Dimension reduction method for river hydrodynamic simulation

Abstract

The invention discloses a dimension reduction method for river hydrodynamic simulation. The method comprises the following specific steps: collecting data information; constructing a planar two-dimensional hydrodynamic model based on a shallow water equation; the influence of curvature-induced secondary flow is added into a shallow water equation in a dispersion stress term mode; further introducing the contribution of the density gradient to the angular momentum into an angular momentum conservation equation; coupling a convection-diffusion equation considering dispersion stress, and constructing a planar two-dimensional hydrodynamic force-substance transport finite element model; and calculating a water depth average flow field and secondary flow intensity. According to the method, the three-dimensional effect of the secondary flow jointly driven by streamline bending and density difference is added into the two-dimensional equation in a dispersion stress term mode, the shallow water equation and the transport equation are solved in a coupling mode, the simulation precision of the two-dimensional model is greatly improved, and rapid and high-precision simulation of long-term evolution of the landform of a large river system is achieved.

Description

Technical Field

[0001] This invention relates to the field of computational hydraulics, specifically to a dimensionality reduction method for river hydrodynamic simulation. Background Technology

[0002] Numerical simulation is an important tool for studying river network flow structure, pollutant diffusion, sediment transport, and riverbed evolution. 3D CFD (Computational Fluid Dynamics) uses Reynolds-averaged Navier-Stokes equations for modeling and solving, or employs advanced methods such as large eddy simulation and separated eddy simulation, to accurately calculate flow fields and describe material transport characteristics under complex boundary conditions. However, the cumbersome and complex nature of 3D CFD simulations of moving bed processes, coupled with the high computational resource consumption, limits the long-term application of large-scale in-situ riverbed morphology dynamics simulations in engineering practice. Against this backdrop, two-dimensional hydrodynamic and geomorphological models based on SWEs (Shallow Water Equations) have become the standard tool for predicting riverbed evolution due to their computational efficiency. However, because 2D SWE models use depth averaging, their main limitation in complex river sections such as bends and confluences is their inability to explicitly consider three-dimensional effects, such as secondary flows that play a crucial role in pollutant and sediment transport, often resulting in insufficient accuracy.

[0003] For a long time, two-dimensional hydrodynamic and geomorphological dynamic models have been improved in various ways to account for the effects of curvature-induced secondary flows. The most common and simplest method is to adjust the direction of bed sediment transport based on the local streamline curvature within the horizontal plane. A more advanced method is to add appropriate dispersion terms to the SWEs, which depend on the intensity of the helical flow. Dispersion stresses can be calculated from the local streamline curvature or by solving the transport equations of the helical flow angular momentum. This method has clear physical meaning, does not significantly increase the computational workload, and is suitable for complex bends in natural river channels. However, these methods can only simulate curvature-driven secondary flows and cannot account for additional secondary flows caused by density gradients (such as uneven distribution of temperature or suspended sediment concentration).

[0004] Furthermore, while existing models can characterize the phase lag in the development and attenuation of secondary flows in river bends and reduce sensitivity to planar and / or topographic singularities, they have not yet addressed the coupling effect of density gradients and curvature-induced secondary flows. Although the additional mixing caused by secondary flows can be reflected by adding dispersion terms to the transport-diffusion equations, current depth-averaged models still lack a unified description of the interaction between density gradients and bend circulation, which is particularly critical in the simulation of suspended sediment transport and density currents. Therefore, there is an urgent need to develop a dimensionality-reduction simulation method for secondary flows that can comprehensively consider the combined driving forces of streamline curvature and density gradients. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a dimensionality reduction method for river hydrodynamic simulation. This method uses a two-dimensional finite element model to solve the coupled shallow water equations and convection-diffusion equations. By adding appropriate dispersion terms to the control equations, the interaction between density gradient and bend circulation can be fully considered, thereby realizing the representation of three-dimensional flow structure effects in the two-dimensional hydrodynamic model and improving simulation accuracy while ensuring computational efficiency.

[0006] To address the above technical problems, according to one aspect of the present invention, a dimensionality reduction method for river hydrodynamic simulation is provided, comprising: Data collection; A two-dimensional planar hydrodynamic model based on the shallow water equation is constructed. A dispersed stress term is added to the shallow water equation to obtain the modified shallow water equation. The influence of curvature-induced secondary flow is added to the shallow water equation through the dispersed stress term. Introducing the contribution of the density gradient to angular momentum into the angular momentum conservation equation, we obtain the angular momentum equation based on the influence of the density gradient. By coupling the convection-diffusion equations considering dispersed stress, a two-dimensional planar hydrodynamic-mass transport finite element model is constructed; the depth-averaged flow field and secondary flow intensity are calculated.

[0007] Furthermore, the data collection specifically includes: The parameter information of the river channel is obtained from the watershed hydrological stations, remote sensing monitoring systems and historical measurement data. The parameter information includes, but is not limited to, hydrological parameters, hydrodynamic parameters and topographic parameters.

