is the flow velocity; q is the flow rate; the superscript 0 indicates the initial time; the subscript 1D indicates the one-dimensional hydrodynamic model; the subscript 2D indicates the two-dimensional hydrodynamic model; and the subscript v indicates the virtual water storage unit.

[0018] Preferably, the HLL solver estimates the water flux at the one- and two-dimensional coupling interface by calculating the solution to the Riemann problem; the formula is,

[0019]

[0020] Among them, F * is the water flux at the interface; F L and F R are the flow fluxes in the one-dimensional region and the two-dimensional region respectively; U R and U L are the state variables of one-dimensional and two-dimensional regions; s L and s R are the characteristic wave velocities on the left and right sides, respectively;

[0021]

[0022] Among them, u L and u R are the flow velocities in the one-dimensional region and the two-dimensional region respectively; h L and h R are the water depths in the one-dimensional and two-dimensional regions respectively; g is the acceleration due to gravity; s L and s R are the characteristic wave velocities in the one-dimensional and two-dimensional regions, respectively.

[0023] Preferably, the state update formula of the virtual water storage unit is:

[0024]

[0025] in, and are the states of the virtual water storage unit at the next time step n+1 and the current time step n respectively; Δt is the time step; A v is the volume or area of ​​the virtual water storage unit; is the sum of all water fluxes passing through the boundaries of the virtual water storage unit; is the water flux through the kth boundary; B k is the length or area of ​​the kth boundary; S is the source and sink term.

[0026] Preferably, step S5 is specifically to divide the one-dimensional river system and the two-dimensional lake system into different calculation areas, use a semi-implicit iterative method to iteratively solve in the one-dimensional river area, and use a fully implicit method to solve in the two-dimensional lake area by constructing a sparse matrix.

[0027] The beneficial effects of the present invention are: 1. The method of the present invention realizes high-precision coupling and efficient solution of one- and two-dimensional models, thereby improving the accuracy and computational efficiency of hydrodynamic simulation of complex river and lake systems, and providing reliable technical support for applications such as flood disaster warning and eco-hydrological process simulation. 2. The method of the present invention improves the coupling accuracy of the hydrodynamic model in complex water systems to a certain extent by introducing a virtual water storage unit (VSU), overcomes the problem of insufficient accuracy of the coupling interface of traditional coupling methods, ensures the accurate transfer of water flow between different regions, and improves the overall accuracy of the hydrodynamic model. 3. The method of the present invention introduces a coupling solution strategy of a semi-implicit iterative method and a fully implicit method, integrating the characteristics of high solution efficiency of the semi-implicit iterative method and strong stability and high accuracy of the fully implicit method, thereby significantly improving the computational efficiency of the hydrodynamic model in complex water systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0029] Figure 2 Schematic diagram of the location of the virtual water storage unit (black grid in the left frame) and the flow space simulation effect (right) in an embodiment of the present invention;

[0030] Figure 3 This is a comparison chart of the flow simulation effect of Datong Station in an embodiment of the present invention. DETAILED DESCRIPTION

[0031] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0032] Example 1

[0033] In this embodiment, in response to the technical deficiencies of existing one- and two-dimensional hydrodynamic coupling methods in terms of interface flux conservation, numerical stability, and large-scale computing efficiency, a one- and two-dimensional hydrodynamic coupling and solution method based on a virtual water storage unit (VSU) is provided. The method embeds the VSU as a flux buffer at the one- and two-dimensional hydrodynamic coupling interface, and combines the HLL Riemann solver to accurately calculate the cross-scale flux, ensuring strict conservation of mass-momentum. On this basis, an explicit fast solver is used in the one-dimensional subdomain, and an implicit sparse matrix technology is used in the two-dimensional subdomain to construct a one- and two-dimensional hydrodynamic fast solution algorithm. The method of the present invention breaks through the bottleneck of traditional coupling methods in conservation and stability, and provides a high-precision and high-efficiency technical solution for applications such as flood risk assessment and hydrological and hydrodynamic process simulation. It can improve the hydrodynamic calculation accuracy and solution efficiency of the model in complex systems such as rivers, lakes, and floodplains. Figure 1 As shown, this method mainly includes the following parts:

[0034] 1. Identifying 1D and 2D Coupling Interfaces

[0035] In the process of coupling one-dimensional and two-dimensional hydrodynamic models, the location of the coupling interface is crucial. To this end, a velocity gradient screening method is introduced to accurately identify the coupling interface. The principle is that, generally speaking, areas with drastic velocity changes indicate that the water flow is obstructed and the flow field no longer meets the one-dimensional assumption. By calculating the spatial gradient of the velocity To achieve accurate screening of coupling interfaces, the following conditions must be met:

[0036]

[0037] Where, Γ is the coupling interface; is the spatial gradient; x, y is a two-dimensional grid; u thresh is the flow rate threshold.

