One-dimensional and two-dimensional hydrodynamic coupling and solving method based on virtual water volume storage unit

Abstract

The invention discloses a one-two-dimensional hydrodynamic coupling and solving method based on a virtual water volume storage unit. The method comprises the following steps: S1, accurately identifying a two-dimensional coupling interface by introducing a flow velocity gradient screening judgment method; s2, on the basis of determining a two-dimensional coupling interface, embedding the virtual water volume storage unit into the two-dimensional coupling interface, and constructing an initialization condition of the virtual water volume storage unit by using a CHM hydrological model; s3, calculating the water flow flux at a two-dimensional coupling interface by using an HLL solver; s4, updating the state of the virtual water volume storage unit by using a time integration method in combination with the water flow volume and the confluence item at the two-dimensional coupling interface; and S5, on the basis of a one-dimensional semi-implicit iteration method and a two-dimensional full implicit method, constructing a one-dimensional and two-dimensional hydrodynamic coupling hybrid solving strategy. The method has the advantages that high-precision coupling and efficient solution of the one-dimensional model and the two-dimensional model are achieved, and the accuracy and the calculation efficiency of hydrodynamic simulation of the complex river and lake system are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of hydrological forecasting, and particularly relates to a one-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 control and disaster reduction, water resources management and ecological restoration. Traditional methods usually simplify the river channel as a one-dimensional model (such as Manning's formula), and regard lakes or floodplains as two-dimensional models (such as shallow water equations), and the two are coupled through interface flux transfer. However, the differences in physical scale, numerical discretization and time step between the one-dimensional and two-dimensional models lead to challenges such as mass-momentum conservation imbalance and insufficient numerical stability in the coupling process, directly affecting the accuracy and reliability of key business scenarios such as runoff evolution simulation and flood inundation analysis.

[0003] First, existing methods mostly use direct interpolation or average flux matching to achieve one-two dimensional data transfer, ignoring the hydraulic continuity characteristics at the interface, resulting in non-strict conservation of mass and momentum fluxes. In long-term simulation, error accumulation causes abnormal fluctuations in water levels, especially when the wet-dry boundary changes dynamically, false mass sources / sinks are likely to occur. Secondly, most existing one-two dimensional hydrodynamic coupling models solve the full implicit sparse linear equations globally, and the complexity of solving the global matrix is large, making it difficult to scale to large-scale grids. Summary of the Invention

[0004] The purpose of the present invention is to provide a one-two dimensional hydrodynamic coupling and solution method based on a virtual water storage unit, so as to solve the foregoing problems existing in the prior art.

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

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

[0007] S1. Accurately identify the one-two dimensional coupling interface by introducing a judgment method for screening velocity gradients;

[0008] S2. On the basis of determining the one-two dimensional coupling interface, embed the virtual water storage unit into the one-two dimensional coupling interface, and use the CHM hydrological model to construct the initial conditions of the virtual water storage unit;

[0009] S3. Use the HLL solver to calculate the water flux at the one-two dimensional coupling interface;

[0010] S4. Combine the water flux and source / sink terms at the one-two dimensional coupling interface, and use 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, construct a hybrid solution strategy for one-two dimensional hydrodynamic coupling.

[0012] Preferably, the judgment method for velocity gradient screening realizes accurate screening of the one-two dimensional coupling interface by calculating the spatial gradient of the velocity; the formula is

[0013]

[0014] where Γ is the coupling interface; is the spatial gradient; x, y are two-dimensional grids; u thresh is the velocity threshold.

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

[0016]

[0017] where h is the water depth; w is the water body width; u is the velocity; q is the flow rate; the superscript 0 represents the initial moment; 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 volume storage unit.

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

[0019]

[0020] where F * is the water flow flux at the interface; F L and F R are the flow rate fluxes in the one-dimensional region and the two-dimensional region respectively; U R and U L are the state variables in the one-dimensional region and the two-dimensional region; s L and s R are the characteristic wave speeds on the left and right sides respectively;

[0021]

[0022] where 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 region and the two-dimensional region respectively; g is the acceleration due to gravity; s L and s R are the characteristic wave speeds in the one-dimensional region and the two-dimensional region respectively.