[0008] Furthermore, to account for the contribution of the bend circulation to the momentum equation, a dispersed stress term is added to the shallow water equation, resulting in a modified shallow water equation. The revised shallow water equation is expressed as follows: , , , in, Represents the mass derivative. This represents the x-axis component of the velocity integrated along the water depth. This represents the equivalent water depth, which is the volume of water per unit area. This represents the Reynolds turbulent stress in the x-direction on a horizontal plane. The horizontal coordinate axis represents the direction parallel to the main channel of the river. This represents the shear component of the Reynolds turbulent stress on a horizontal surface. The horizontal coordinate axis represents the direction perpendicular to the main channel of the river. This represents the kinetic energy of the velocity fluctuations along the x-axis, which is the result of the vertical integral. , The vertical coordinate axis represents the direction along the water depth, with the riverbed at z=0 and the water surface at z=Y. This represents the difference between the actual value of the velocity component along the x-axis and the average value of the water depth. , This represents the distribution of instantaneous flow velocity along the vertical direction in the x-direction. This represents the average velocity across the water in the x-direction. , Both represent the xy-direction velocity fluctuation cocorrelation terms of the vertical integral. Due to symmetry, therefore... , This represents the difference between the actual value of the velocity component along the y-axis and the average value of the water depth. , This represents the distribution of instantaneous flow velocity along the vertical direction in the y-direction. This represents the average velocity across the water in the y-direction. The x-axis component represents the shear stress on the bed surface. This indicates the density of water. Represents gravitational acceleration. This represents the free surface elevation relative to the horizontal datum plane. This represents the y-axis component of the velocity integrated along the water depth. This represents the Reynolds turbulent stress in the y-direction on a horizontal plane. This represents the kinetic energy of the pulsating velocity along the y-axis, which is the result of the vertical integral. ; The y-axis component represents the shear stress on the bed surface. Representing the wetted area fraction, it is a storage coefficient related to water depth. , Indicates time.

[0009] The steps involve constructing a two-dimensional planar hydrodynamic model based on shallow water equations, adding a dispersed stress term to the shallow water equations to obtain a modified shallow water equation, and adding the influence of curvature-induced secondary flow into the shallow water equations through the dispersed stress term.

[0010] Using a local reference frame, where s represents the longitudinal direction (mainstream direction) and n represents the transverse direction; and assuming a simple vertical distribution of velocity in the s and n directions, and further assuming that the velocity component in the mainstream direction follows a power-law distribution, a closed-form expression for the dispersed stress term is obtained through coordinate transformation: , , , in, This indicates the magnitude of the average flow velocity at water depth. ; The specific calculation formulas for the three components of the dispersed stress represented in the local coordinate system are as follows: , , , in, Indicates friction parameters; The streamline radius represents the average water depth. R is positive when the water flow bends clockwise and negative otherwise. This represents the dimensionless transverse velocity at the free surface; Calculated using the eddy transport method.

[0011] in, The calculation steps are as follows: First, the flow vorticity transport equation on the horizontal plane is: , in, Indicates the flow direction component of vorticity; Indicates a production item; Represents dissipation terms; Assuming a linear distribution of spanwise velocity, the streamwise component of vorticity is expressed as: , in, Indicates angular velocity, Indicates the lateral velocity at the free surface; Assuming a slow change in water depth, the flow vorticity transport equations on the horizontal surface are directly applied. Rewritten as: , in, The coefficient representing the production item; Denotes the von Kármán constant. ; Represents the coefficient of the dissipation term; The dimensionless transverse velocity at the free surface can be expressed as: .

[0012] Furthermore, the contribution of the density gradient to angular momentum is introduced into the angular momentum conservation equation. The angular momentum conservation equation is enhanced by adding an additional production term. The interaction between the density gradient and the bend circulation and its net effect on the momentum equation are considered in terms of the relative directions of curvature and density gradient, resulting in an angular momentum equation based on the influence of the density gradient. The expression for the angular momentum equation considering the density gradient is as follows: , in, All of these represent empirical coefficients. Indicates friction parameters, This indicates the lateral coordinate pointing to the inside of the curve; Based on the assumption that the water depth changes slowly, the angular momentum equation considering the density gradient is modified as follows: .

[0013] Furthermore, to account for the lateral net flux of sediment resulting from the combined effects of the non-uniform distribution of suspended sediment vertical concentration and the lateral spiral flow, the interpretation is enhanced by adding an appropriate dispersion stress term to the original convection-diffusion equation. The convection-diffusion equation describes the temporal and spatial evolution of the vertical average concentration of tracers and substances moving with the flow. The original convection-diffusion equation is expressed as: , in, Indicates concentration; Represents a two-dimensional divergence operator; The convection term represents the mass flux. A two-dimensional gradient representing concentration; Indicates turbulent diffusion. , Indicates turbulent eddy viscosity. This represents the Schmitt number, which is typically taken as 1. Represents the anisotropic diffusivity tensor, used to explain dispersion in the longitudinal and transverse directions; Indicates the source term; Given the vertical distribution of spanwise velocity and concentration distribution, the dispersion stress is calculated by integrating the difference between the depth-dependent flux and the average depth value; the convection-diffusion equation describing suspended mass transport is rewritten as: , in, This represents the vertical integral diffuse flux component in the x-direction. This represents the vertical integral diffuse flux component in the y-direction. Indicates erosion flux, Indicates deposition flux; , , in, This represents the difference between the vertical distribution of suspended sediment concentration C(z) and the depth-average concentration C. This represents the flow component of the dispersed stress in the local reference frame. This represents the spanwise component of the dispersed stress in the local reference frame; Assuming the longitudinal velocity component follows a power-law distribution in the vertical direction and the lateral velocity component follows a linear distribution with a mean of 0 in the vertical direction, the vertical concentration distribution of the suspended matter is assumed to be a simplified Rouse distribution and calculated using the following formula: , in, Represents the normalization coefficient. , Indicates the height of the bedrock; Represents the Routh number; Thus, dispersed stress and It can be represented as: , , in, Indicates the average velocity of the flow direction. This represents the average lateral flow velocity. These represent the simplification coefficients in the equation, have no physical meaning, and are expressed mathematically as follows: , .