[0038] 2. Embedding and Initializing the Virtual Water Storage Unit (VSU)

[0039] After determining the coupling interface Γ, the VSU unit is further embedded into the coupling interface. The VSU unit is a virtual computing unit that acts as a buffer between the one-dimensional and two-dimensional models, avoiding discontinuities at the interface by adjusting water flow and water level changes. To this end, based on the water depth and flow in the one-dimensional and two-dimensional models, the CHM hydrological model is used to calculate the initial fields of water depth and flow velocity, thereby constructing the initial conditions of the VSU unit:

[0040]

[0041] Where h is the water depth, w is the width of the water body, u is the flow velocity, q is the flow rate, the superscript 0 indicates the initial time, the subscript 1D indicates the one-dimensional hydrodynamic model, the subscript 2D indicates the two-dimensional hydrodynamic model, and the subscript v indicates the virtual water storage unit. This allows the state of the VSU to transition smoothly during the initial phase, providing a stable starting point for subsequent calculations.

[0042] 3. Calculate the water flux at the interface

[0043] The core function of the VSU is to achieve dynamic coupling between one-dimensional and two-dimensional models through accurate water flux calculations. To ensure the accuracy of the flux calculations, the HLL (Harten-Lax-van Leer) solver is used. This method is widely used in the numerical solution of cross-regional discontinuous flows and can effectively handle the flow transition between one-dimensional and two-dimensional. The HLL solver estimates the interfacial flux by calculating the solution to the Riemann problem. Specifically, the HLL flux calculation formula is as follows:

[0044]

[0045] Among them, F * is the water flux at the interface; F L and F R are the flow fluxes in the one-dimensional region and the two-dimensional region respectively; U R and U L are the state variables of one-dimensional and two-dimensional regions; s L and s R are the characteristic wave velocities on the left and right sides, respectively.

[0046]

[0047] Among them, u L and u R are the flow velocities in the one-dimensional region and the two-dimensional region (m / s); h L and h R are the water depths (m) in the one-dimensional and two-dimensional regions respectively; g is the acceleration due to gravity, which is approximately 9.81 m / s 2 ;s L and sR are the characteristic wave velocities (m / s) in the one-dimensional and two-dimensional regions, respectively.

[0048] The HLL solver can handle water flow states under different flow conditions and adjust the flux calculation in real time according to changes in flow velocity and water depth to ensure physical rationality and calculation accuracy.

[0049] 4. VSU status variable update

[0050] Based on the water flux calculated by the HLL solver, the state of the VSU unit is updated using the time integration method combined with the flux and source terms. The specific update formula is:

[0051]

[0052] in, and are the states of the virtual water storage unit at the next time step n+1 and the current time step n respectively; Δt is the time step; A v is the volume or area of ​​the virtual water storage unit; is the sum of all water fluxes passing through the boundaries of the virtual water storage unit; is the water flux through the kth boundary; B k is the length or area of ​​the kth boundary; S is the source and sink term.

[0053] 5. Building a Hybrid Solving Strategy

[0054] Based on the one-dimensional semi-implicit iterative method and the two-dimensional fully implicit method, a hybrid solution method for one- and two-dimensional hydrodynamic coupling is constructed.

[0055] The semi-implicit iterative method is an explicit or semi-implicit method commonly used in one-dimensional hydrodynamic simulations. Its main feature is that it iteratively solves the water level changes at each grid point, explicitly processes the water levels of the surrounding grids, and implicitly processes the water level at the center point. This method is simple to calculate and has high computational efficiency, but it has poor adaptability to complex two-dimensional water bodies, especially at the junction of rivers and lakes or in areas with complex hydraulic connections, where convergence problems often occur.

[0056] The fully implicit method solves the hydrodynamic equations by constructing a sparse matrix, enabling it to handle more complex two-dimensional water systems. In this method, the water level update equations for all grid cells are combined, and the water level update is obtained by solving a large system of linear equations. The main advantage of the fully implicit method is its high computational accuracy and numerical stability, making it suitable for complex river, lake, and floodplain systems. However, due to its global solution requirements, the computational complexity increases significantly with increasing grid size, making it computationally expensive for large-scale regions.

[0057] To fully combine the advantages of both methods, the hybrid solution method divides the one-dimensional river system and the two-dimensional lake system into different computational regions, using semi-implicit iterative methods and fully implicit methods for solution, respectively. Specifically, the semi-implicit iterative method is used for iterative solution in the one-dimensional river region, while the fully implicit method is used to solve the large sparse matrix in the two-dimensional river and lake region. VSU units are used at the one-dimensional coupling interface to ensure hydraulic continuity and consistency (Parts 1 to 4). This method can balance computational efficiency and accuracy, avoiding the limitations of a single method in complex hydrodynamic systems.