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

[0024]

[0025] where and are the states of the virtual water volume 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 volume storage unit; is the sum of all water fluxes passing through the boundary of the virtual water volume storage unit; is the water flux passing through the k-th boundary; B k is the length or area of the k-th boundary; S is the source-sink term.

[0026] Preferably, step S5 is specifically as follows: divide the one-dimensional river system and the two-dimensional lake system into different calculation regions, use the semi-implicit iterative method for iterative solution in the one-dimensional river region, and use the fully implicit method to solve by constructing a sparse matrix in the two-dimensional lake region.

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

[0028] Figure 1 is the flow chart of the method in the embodiment of the present invention;

[0029] Figure 2 is a schematic diagram of the position of the virtual water volume storage unit (black grid in the left box) and the simulation effect of the flow space (right) in the embodiment of the present invention;

[0030] Figure 3 is a comparison diagram of the simulation effects of the discharge at Datong Station in the embodiment of the present invention. Detailed Embodiments

[0031] To make the objectives, technical solutions and advantages of the present invention more clear and understandable, 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 merely used to explain the present invention and are not intended to limit the present invention.

[0032] Embodiment 1

[0033] In this embodiment, in view of the technical defects of an existing two-dimensional hydrodynamic coupling method in terms of interface flux conservation, numerical stability and large-scale calculation efficiency, a one-two dimensional hydrodynamic coupling and solution method based on a virtual water storage unit (VSU) is provided. By embedding a VSU as a flux buffer at the one-two dimensional hydrodynamic coupling interface and combining with the HLL Riemann solver to accurately calculate the cross-scale flux, mass-momentum strict conservation is ensured. 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-two dimensional hydrodynamic fast solution algorithm. The method of the present invention breaks through the bottleneck of traditional coupling methods in terms of conservation and stability, provides a high-precision and high-efficiency technical solution for applications such as flood risk assessment and hydro-hydraulic process simulation, and can improve the hydrodynamic calculation accuracy and solution efficiency of the model in complex systems such as rivers, lakes and floodplains. As Figure 1 shown, the method mainly includes the following parts:

[0034] I. Identify the one-two dimensional coupling interface

[0035] In the process of coupling a one-dimensional and a two-dimensional hydrodynamic model, the position of the coupling interface is crucial. For this reason, a judgment method of velocity gradient screening is introduced to accurately identify the coupling interface. The principle is that generally, the area where the velocity changes violently indicates that the water flow is blocked and the flow field no longer satisfies the one-dimensional assumption. By calculating the spatial gradient of the velocity the accurate screening of the coupling interface is realized, which satisfies the following conditions:

[0036]

[0037] where Γ is the coupling interface; is the spatial gradient; x, y are two-dimensional grids; u thresh is the velocity threshold.

[0038] II. Embed and initialize the virtual water storage unit (VSU)

[0039] Based on the determination of the coupling interface Γ, the VSU element is further embedded into the coupling interface. The VSU element is a virtual computing unit, whose role is to act as a buffer between one - dimensional and two - dimensional, and avoid discontinuity at the interface by adjusting water flow and water level changes. To this end, based on the water depth and flow rate 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, and the initialization conditions of the VSU element are constructed as follows:

[0040]

[0041] Among them, h is the water depth; w is the water body width; u is the flow velocity; q is the flow rate; the superscript 0 represents the initial moment; 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 volume storage unit. In this way, the state of the VSU element can smoothly transition in the initial stage, thus providing a stable initial point for subsequent calculations.

[0042] III. Calculate the water flow flux at the interface

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

[0044]

[0045] Among them, F * is the water flow 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 in the one - dimensional and two - dimensional regions; s L and s R are the characteristic wave speeds on the left and right sides respectively.