[0014] Furthermore, based on the modified shallow water equation, the angular momentum equation considering the influence of density gradient, and coupled with the convection-diffusion equation considering dispersed stress, a two-dimensional planar hydrodynamic-mass transport finite element model is constructed. The expression for the two-dimensional planar hydrodynamic-mass transport finite element model is as follows: , , ,, , .

[0015] Furthermore, satellite remote sensing topographic data or ADCP measured water depth data are used as topographic boundary conditions to input into the two-dimensional planar hydrodynamic-mass transport finite element model to complete the mapping and mesh generation of the study area.

[0016] Based on this computational domain, the flow rate and water temperature data of the upstream tributaries are input, which correspond to the flow velocity and density parameters in the governing equations, respectively. At the same time, the measured water level data of the downstream ADCP are input, and together with the initially set topographic boundary conditions, they are converted into water depth, coordinates and other governing equation parameters.

[0017] The flow velocity field in the computational domain is finally output by the model dimensionality reduction algorithm, thus obtaining the dimensionality reduction simulation results that integrate measured data, realizing the dimensionality reduction of three-dimensional hydrodynamic structures to two-dimensional efficient calculation.

[0018] According to one aspect of the present invention, a storage medium is provided, wherein the storage medium stores instructions that, when read by a computer, cause the computer to execute the dimensionality reduction method for river hydrodynamic simulation described in any of the preceding claims.

[0019] According to another aspect of the present invention, an electronic device is provided, comprising a processor and the aforementioned storage medium, wherein the processor executes instructions in the storage medium.

[0020] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0021] This invention incorporates curvature-induced secondary flow and density difference effects, as well as their interactions, into the two-dimensional shallow water equations through a diffuse stress term. By solving the shallow water equations and transport equations in a coupled manner, the simulation accuracy of the two-dimensional model is greatly improved, and a high-precision simulation of three-dimensional water flow structures is achieved through dimensionality reduction.

[0022] This invention is applicable to long-term, large-scale simulation of river water and sediment processes. It can accurately predict the entire process of secondary flow generation, evolution, interaction, and decay, providing a more reliable tool for long-term river geomorphological evolution prediction and simulation. Attached Figure Description

[0023] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention.

[0024] Unless otherwise defined, the technical or scientific terms used herein shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0025] Figure 1 This is a schematic diagram of a method flow according to a preferred embodiment of the present invention; Figure 2 This is a schematic diagram of the field monitoring cross-section layout in a preferred embodiment of the present invention; wherein IL and IR represent the positions of the left and right branching cross-sections before the confluence of the inflow from the A River side, respectively; Y1 and Y2 represent the positions of the two cross-sections after the confluence of the inflow from the A River side; P1, P2, and P3 represent the positions of the three cross-sections of the inflow from the B Lake side; CYP0 to CYP9 and CYP8NEW represent the positions of each experimental cross-section after the confluence of the A River and the B Lake. Figure 3This is a preferred embodiment of the invention, showing the lateral velocity component at the free surface predicted by a fixed-bed simulation under medium-high flow conditions. Planar distribution diagrams, where (a) only considers the effect of curvature-induced secondary flow, and (b) simultaneously considers the interaction between density gradient and bend circulation. Positive signs indicate counterclockwise rotation, and negative signs indicate clockwise rotation. Figure 4 This is a preferred embodiment of the invention, showing the transverse velocity components at the free surfaces of cross sections CYP2 to CYP7 predicted by a fixed-bed simulation under medium-high flow conditions 1. The comparison chart shows the results of ADCP. The red dashed line represents the measured data of ADCP, the green line represents the effect of curvature-induced secondary flow only, and the blue line represents the effect of density gradient and bend circulation interaction. Among them, (a) is the comparison chart of the simulated and measured results of secondary flow intensity of CYP2 in the interruption section of condition 1, (b) is the comparison chart of the simulated and measured results of secondary flow intensity of CYP3 in the interruption section of condition 1, (c) is the comparison chart of the simulated and measured results of secondary flow intensity of CYP4 in the interruption section of condition 1, (d) is the comparison chart of the simulated and measured results of secondary flow intensity of CYP5 in the interruption section of condition 1, (e) is the comparison chart of the simulated and measured results of secondary flow intensity of CYP6 in the interruption section of condition 1, and (f) is the comparison chart of the simulated and measured results of secondary flow intensity of CYP7 in the interruption section of condition 1. Figure 5 This is a preferred embodiment of the invention, showing the lateral velocity component at the free surface predicted by a fixed bed simulation under low-flow conditions. Planar distribution diagrams, where (a) only considers the effect of curvature-induced secondary flow, and (b) considers the interaction between density gradient and bend circulation. Positive signs indicate counter-clockwise rotation, and negative signs indicate clockwise rotation. Figure 6 This is a preferred embodiment of the invention, showing the transverse velocity components at the free surfaces of sections CYP2 to CYP7 predicted by a fixed-bed simulation under low-flow conditions. The comparison chart shows the results of ADCP measurements. The red dashed line represents the actual ADCP data, the green line represents the effect of curvature-induced secondary flow only, and the blue line represents the effect of density gradient and bend circulation interaction. Specifically, (a) compares the simulated and measured results of secondary flow intensity at the CYP2 section of condition 2; (b) compares the simulated and measured results of secondary flow intensity at the CYP3 section of condition 2; (c) compares the simulated and measured results of secondary flow intensity at the CYP4 section of condition 2; (d) compares the simulated and measured results of secondary flow intensity at the CYP5 section of condition 2; (e) compares the simulated and measured results of secondary flow intensity at the CYP6 section of condition 2; and (f) compares the simulated and measured results of secondary flow intensity at the CYP7 section of condition 2. Detailed Implementation

