Dimension reduction method for river hydrodynamic simulation

Abstract

The application discloses a dimension reduction method for river hydrodynamic simulation, and specifically comprises the following steps: data collection; constructing a two-dimensional plane hydrodynamic model based on shallow water equation; adding the influence of curvature-induced secondary flow into the shallow water equation through a dispersion stress term; further introducing the contribution of the density gradient to the angular momentum into the angular momentum conservation equation; coupling the convection-diffusion equation of the dispersion stress to construct a two-dimensional plane hydrodynamic-matter transport finite element model; and calculating the average flow field of water depth and the secondary flow intensity. The three-dimensional effect of the secondary flow driven by the streamline bending and the density difference is added into the two-dimensional equation through the dispersion stress term, and the shallow water equation and the transport equation are coupled and solved, so that the simulation precision of the two-dimensional model is greatly improved, and fast and high-precision simulation of long-term evolution of the large river system topography is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computational hydraulics, and particularly relates to a dimension reduction method for river hydrodynamic simulation. BACKGROUND

[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) can accurately calculate the flow field and describe the characteristics of material transport under complex boundary conditions by modeling and solving the Reynolds-averaged Navier-Stokes equations or using advanced methods such as large eddy simulation and detached eddy simulation. However, due to the complexity of 3-D CFD simulation of movable bed processes and the need for large amounts of computing resources, large-scale field riverbed morphology dynamics simulation has been limited in long-term application in engineering practice. Under this background, two-dimensional hydrodynamic and geomorphic dynamic models based on SWEs (Shallow Water Equations) have become standard tools for predicting riverbed evolution due to their computational efficiency. However, due to the depth-averaged method used by the 2D SWEs model, the main limitation of its application in complex river sections such as bends and river junctions is that it cannot explicitly consider three-dimensional effects, such as secondary flows that play an important role in pollutant and sediment transport, and the accuracy is often insufficient.

[0003] For a long time, two-dimensional hydrodynamic and geomorphic dynamic models have been improved by various methods to consider the influence of curvature-induced secondary flow. The most common and simple method is to adjust the bed sediment transport direction according to the local streamline curvature in the horizontal plane. A more advanced method is to add appropriate dispersion terms to the SWEs, which depend on the strength of the spiral flow. The dispersion stress can be calculated by the local streamline curvature, or by solving the transport equation of the angular momentum of the spiral flow. This method has clear physical meaning and does not require much additional computational effort, and is suitable for complex bends in natural river channels. However, these methods can only simulate curvature-driven secondary flows, and cannot consider additional secondary flows caused by density gradients (such as uneven distribution of temperature or suspended sediment concentration).

[0004] In addition, although existing models can depict the phase lag in the development and decay of secondary flow in river bends and reduce sensitivity to planar and / or topographic singularities, they have not yet addressed the coupling of density gradients and curvature-induced secondary flow. Although the additional mixing caused by secondary flow can also be represented by adding a dispersion term to the transport-diffusion equation, current depth-averaged models still lack a unified description of the interaction between density gradients and bend circulation, which is particularly important in suspended sediment transport and density current simulation. Therefore, there is an urgent need to develop a dimension reduction simulation method that can comprehensively consider the secondary flow driven by streamline curvature and density gradient. SUMMARY

[0005] The technical problem solved by the present application is to provide a dimension reduction method for river hydrodynamic simulation, which uses a two-dimensional finite element model to solve coupled shallow water equations and convection-diffusion equations, and by adding a suitable dispersion term in the control equation, the interaction between the density gradient and the bend circulation can be fully considered, the three-dimensional flow structure effect can be realized in the two-dimensional hydrodynamic model, and the simulation accuracy is improved while the calculation efficiency is ensured.

[0006] In order to solve the above technical problems, according to one aspect of the present application, a dimension reduction method for river hydrodynamic simulation is provided, comprising:

[0007] Data collection;

[0008] A two-dimensional plane hydrodynamic model based on shallow water equation is constructed, a dispersion stress term is added in the shallow water equation to obtain a modified shallow water equation, and the influence of curvature-induced secondary flow is added to the shallow water equation through the dispersion stress term;

[0009] The contribution of the density gradient to the angular momentum is introduced into the angular momentum conservation equation to obtain an angular momentum equation based on the influence of the density gradient;

[0010] A two-dimensional plane hydrodynamic-material transport finite element model is constructed by coupling the convection-diffusion equation considering the dispersion stress, and the average flow field and the secondary flow intensity are calculated.