[0046]

[0047] Among them, u L and u R are the flow velocities (m / s) in the one - dimensional region and the two - dimensional region respectively; h L and h R are the water depths (m) in the one - dimensional region and the two - dimensional region respectively; g is the acceleration due to gravity, approximately 9.81m / 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 in combination with the flux and source term. 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 solution 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 two-dimensional complex 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, and is able to handle more complex two-dimensional water systems. In this method, the water level update equations for all grids are combined, and the water level update results are obtained by solving a large set of linear equations. The main advantage of the fully implicit method is that it has high computational accuracy and numerical stability, and is suitable for handling complex river, lake and floodplain systems. However, due to its global solution characteristics, the amount of calculation increases significantly with the increase of the grid size, and the computational cost is high for large-scale areas.

[0057] To fully combine the advantages of the two methods, the hybrid solution method divides the one-dimensional river system and the two-dimensional lake system into different computational regions, and uses the semi-implicit iterative method and the fully implicit method 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-lake region, and the VSU element is adopted at the one-two dimensional coupling interface to ensure hydraulic continuity and consistency (from the first part to the fourth part). This method can take into account both computational efficiency and accuracy, and avoid the limitations of a single method in complex hydrodynamic systems.

[0058] Embodiment 2

[0059] In this embodiment, a river-lake confluence system in the main stream of the Yangtze River and the Poyang Lake area and the nearby area are selected, and a one-two dimensional coupled hydrodynamic model is constructed under the framework of the CHM hydrological model. The computational area is about 62,000 km 2 , with a spatial resolution of 1000 m; the selected research period is the flood season (from June to October) in 2020 to verify the performance of the method proposed by the present invention in flood routing simulation.

[0060] I. Identifying the one-two dimensional coupling interface

[0061] In the process of coupling the one-dimensional and two-dimensional flow models, the position of the coupling interface is crucial. For this reason, a judgment method of velocity gradient screening is introduced to accurately identify the coupling interface. Its principle is that generally, the area where the velocity changes violently indicates that the water flow is blocked and the flow field no longer satisfies the one-dimensional assumption. By calculating the spatial gradient of the velocity the accurate screening of the coupling interface is realized, and it satisfies the following conditions:

[0062]

[0063] In the formula, where Γ is the coupling interface; is the spatial gradient; x, y are two-dimensional grids; u thresh is the velocity threshold. The velocity gradient threshold u is determined by historical flood event inversion thresh = 0.3 m 3 / s.

[0064] II. 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 Hukou ([[]] Figure 2 ), which involves a total of 6 1000 m × 1000 m grids (the black highlighted area within the left frame). The measured initial flow rate of 50,000 m 3 / s and 27,078 m 3 / s, calculate the initial fields of water depth and velocity by the CHM hydrological model, and construct the initialization conditions of the VSU unit accordingly:

[0066]

[0067] In the formula, h is the water depth; w is the water body width; u is the velocity; q is the discharge; the superscript 0 represents the initial moment; 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 volume storage unit.

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

[0069] Use the HLL solver to estimate the interface flux. Taking the initial moment as an example, calculate the water flux F * as follows:

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

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

[0072] 3) Calculate the characteristic wave speed:

[0073]

[0074] In the formula, s L and s R are the characteristic wave speeds on the left and right sides respectively.

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

[0076]

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

[0078] IV. Update the VSU state variables

[0079] On the basis of calculating the water flux using the HLL solver, combined with the flux and source-sink terms, use the time integration method to update the state of the VSU unit. Select the time step Δt = 10 to update the state variables of the VSU:

[0080]

[0081] In the formula, 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 represents the volume or area of the VSU unit; represents the sum of all water fluxes passing through the boundaries of the VSU unit; is the water flux through the k-th boundary, Γ k is the length or area of the k-th boundary; S is the source-sink term.

[0082] Substituting the initial conditions, the

[0083] V. Constructing a Hybrid Solution Strategy

[0084] Based on the one-dimensional semi-implicit iterative method and the two-dimensional implicit method, the present invention constructs a hybrid solution method for one-two dimensional hydrodynamic coupling.