[0026] To better understand the technical content of this invention, specific embodiments are described below in conjunction with the accompanying drawings. Various aspects of this invention are described with reference to the accompanying drawings, which illustrate numerous illustrative embodiments. The embodiments of this invention are not limited to those shown in the drawings. It should be understood that this invention is implemented through any of the various concepts and embodiments described above, as well as the concepts and embodiments described in detail below, because the concepts and embodiments disclosed in this invention are not limited to any particular implementation. Furthermore, some aspects of this invention can be used alone or in any suitable combination with other aspects disclosed in this invention.

[0027] Example 1: like Figure 1-6 As shown, a dimensionality reduction method for river hydrodynamic simulation includes the following steps: S1. Obtain parameter information of the river channel from the watershed hydrological stations, remote sensing monitoring systems and historical measurement data. This information includes the river channel's hydrological parameters, hydrodynamic parameters, topographic parameters, etc. S2. To account for the contribution of the bend circulation to the momentum equation, a diffuse stress term is added to the shallow water equation, resulting in the modified shallow water equation. S3. The contribution of the density gradient to angular momentum is introduced into the angular momentum conservation equation. An additional production term is added to enhance the angular momentum conservation equation. The interaction between the density gradient and the bend circulation and its net effect on the momentum equation are considered in terms of the relative directions of curvature and density gradient, resulting in an angular momentum equation based on the influence of density gradient. S4. In order to take into account the net lateral flux of sediment generated by the combined effect of the non-uniform distribution of suspended sediment vertical concentration and the lateral spiral flow, the interpretation is enhanced by adding an appropriate dispersion stress term to the original convection-diffusion equation. S5. Based on the modified shallow water equation, the angular momentum equation considering the influence of density gradient, and coupled with the convection-diffusion equation considering the dispersed stress, a two-dimensional planar hydrodynamic-mass transport finite element model is constructed. S6. Using satellite remote sensing topographic data or ADCP-measured water depth data as topographic boundary conditions, input the model into a two-dimensional planar hydrodynamic-mass transport finite element model to complete the mapping and mesh generation of the study area. Based on this computational domain, input the flow rate and water temperature data of the upstream tributaries, corresponding to the flow velocity and density parameters in the governing equations, respectively. Simultaneously, input the downstream ADCP-measured water level data, which, together with the initially set topographic boundary conditions, are converted into water depth, coordinates, and other governing equation parameters. Through model dimensionality reduction algorithms, the final output is the velocity field of the computational domain, thus obtaining the dimensionality-reduced simulation results that integrate measured data, achieving efficient dimensionality reduction from three-dimensional hydrodynamic structures to two-dimensional computation.

[0028] In step S2, the modified shallow water equation is expressed as follows: , ,, , in, Represents the mass derivative. This represents the x-axis component of the velocity integrated along the water depth. This represents the equivalent water depth, which is the volume of water per unit area. This represents the Reynolds turbulent stress in the x-direction on a horizontal plane. The horizontal coordinate axis is parallel to the direction of the main channel of the river (usually positive in the direction of the flow). This represents the shear component of the Reynolds turbulent stress on a horizontal surface. The horizontal coordinate axis represents the direction perpendicular to the main channel of the river. The x-axis velocity fluctuation kinetic energy, representing the vertical integral, is physically determined by the additional normal stress in the x-axis caused by the uneven distribution of vertical velocity. , The vertical coordinate axis represents the direction of water depth (z=0 for the riverbed and z=Y for the water surface). This represents the difference between the actual value of the velocity component along the x-axis and the average value of the water depth. , This represents the distribution of instantaneous flow velocity along the vertical direction in the x-direction. This represents the average velocity across the water in the x-direction. , Both represent the xy-direction velocity fluctuation cocorrelation terms of the vertical integral, and their physical meaning reflects the momentum exchange caused by vertical shear. Due to symmetry, therefore... , This represents the difference between the actual value of the velocity component along the y-axis and the average value of the water depth. , This represents the distribution of instantaneous flow velocity along the vertical direction in the y-direction. This represents the average velocity across the water in the y-direction. The x-axis component represents the shear stress on the bed surface. This indicates the density of water. Represents gravitational acceleration. This represents the free surface elevation relative to the horizontal datum plane. This represents the y-axis component of the velocity integrated along the water depth. This represents the Reynolds turbulent stress in the y-direction on a horizontal plane. This represents the kinetic energy of the pulsating velocity along the y-axis, which is the result of the vertical integral. ; The y-axis component represents the shear stress on the bed surface. Representing the wetted area fraction, it is a storage coefficient related to water depth. , Indicates time.