[0011] Further, the data collection specifically includes:

[0012] Parameter information of the river channel is obtained from the basin hydrological station, remote sensing monitoring system and historical measurement data, and the parameter information includes, but is not limited to, hydrological parameters, hydrodynamic parameters and topographic parameters.

[0013] Further, in order to consider the contribution of the bend circulation to the momentum equation, a dispersion stress term is added in the shallow water equation to obtain a modified shallow water equation;

[0014] The expression of the modified shallow water equation is:

[0015] ,

[0016] ,

[0017] ,

[0018] wherein, represents the material derivative, represents the x-axis component of the velocity integrated along the water depth, represents the equivalent water depth, i.e. the volume of water per unit area, represents the x-direction Reynolds turbulent stress on the 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.

[0019] 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.

[0020] 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:

[0021] ,

[0022] ,

[0023] ,

[0024] where, represents the magnitude of the depth-averaged velocity, ;

[0025] The three components of the dispersion stress expressed in the local coordinate system are calculated as follows:

[0026] ,

[0027] ,

[0028] ,

[0029] where, represents the friction parameter; represents the radius of curvature of the stream line averaged over the water depth, R is positive when the flow is bending in the clockwise direction and negative otherwise; represents the dimensionless transverse velocity at the free surface; It is calculated by the vorticity advection method.

[0030] where, The calculation steps are as follows:

[0031] First, the streamwise vorticity advection equation on the horizontal plane is:

[0032] ,

[0033] where, represents the streamwise component of the vorticity; represents the production term; represents the dissipation term;

[0034] The streamwise component of the vorticity is expressed as:

[0035] ,

[0036] where, represents the angular velocity, represents the transverse velocity at the free surface;

[0037] The streamwise vorticity advection equation on the horizontal plane is directly rewritten as:

[0038] ,

[0039] ​where, represents the coefficient of production term; represents the Von Karman constant, ; represents the coefficient of dissipation term;

[0040] The dimensionless transverse velocity at the free surface can be expressed as:

[0041] .

[0042] Further, the contribution of density gradient to angular momentum is introduced into the angular momentum conservation equation by adding an extra production term to the angular momentum conservation equation to consider the interaction of density gradient and the curvature of the channel and its net effect on the momentum equation by considering the relative direction of curvature and density gradient, and the equation of angular momentum based on the influence of density gradient is obtained;

[0043] The expression of the angular momentum equation considering the density gradient is:

[0044] ,

[0045] where, all represent empirical coefficients, represents the friction parameter, represents the transverse coordinate pointing to the inside of the channel;

[0046] Based on the assumption that the water depth changes slowly, the angular momentum equation considering the density gradient is changed to:

[0047] .

[0048] Further, in order to consider the net sediment flux in the transverse direction caused by the combined action of the non-uniform distribution of vertical concentration of suspended sediment and the flow helical flow, the original convection-diffusion equation is enhanced by adding a suitable dispersion stress term; the convection-diffusion equation describes the evolution of the vertical average concentration of tracers and substances in time and space, and the original convection-diffusion equation is expressed as:

[0049] ,

[0050] where, represents the concentration; represents the two-dimensional divergence operator; represents the convection term of the substance flux; represents the two-dimensional gradient of concentration; represents the turbulent diffusion property, , represents the turbulent eddy viscosity, represents the Schmidt number, generally taken as 1; denotes the anisotropic diffusivity tensor, which is used to account for the longitudinal and transverse diffusion; denotes the source term;

[0051] Given the vertical distribution of the along-stream velocity and the concentration distribution, the dispersion stress is analyzed and calculated by integrating the difference between the depth-dependent flux and the depth-averaged value. The convection-diffusion equation describing the transport of suspended sediment is rewritten as:

[0052] ,

[0053] where, denotes the vertical-integrated dispersion flux component in the x direction, denotes the vertical-integrated dispersion flux component in the y direction, denotes the erosion flux, denotes the deposition flux;

[0054] ,

[0055] ,

[0056] where, denotes the difference between the vertical distribution of the suspended sediment concentration C(z) and the depth-averaged concentration value C, denotes the streamwise component of the dispersion stress in the local reference frame, denotes the spanwise component of the dispersion stress in the local reference frame;

[0057] Assuming that the longitudinal velocity component follows a power-law distribution in the vertical direction and the transverse velocity component follows a linear distribution with a mean value of 0 in the vertical direction, the vertical concentration distribution of the suspended sediment is assumed to be a simplified Rouse distribution, which is calculated using the following formula:

[0058] ,

[0059] where, denotes the normalized coefficient, , denotes the height of the bed load layer; denotes the Rouse number;

[0060] Thus, the dispersion stress and can be represented as:

[0061] ,

[0062] ,

[0063] where, denotes the streamwise mean velocity, denotes the transverse mean velocity, The simplified coefficient in the equation has no physical meaning, and the mathematical expression is as follows:

[0064] ,

[0065] .