[0085] The semi-implicit iterative method is an explicit or semi-implicit method commonly used in one-dimensional hydrodynamic simulations. By iteratively solving the water level changes at each grid point, it explicitly processes the water levels of the surrounding grids and implicitly processes the water level at the central point. In this embodiment, the central implicit iterative method is used to update the water level of the one-dimensional system. The fully implicit method solves large-scale hydrodynamic equations by constructing a sparse matrix and can handle more complex two-dimensional water body systems. In this embodiment, the conjugate gradient method is used to solve the sparse matrix to update the water level of the two-dimensional system.

[0086] The application of this method in the Yangtze River-Poyang Lake river-lake system has significantly improved the calculation efficiency and simulation accuracy. The simulation accuracy verification shows that the coefficient of determination of the improved model has increased from 0.87 of the traditional method to 0.89( Figure 3 ), the prediction error of the flood peak water level has decreased from 0.51 m to 0.49 m, the error reduction is 2.7%, and the water balance error has been optimized from 1.8% to 1.5%, indicating that the flux conservation has been significantly enhanced. In the comparison of typical cross-sections, the error of the flood peak propagation time in the main stream of the Yangtze River has decreased from 25 minutes to 12 minutes, proving that this method can accurately depict complex hydraulic processes.

[0087] In terms of calculation efficiency, through the optimization of the hybrid solution strategy, the total model calculation time has been shortened from 14.2 hours of the traditional fully implicit method to 8.7 hours, the efficiency has increased by 38.7%, and the memory occupancy has decreased by 42.6% (from 38.5 GB to 22.1 GB), greatly saving computational resources.

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

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

[0090] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also fall within the protection scope of the present invention.

Claims

1. A one-two dimensional hydrodynamic coupling and solution method based on a virtual water volume storage unit, characterized in that: It includes the following steps: S1. Accurately identify the one-dimensional and two-dimensional coupling interface by introducing a judgment method for screening the velocity gradient; S2. On the basis of determining the one-dimensional and two-dimensional coupling interface, embed the virtual water volume storage unit into the one-dimensional and two-dimensional coupling interface, and use the CHM hydrological model to construct the initial conditions of the virtual water volume storage unit; S3. Use the HLL solver to calculate the water flux at the one-dimensional and two-dimensional coupling interface; S4. Combine the water flux and the source and sink terms at the one-dimensional and two-dimensional coupling interface, and use the time integration method to update the state of the virtual water volume storage unit; S5. Based on the one-dimensional semi-implicit iterative method and the two-dimensional fully implicit method, construct a hybrid solution strategy for one-dimensional and two-dimensional hydrodynamic coupling.

2. The one-two dimensional hydrodynamic coupling and solution method based on a virtual water storage unit according to claim 1, characterized in that: The judgment method for screening the velocity gradient realizes the accurate screening of the one-dimensional and two-dimensional coupling interface by calculating the spatial gradient of the velocity; the formula is where Γ is the coupling interface; is the spatial gradient; x, y are two-dimensional grids; u thresh is the flow velocity threshold.

3. The one- and two-dimensional hydrodynamic coupling and solution method based on a virtual water volume storage unit according to claim 2, wherein: In step S2, based on the water depth and flow rate in the one-dimensional and two-dimensional hydrodynamic models, use the CHM hydrological model to calculate the initial fields of the water depth and velocity to construct the initial conditions of the virtual water volume storage unit. The formula is where h is the water depth; w is the water body width; u is the velocity; q is the flow rate; the superscript 0 represents the initial moment; 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 volume storage unit.

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

5. The one-two dimensional hydrodynamic coupling and solution method based on a virtual water volume storage unit according to claim 4, wherein: The state update formula of the virtual water volume storage unit is wherein, 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 boundary of the virtual water storage unit; is the water flux passing through the k-th boundary; B k is the length or area of the k-th boundary; S is the source-sink term.

6. The one-two dimensional hydrodynamic coupling and solution method based on a virtual water volume storage unit according to claim 5, wherein: Specifically, step S5 divides the one-dimensional river system and the two-dimensional lake system into different calculation regions, uses the semi-implicit iterative method for iterative solution in the one-dimensional river region, and uses the fully implicit method to solve by constructing a sparse matrix in the two-dimensional lake region.

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