[0029] The dispersed stress term reflects the subscale spatial variation of the unanalyzed velocity field. To derive the closed-form expression for the dispersed stress term, a local reference frame is typically used, where s represents the longitudinal direction (i.e., the mainstream direction) and n represents the transverse direction. It is also assumed that the flow velocity has a simple vertical distribution in the s and n directions, and that the velocity components in the mainstream direction follow a power-law distribution; these assumptions help simplify the derivation of the dispersed stress. Finally, through coordinate transformation, we obtain: , , , in, This indicates the magnitude of the average flow velocity at water depth. ; It does not depend on secondary flow; it acts along the mainstream direction, influencing flow by suppressing spatial acceleration and deceleration. It is the most important term in simulating secondary flow. Its spatial gradient may cause additional drag on the inside of the curve and acceleration on the outside of the curve, thus explaining the additional momentum transfer effect caused by helical flow. This may generate net transverse stress, the magnitude of which depends on the transverse velocity gradient and the transverse gradient of the secondary flow intensity. The specific calculation formulas for the three components of the dispersed stress, represented in the local coordinate system, are as follows: , , , in, Indicates friction parameters; The streamline radius represents the average water depth. R is positive when the water flow bends clockwise and negative otherwise. It represents the dimensionless transverse velocity at the free surface, reflecting the intensity of the secondary flow. It can be calculated using the eddy transport method, and the specific steps are as follows: First, the general form of the flow-directed vorticity transport equation on the horizontal plane can be written as: , in, Indicates the flow direction component of vorticity; This represents the production item, which depends on the imbalance between centrifugal acceleration and the lateral pressure gradient; Represents dissipation terms; Assuming a linear distribution of spanwise velocity, the streamwise component of vorticity is expressed as: , in, Indicates angular velocity, Indicates the lateral velocity at the free surface; Assuming a slow change in water depth, the flow-directed vorticity transport equations on the horizontal surface can be directly applied. Rewritten as: , in, The coefficient representing the production item; Denotes the von Kármán constant. ; Represents the coefficient of the dissipation term; The dimensionless transverse velocity at the free surface can be expressed as: .

[0030] In step S3, the expression for the angular momentum equation considering the density gradient is: , in, All of these represent empirical coefficients. Indicates friction parameters, This indicates the lateral coordinate pointing to the inside of the curve; Based on the assumption that the water depth changes slowly, the angular momentum equation considering the density gradient is modified as follows: .

[0031] In step S4, the convection-diffusion equation describes the temporal and spatial evolution of the vertical average concentration of tracers and substances moving with the flow. The original convection-diffusion equation is expressed as: , in, Indicates concentration; Represents a two-dimensional divergence operator; The convection term represents the mass flux. A two-dimensional gradient representing concentration; Indicates turbulent diffusion. , Indicates turbulent eddy viscosity. This represents the Schmitt number, which is typically taken as 1. Represents the anisotropic diffusivity tensor, used to explain dispersion in the longitudinal and transverse directions; Indicates the source term.

[0032] Convection-diffusion equations are generally based on the assumption of a constant passive scalar concentration in the vertical direction; however, this assumption is usually not valid. When simulating suspended sediment transport, its highest concentration often occurs near the riverbed bottom. This non-uniform vertical concentration distribution, combined with the flow-oriented helical flow, generates a net sediment flux in the lateral direction, which can be explained in the equations using appropriate dispersion terms. Given the vertical distribution of spanwise velocity and concentration distribution, dispersion stress is calculated by integrating the difference between the depth-dependent flux and its depth-average value. The convection-diffusion equations describing suspended sediment transport can be rewritten as follows: , in, This represents the vertical integral diffuse flux component in the x-direction. This represents the vertical integral diffuse flux component in the y-direction. Indicates erosion flux, Indicates deposition flux; , , in, This represents the difference between the vertical distribution of suspended sediment concentration C(z) and the depth-average concentration C. This represents the flow component of the dispersed stress in the local reference frame. This represents the spanwise component of the dispersed stress in the local reference frame; This indicates the settling velocity of sediment particles.