[0066] Further, based on the modified shallow water equation, the angular momentum equation considering the influence of the density gradient, and the convection-diffusion equation considering the coupling of the dispersion stress, a plane two-dimensional hydrodynamic-matter transport finite element model is formed.

[0067] The expression of the plane two-dimensional hydrodynamic-matter transport finite element model is as follows:

[0068] ,

[0069] ,

[0070] ,,

[0071] ,

[0072] .

[0073] Further, satellite remote sensing topographic data or water depth data measured by ADCP is input as a topographic boundary condition into the plane two-dimensional hydrodynamic-matter transport finite element model, so as to complete the drawing and mesh division of the research area.

[0074] Based on the calculation domain, the flow rate and water temperature data of the upstream branch are input, which correspond to the flow rate and density parameters in the control equation, respectively, and the downstream ADCP measured water level data is input, which is converted into water depth, coordinate and other control equation parameters together with the initially set topographic boundary condition.

[0075] Through model dimension reduction algorithm calculation, the flow rate field of the calculation domain is finally output, so as to obtain the dimension reduction simulation result fused with the measured data, and realize the dimension reduction from three-dimensional hydrodynamic structure to two-dimensional efficient calculation.

[0076] According to one aspect of the present application, a storage medium is provided, and instructions are stored in the storage medium, when a computer reads the instructions, the computer executes the dimension reduction method of river hydrodynamic simulation according to any one of the above.

[0077] According to another aspect of the present application, an electronic device is provided, which includes a processor and the above-mentioned storage medium, and the processor executes the instructions in the storage medium.

[0078] Compared with the prior art, the above technical scheme has the following technical effects:

[0079] The application adds the curvature-induced secondary flow and the density difference effect and the interaction therebetween into the two-dimensional shallow water equation through the dispersion stress term, solves the shallow water equation and the transport equation in a coupled manner, greatly improves the simulation precision of the two-dimensional model, and realizes the dimension reduction high-precision simulation of the three-dimensional water flow structure.

[0080] The application is suitable for long-term and large-scale river water and sediment process simulation, can accurately predict the generation, evolution, interaction and recession of the secondary flow, and provides a more reliable tool for long-term river geomorphology evolution prediction simulation. BRIEF DESCRIPTION OF DRAWINGS

[0081] In order to make the objects, technical solutions and advantages of the embodiments of the application clearer, the technical solutions of the embodiments of the application will be described clearly and completely below with reference to the drawings of the embodiments of the application. Obviously, the described embodiments are part of the embodiments of the application, rather than all the embodiments of the application.

[0082] Unless otherwise defined, the technical terms or scientific terms used herein should be understood as the general meanings understood by those skilled in the art in the field of the application.

[0083] Figure 1 is a method flowchart of a preferred embodiment of the application;

[0084] Figure 2 is a field monitoring section arrangement schematic diagram in the preferred embodiment of the application; wherein I-L and I-R respectively represent the left and right branch section positions before the A river side inflow confluence; Y1 and Y2 represent two section positions after the A river side inflow confluence; P1, P2 and P3 represent three section positions of the B lake side inflow; CYP0-CYP9 and CYP8NEW represent each experimental section position after the A river-B lake intersection;

[0085] Figure 3 is a transverse velocity component at a free surface predicted by fixed bed simulation under high flow condition 1 in the preferred embodiment of the application is a planar distribution diagram, wherein (a) is only the curvature-induced secondary flow effect, (b) is the density gradient and the bend circulation interaction, the positive sign represents counterclockwise rotation, and the negative sign represents clockwise rotation;