[0058] Example 2

[0059] In this example, the river-lake confluence system of the Yangtze River mainstream and Poyang Lake and its surrounding areas were selected to construct a one- and two-dimensional coupled hydrodynamic model under the CHM hydrological model framework. The calculation area is approximately 62,000 km. 2 , spatial resolution 1000m; the research period was selected as the flood season of 2020 (June-October) to verify the performance of the method proposed in this invention in flood evolution simulation.

[0060] 1. Identifying 1D and 2D Coupling Interfaces

[0061] In the process of coupling one-dimensional and two-dimensional water flow models, the location of the coupling interface is crucial. To this end, a velocity gradient screening method is introduced to accurately identify the coupling interface. The principle is that, generally speaking, areas with drastic velocity changes indicate that the water flow is obstructed and the flow field no longer meets the one-dimensional assumption. By calculating the spatial gradient of the velocity To achieve accurate screening of coupling interfaces, the following conditions must be met:

[0062]

[0063] Where, Γ is the coupling interface; is the spatial gradient; x, y is a two-dimensional grid; u thresh is the velocity threshold. The velocity gradient threshold u is determined by inversion of historical flood events. thresh =0.3m 3 / s.

[0064] 2. Embedding and Initializing the Virtual Water Storage Unit (VSU)

[0065] On the basis of determining the coupling interface Γ, the VSU unit is further embedded into the coupling interface. An arc-shaped coupling interface is formed 3.2 km west of the lake mouth ( Figure 2 ), involving a total of 6 1000m×1000m grids (black highlighted area in the left frame), and the measured initial flow of 50000m was obtained from the hydrological station 3 / s and 27078m 3 / s, the initial fields of water depth and velocity are calculated by the CHM hydrological model, and the initial conditions of the VSU unit are constructed based on this:

[0066]

[0067] Where h is the water depth; w is the width of the water body; u is the flow velocity; q is the flow rate; the superscript 0 represents the initial time; the subscript 1D represents the one-dimensional hydrodynamic model; the subscript 2D represents the two-dimensional hydrodynamic model; and the subscript v represents the virtual water storage unit.

[0068] 3. Calculate the water flux at the interface

[0069] The HLL solver is used to estimate the interface flux. Taking the initial moment as an example, the water flux F is calculated. * as follows:

[0070] 1) One-dimensional river: h L =20.1m,u L =2.1m / s

[0071] 2) Two-dimensional lake area: h R =19.2m,u R =0.8m / s

[0072] 3) Calculation of characteristic wave velocity:

[0073]

[0074] Where s L and s R are the characteristic wave velocities on the left and right sides, respectively.

[0075] 4) On this basis, calculate the water flow rate F * :

[0076]

[0077] Where, F * is the water flux at the interface.

[0078] 4. VSU status variable update

[0079] Based on the water flux calculated by the HLL solver, the state of the VSU unit is updated using the time integration method, combining the flux and source and sink terms. Select the time step Δt = 10 and update the state variables of the VSU:

[0080]

[0081] Where, and are the states of the VSU unit at the next time step n+1 and the current time step n respectively; Δt is the time step; A v Indicates the volume or area of ​​the VSU unit; It represents the sum of all water fluxes passing through the VSU unit boundary; is the water flux through the kth boundary, Γ k is the length or area of ​​the kth boundary; S is the source and sink term.

[0082] Substituting the initial conditions, we get the next step length

[0083] 5. Building a Hybrid Solving Strategy

[0084] The present invention is based on a one-dimensional semi-implicit iterative method and a two-dimensional implicit method to construct a hybrid solution method for one- and two-dimensional hydrodynamic coupling.

[0085] The semi-implicit iteration method is an explicit or semi-implicit method commonly used in one-dimensional hydrodynamic simulations. It iteratively solves for the water level changes at each grid point, explicitly processing the water levels of surrounding grids while implicitly processing the water level at the center point. This example uses the central implicit iteration method to update the water level of a one-dimensional system. Fully implicit methods solve large-scale hydrodynamic equations by constructing a sparse matrix, capable of handling more complex two-dimensional water systems. This example uses the conjugate gradient method to solve the sparse matrix and update the water level of the two-dimensional system.

[0086] The application of this method to the Yangtze River-Poyang Lake river-lake system has significantly improved computational efficiency and simulation accuracy. Simulation accuracy verification shows that the deterministic coefficient of the improved model has increased from 0.87 of the traditional method to 0.89 ( Figure 3 ), the peak water level prediction error decreased from 0.51 to 0.49 meters, a 2.7% reduction, and the water balance error was optimized from 1.8 to 1.5%, demonstrating a significant improvement in flux conservation. A comparison of typical cross-sections showed a reduction in the propagation time error of the Yangtze River flood peak from 25 minutes to 12 minutes, demonstrating that this method can accurately depict complex hydraulic processes.