[0033] Assuming the longitudinal velocity component follows a power-law distribution in the vertical direction and the lateral velocity component follows a linear distribution with a mean of 0 in the vertical direction, and assuming the vertical concentration distribution of suspended matter to be a simplified Rouse distribution, it can be calculated using the following formula: , in, Represents the normalization coefficient. , Indicates the height of the bedrock; Represents the Routh number; Thus, dispersed stress and It can be represented as: , , in, Indicates the average velocity of the flow direction. This represents the average lateral flow velocity. These represent the simplification coefficients in the equation, have no physical meaning, and are expressed mathematically as follows: , ; S5. Based on the modified shallow water equation, the angular momentum equation considering the influence of density gradient, and coupled with the convection-diffusion equation considering the dispersed stress, a two-dimensional planar hydrodynamic-mass transport finite element model is constructed. In step S5, the expression for the two-dimensional planar hydrodynamic-mass transport finite element model is: , , , ,, ; S6. Using satellite remote sensing topographic data or ADCP-measured water depth data as topographic boundary conditions, input the model into a two-dimensional planar hydrodynamic-mass transport finite element model to complete the mapping and mesh generation of the study area. Based on this computational domain, input the flow rate and water temperature data of the upstream tributaries, corresponding to the flow velocity and density parameters in the governing equations, respectively. Simultaneously, input the downstream ADCP-measured water level data, which, together with the initially set topographic boundary conditions, are converted into water depth, coordinates, and other governing equation parameters. Through model dimensionality reduction algorithms, the final output is the velocity field of the computational domain, thus obtaining the dimensionality-reduced simulation results that integrate measured data, achieving efficient dimensionality reduction from three-dimensional hydrodynamic structures to two-dimensional computation.

[0034] The following example uses a fixed-bed simulation at a confluence of the A River basin. Through two field monitoring operations in 2018, data from multiple river cross-sections were measured using an Acoustic Doppler Current Profiler (ADCP). The cross-section layout is shown in the diagram below. Figure 2 As shown, the monitoring range covers 7 km of the A River section and 4 km of the B Lake waterway connecting to the river. Detailed hydrological and topographic data of a tributary of the A River, a tributary of the B Lake and their confluence area were collected. The basic hydraulic parameters of the two working conditions are shown in Table 1.

[0035] Table 1 Basic hydraulic parameters under measured working conditions

[0036] To account for the contribution of bend circulation to the momentum equation, the dispersed stress corresponding to the curvature-induced secondary flow in the two-dimensional shallow water equation is represented by the dimensionless transverse velocity at the free surface and calculated using the vortex transport method. Furthermore, the contribution of the density gradient to angular momentum is introduced into the angular momentum conservation equation, and the interaction between the density gradient and bend circulation and its net effect on the momentum equation is considered through the relative directions of curvature and density gradient. Then, the convection-diffusion equations considering dispersed stress are coupled to construct a two-dimensional planar hydrodynamic-mass transport finite element model. The specific derivation process of the governing equations and formulas involved is as described above and will not be repeated here.

[0037] A two-dimensional planar hydrodynamic-mass transport finite element model considering the interaction of density gradient and bend circulation was applied to a fixed-bed simulation of a confluence zone in the A River basin, simulating two different operating conditions. In high-flow-rate condition 1, the flow rate of a tributary of the A River was much greater than that of a tributary of Lake B, and the average velocity of the tributary of the A River was almost four times that of the tributary of Lake B. At the confluence zone, the flows of the tributary of the A River and the tributary of Lake B deflected to the left and right, respectively. Due to the curvature of the streamlines, a spiral flow was generated in the transverse plane, consisting of two opposing rotating secondary flows. From the confluence apex, the two opposing rotating secondary flows influenced and interacted with each other. In the simulation considering only the curvature-induced secondary flow effect, the intensity of the clockwise rotating secondary flow on the side of the tributary of the A River was much greater than that on the side of the tributary of Lake B. Figure 3 However, field measurement data shows that the counterclockwise secondary flow formed on one side of a tributary of Lake B was not suppressed. This is because the water temperature on the side of a tributary of River A was lower than that on the side of a tributary of Lake B under this condition, forming a horizontal density gradient at the mixing interface and generating a density-driven counterclockwise transverse circulation. This helps to suppress the clockwise circulation on the side of a tributary of River A, while enhancing the counterclockwise circulation on the side of a tributary of Lake B, thus forming two opposing rotating circulations of similar intensity.

[0038] Figure 4 The transverse velocity components at the free surfaces of sections CYP2 to CYP7 are predicted by the fixed-bed simulation under high-flow-rate condition 1 in this embodiment of the invention. (i.e., secondary flow intensity) effect comparison chart. The red dashed line in the chart represents the measured data results of ADCP, the green line represents only considering the influence of curvature-induced secondary flow, and the blue line represents considering the interaction of density gradient and bend circulation. Figure 4 (a) is a comparison of the simulated and measured results of the secondary flow intensity at the CYP2 cross section in operating condition 1. Figure 4 (b) is a comparison chart of the simulated and measured results of the secondary flow intensity at the CYP3 cross section in operating condition 1. Figure 4 (c) is a comparison chart of the simulated and measured results of the secondary flow intensity at the CYP4 cross section in operating condition 1. Figure 4(d) is a comparison chart of the simulated and measured results of the secondary flow intensity at the CYP5 cross section in operating condition 1. Figure 4 (e) is a comparison chart of the simulated and measured results of the secondary flow intensity at the CYP6 cross section in operating condition 1. Figure 4 (f) is a comparison chart of the simulated and measured results of the secondary flow intensity at the CYP7 cross section in condition 1. Figure 3 and Figure 4 As shown, the planar two-dimensional hydrodynamic-mass transport finite element model considering the interaction of density gradient and bend circulation proposed in this invention accurately predicts the formation of this pair of counter-rotating secondary flows, and the results are in good agreement with the measured data, with high accuracy.

[0039] In low-flow condition 2, the flow rate of a tributary of River A is approximately twice that of a tributary of Lake B. The average flow velocities of the tributaries on the River A and Lake B sides are similar, and the water temperature on the Lake B side is lower than that on the River A side. Due to the reverse curvature of the incoming streams on both sides, two opposing spiral flows are formed at the initial confluence point, both with relatively weak intensity. Figure 5 After the confluence of the two streams, the clockwise rotating secondary flow originating from a tributary of River A gradually becomes dominant, stronger than the counterclockwise rotating secondary flow from a tributary of Lake B. This is mainly because the downstream streamline deflects to the left, enhancing the secondary flow of the tributary on the River A side and weakening the counterclockwise rotating secondary flow of the tributary on the Lake B side. The presence of a horizontal water temperature gradient further enhances the clockwise secondary flow of the tributary on the River A side, which is clearly visible at the confluence apex (see...). Figure 5 This is because the streamline curvature at the confluence vertices has a smaller impact, while the effect of the water temperature gradient is more significant.

[0040] Figure 6 The transverse velocity components at the free surfaces of sections CYP2 to CYP7 are predicted by the fixed-bed simulation under low-flow condition 2 in this embodiment of the invention. (i.e., secondary flow intensity) effect comparison chart. The red dashed line in the chart represents the measured data results of ADCP, the green line represents only considering the influence of curvature-induced secondary flow, and the blue line represents considering the interaction of density gradient and bend circulation. Figure 6 (a) is a comparison of the simulated and measured results of the secondary flow intensity at the CYP2 cross section in condition 2. Figure 6 (b) is a comparison chart of the simulated and measured results of the secondary flow intensity at the CYP3 cross section in condition 2. Figure 6 (c) is a comparison chart of the simulated and measured results of the secondary flow intensity at the CYP4 cross section in working condition 2. Figure 6 (d) is a comparison chart of the simulated and measured results of the secondary flow intensity at the CYP5 cross section in working condition 2. Figure 6 (e) is a comparison chart of the simulated and measured results of the secondary flow intensity at the CYP6 cross section in working condition 2. Figure 6Figure (f) is a comparison of the simulated and measured results of the secondary flow intensity at the CYP7 cross section in condition 2. From... Figure 6 It can be seen that, compared with the two-dimensional model that only considers the influence of curvature-induced secondary flow, the two-dimensional planar hydrodynamic-mass transport finite element model that considers the interaction between density gradient and bend circulation is more consistent with the measured data results.

[0041] Example 2: The computer-readable storage medium of this embodiment stores a computer program that, when executed by a processor, implements the steps in the dimensionality reduction method for river hydrodynamic simulation of Embodiment 1.

[0042] The computer-readable storage medium in this embodiment can be an internal storage unit of the terminal, such as the terminal's hard disk or memory; the computer-readable storage medium in this embodiment can also be an external storage device of the terminal, such as a plug-in hard disk, smart memory card, secure digital card, flash memory card, etc. equipped on the terminal; furthermore, the computer-readable storage medium can include both the terminal's internal storage unit and external storage devices.

[0043] The computer-readable storage medium of this embodiment is used to store computer programs and other programs and data required by the terminal. The computer-readable storage medium can also be used to temporarily store data that has been output or will be output.

[0044] Example 3: The computer device of this embodiment includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps of the dimensionality reduction method for river hydrodynamic simulation in Embodiment 1.

[0045] In this embodiment, the processor can be a central processing unit, or other general-purpose processors, digital signal processors, application-specific integrated circuits, off-the-shelf programmable gate arrays or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc. The memory can include read-only memory and random access memory, and provides instructions and data to the processor. A portion of the memory can also include non-volatile random access memory. For example, the memory can also store device type information.

[0046] Those skilled in the art will understand that the content disclosed in the embodiments can be provided as a method, system, or computer program product. Therefore, this solution can take the form of a hardware embodiment, a software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this solution can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage and optical storage) containing computer-usable program code.

[0047] This solution is described with reference to flowchart illustrations and / or block diagrams of methods and computer program products according to embodiments of this solution. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing device, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0048] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0049] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0050] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0051] The examples described herein are merely preferred embodiments of the invention and are not intended to limit the concept and scope of the invention. Any modifications and improvements made by those skilled in the art to the technical solutions of the invention without departing from the design concept of the invention should fall within the protection scope of the invention.