[0087] In terms of computational efficiency, through the optimization of the hybrid solution strategy, the total model time was shortened from 14.2 hours of the traditional fully implicit method to 8.7 hours, the efficiency was improved by 38.7%, and the memory usage was reduced by 42.6% (from 38.5GB to 22.1GB), which greatly saved computing resources.

[0088] By adopting the above technical solution disclosed in the present invention, the following beneficial effects are obtained:

[0089] The present invention provides a one- and two-dimensional hydrodynamic coupling and solution method for a hydrological model based on a virtual water storage unit, which realizes high-precision coupling and efficient solution of a one- and two-dimensional model, thereby improving the accuracy and computational efficiency of hydrodynamic simulation of complex river and lake systems, and providing reliable technical support for applications such as flood disaster warning and eco-hydrological process simulation. By introducing a virtual water storage unit (VSU), the method of the present invention improves the coupling accuracy of the hydrodynamic model in a complex water system to a certain extent, overcomes the problem of insufficient accuracy of the coupling interface of the traditional coupling method, ensures the accurate transfer of water flow between different regions, and improves the overall accuracy of the hydrodynamic model. By introducing a coupling solution strategy of a semi-implicit iterative method and a fully implicit method, the method of the present invention combines the characteristics of high solution efficiency of the semi-implicit iterative method and strong stability and high accuracy of the fully implicit method, significantly improving the computational efficiency of the hydrodynamic model in a complex water system.

[0090] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A one- and two-dimensional hydrodynamic coupling and solution method based on a virtual water storage unit, characterized by: The following steps are included: S1. Accurately identify one- and two-dimensional coupling interfaces by introducing a velocity gradient screening method; S2. On the basis of determining the one- and two-dimensional coupling interface, the virtual water storage unit is embedded in the one- and two-dimensional coupling interface, and the initialization conditions of the virtual water storage unit are constructed using the CHM hydrological model; In step S2, based on the water depth and flow in the one-dimensional and two-dimensional hydrodynamic models, the CHM hydrological model is used to calculate the initial fields of water depth and flow velocity to construct the initialization conditions of the virtual water storage unit. The formula is: Where h is the water depth; w is the width of the water body; u is the flow velocity; q is the flow rate; the superscript 0 represents the initial time; the subscript 1D represents the one-dimensional hydrodynamic model; the subscript 2D represents the two-dimensional hydrodynamic model; the subscript v represents the virtual water storage unit; S3, using the HLL solver to calculate the water flux at the one- and two-dimensional coupling interface; S4, combining the water flux and sink-source terms at the one- and two-dimensional coupling interface, and using the time integration method to update the state of the virtual water storage unit; The state update formula of the virtual water storage unit is: in, and are the states of the virtual water storage unit at the next time step n+1 and the current time step n respectively; Δt is the time step; A v is the volume or area of ​​the virtual water storage unit; is the sum of all water fluxes passing through the boundaries of the virtual water storage unit; is the water flux through the kth boundary; B k is the length or area of ​​the kth boundary; S is the source and sink term; S5. Based on the one-dimensional semi-implicit iterative method and the two-dimensional fully implicit method, a hybrid solution strategy for one- and two-dimensional hydrodynamic coupling is constructed.

2. The one- and two-dimensional hydrodynamic coupling and solution method based on a virtual water storage unit according to claim 1 is characterized in that: The velocity gradient screening method calculates the spatial gradient of the velocity to achieve accurate screening of the one- and two-dimensional coupling interface; the formula is, Where, Γ is the coupling interface; is the spatial gradient; x, y is a two-dimensional grid; u thresh is the flow rate threshold.

3. The one- and two-dimensional hydrodynamic coupling and solution method based on a virtual water storage unit according to claim 1 is characterized in that: The HLL solver estimates the water flux at the one- and two-dimensional coupled interface by calculating the solution to the Riemann problem; the formula is, Among them, F * is the water flux at the interface; F L and F R are the flow fluxes in the one-dimensional region and the two-dimensional region respectively; U R and U L are the state variables of one-dimensional and two-dimensional regions; s L and s R are the characteristic wave velocities on the left and right sides, respectively; Among them, u L and u R are the flow velocities in the one-dimensional region and the two-dimensional region respectively; h L and h R are the water depths in the one-dimensional and two-dimensional regions respectively; g is the acceleration due to gravity; s L and s R are the characteristic wave velocities in the one-dimensional and two-dimensional regions, respectively.

4. The one- and two-dimensional hydrodynamic coupling and solution method based on a virtual water storage unit according to claim 1 is characterized in that: Specifically, step S5 divides the one-dimensional river system and the two-dimensional lake system into different calculation areas, uses a semi-implicit iterative method to iteratively solve in the one-dimensional river area, and uses a fully implicit method to solve in the two-dimensional lake area by constructing a sparse matrix.

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