Claims

1. A dimensionality reduction method for river hydrodynamic simulation, characterized in that, include: Data collection; A two-dimensional planar hydrodynamic model based on the shallow water equation is constructed. The influence of curvature-induced secondary flow is added to the shallow water equation through the dispersive stress term, resulting in the modified shallow water equation. The contribution of the density gradient to angular momentum is introduced into the angular momentum conservation equation; The angular momentum equation based on the influence of the density gradient is obtained; By coupling the convection-diffusion equations that take into account dispersed stress, a two-dimensional planar hydrodynamic-mass transport finite element model is constructed. Calculate the average flow field and secondary flow intensity at water depth.

2. The method according to claim 1, characterized in that, The data collection specifically includes: The parameter information of the river channel is obtained from the watershed hydrological stations, remote sensing monitoring systems and historical measurement data. The parameter information includes, but is not limited to, hydrological parameters, hydrodynamic parameters and topographic parameters.

3. The method according to claim 1, characterized in that, The revised shallow water equation is expressed as follows: ， ， ， in, Represents the mass derivative. This represents the x-axis component of the velocity integrated along the water depth. This represents the equivalent water depth, which is the volume of water per unit area. This represents the Reynolds turbulent stress in the x-direction on a horizontal plane. The horizontal coordinate axis represents the direction parallel to the main channel of the river. This represents the shear component of the Reynolds turbulent stress on a horizontal surface. The horizontal coordinate axis represents the direction perpendicular to the main channel of the river. This represents the kinetic energy of the velocity fluctuations along the x-axis, which is the result of the vertical integral. , The vertical coordinate axis represents the direction along the water depth, with the riverbed at z=0 and the water surface at z=Y. This represents the difference between the actual value of the velocity component along the x-axis and the average value of the water depth. , This represents the distribution of instantaneous flow velocity along the vertical direction in the x-direction. This represents the average velocity across the water in the x-direction. , Both represent the xy-direction velocity fluctuation cocorrelation terms of the vertical integral. Due to symmetry, therefore... , This represents the difference between the actual value of the velocity component along the y-axis and the average value of the water depth. , This represents the distribution of instantaneous flow velocity along the vertical direction in the y-direction. This represents the average velocity across the water in the y-direction. The x-axis component represents the shear stress on the bed surface. This indicates the density of water. Represents gravitational acceleration. This represents the free surface elevation relative to the horizontal datum plane. This represents the y-axis component of the velocity integrated along the water depth. This represents the Reynolds turbulent stress in the y-direction on a horizontal plane. This represents the kinetic energy of the pulsating velocity along the y-axis, which is the result of the vertical integral. ; The y-axis component represents the shear stress on the bed surface. Representing the wetted area fraction, it is a storage coefficient related to water depth. , Indicates time.

4. The method according to claim 3, characterized in that, Using a local reference frame, where s represents the longitudinal direction (mainstream direction) and n represents the transverse direction; and assuming a simple vertical distribution of flow velocity in the s and n directions, and further assuming that the velocity component in the mainstream direction follows a power-law distribution, a closed-form expression for the dispersed stress term is obtained through coordinate transformation: ， ， ， in, This indicates the magnitude of the average flow velocity at water depth. The specific calculation formulas for the three components of the dispersed stress represented in the local coordinate system are as follows: ， ， ， in, Indicates friction parameters; The streamline radius represents the average water depth. R is positive when the water flow bends clockwise and negative otherwise. This represents the dimensionless transverse velocity at the free surface; Calculated using the eddy transport method.

5. The method according to claim 4, characterized in that, The calculation steps are as follows: First, the flow vorticity transport equation on the horizontal plane is: ， in, Indicates the flow direction component of vorticity; Indicates a production item; Represents dissipation terms; Assuming a linear distribution of spanwise velocity, the streamwise component of vorticity is expressed as: ， in, Indicates angular velocity. Indicates the lateral velocity at the free surface; Assuming a slow change in water depth, the flow vorticity transport equations on the horizontal surface are directly applied. Rewritten as: ， in, The coefficient representing the production item; Denotes the von Kármán constant. ; Represents the coefficient of the dissipation term; The dimensionless transverse velocity at the free surface can be expressed as: 。 6. The method according to claim 5, characterized in that, The expression for the angular momentum equation considering the density gradient is as follows: ， in, All of these represent empirical coefficients. Indicates friction parameters, This indicates the lateral coordinate pointing to the inside of the curve; Based on the assumption that the water depth changes slowly, the angular momentum equation considering the density gradient is modified as follows: 。 7. The method according to claim 6, characterized in that, Given the vertical distribution of spanwise velocity and concentration distribution, the dispersion stress is analyzed and calculated by integrating the difference between the depth-dependent flux and the average depth value; the convection-diffusion equation describing suspended mass transport is rewritten as: ， in, This represents the vertical integral diffuse flux component in the x-direction. This represents the vertical integral diffuse flux component in the y-direction. Indicates erosion flux, This represents the deposition flux.

8. The method according to claim 1, characterized in that, The expression for the two-dimensional planar hydrodynamic-mass transport finite element model is as follows: ， ， ， ， 。 9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by the processor, it implements the steps in the dimensionality reduction method for river hydrodynamic simulation as described in any one of claims 1 to 8.

10. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the dimensionality reduction method for river hydrodynamic simulation as described in any one of claims 1 to 8.

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