[0086] Figure 4 is a transverse velocity component at a free surface of sections CYP2-CYP7 predicted by fixed bed simulation under high flow condition 1 in the preferred embodiment of the application Effect comparison chart, the red dotted line in the figure represents the ADCP measured data result, the green line represents only considering the influence of curvature induced secondary flow, the blue line represents considering the interaction of density gradient and bend circulation at the same time; wherein (a) is the secondary flow intensity simulation result and measured result comparison chart of section CYP2 in working condition 1, (b) is the secondary flow intensity simulation result and measured result comparison chart of section CYP3 in working condition 1, (c) is the secondary flow intensity simulation result and measured result comparison chart of section CYP4 in working condition 1, (d) is the secondary flow intensity simulation result and measured result comparison chart of section CYP5 in working condition 1, (e) is the secondary flow intensity simulation result and measured result comparison chart of section CYP6 in working condition 1, (f) is the secondary flow intensity simulation result and measured result comparison chart of section CYP7 in working condition 1;

[0087] Figure 5 The transverse velocity component at the free surface predicted by the fixed bed simulation of the medium-low flow working condition 2 of the preferred embodiment of the present application Plane distribution chart, wherein (a) is only considering the influence of curvature induced secondary flow, (b) is considering the interaction of density gradient and bend circulation at the same time. The positive sign represents counterclockwise rotation, and the negative sign represents clockwise rotation;

[0088] Figure 6 The transverse velocity component at the free surface of sections CYP2-CYP7 predicted by the fixed bed simulation of the medium-low flow working condition 2 of the preferred embodiment of the present application Effect comparison chart, the red dotted line in the figure represents the ADCP measured data result, the green line represents only considering the influence of curvature induced secondary flow, the blue line represents considering the interaction of density gradient and bend circulation at the same time. Wherein (a) is the secondary flow intensity simulation result and measured result comparison chart of section CYP2 in working condition 2, (b) is the secondary flow intensity simulation result and measured result comparison chart of section CYP3 in working condition 2, (c) is the secondary flow intensity simulation result and measured result comparison chart of section CYP4 in working condition 2, (d) is the secondary flow intensity simulation result and measured result comparison chart of section CYP5 in working condition 2, (e) is the secondary flow intensity simulation result and measured result comparison chart of section CYP6 in working condition 2, (f) is the secondary flow intensity simulation result and measured result comparison chart of section CYP7 in working condition 2. DETAILED DESCRIPTION

[0089] For a more complete understanding of the technical content of the present application, specific embodiments are described below with reference to the accompanying drawings. In the present application, aspects of the present application are described with reference to the accompanying drawings, which show many illustrative embodiments. The embodiments of the present application are not limited to the drawings described. It should be understood that the present application is implemented by any one of the above-mentioned concepts and embodiments, as well as the concepts and embodiments described in detail below, because the concepts and embodiments disclosed by the present application are not limited to any implementation. In addition, some aspects disclosed by the present application can be used alone, or in any appropriate combination with other aspects disclosed by the present application.

[0090] Embodiment 1:

[0091] As Figures 1-6 shown, a dimension reduction method for river hydrodynamic simulation includes the following steps:

[0092] S1, obtaining parameter information of the river channel from the hydrological station of the river basin, the remote sensing monitoring system and the historical measurement data, the information including hydrological parameters, hydrodynamic parameters and topographic parameters of the river channel;

[0093] S2, to consider the contribution of bend circulation to the momentum equation, a dispersion stress term is added to the shallow water equation to obtain a modified shallow water equation;

[0094] S3, the contribution of the density gradient to the angular momentum is introduced into the angular momentum conservation equation, and an additional production term is added to enhance the angular momentum conservation equation, to consider the interaction between the density gradient and the bend circulation and its net effect on the momentum equation by considering the relative direction of the curvature and the density gradient, to obtain the angular momentum equation based on the influence of the density gradient;

[0095] S4, to consider the net sediment flux in the transverse direction caused by the combined action of the non-uniform distribution of the vertical concentration of suspended sediment and the flow helical flow, a suitable dispersion stress term is added to the original convection-diffusion equation to enhance the explanation;

[0096] S5, based on the modified shallow water equation, the angular momentum equation considering the influence of the density gradient, and the convection-diffusion equation considering the dispersion stress, a two-dimensional hydrodynamic-matter transport finite element model is constructed;

[0097] S6, input the satellite remote sensing terrain data or the water depth data measured by ADCP as the terrain boundary condition into the plane two-dimensional hydrodynamic-mass transport finite element model, complete the drawing and grid division of the study area. Based on the calculation domain, input the flow and water temperature data of the upstream branch into the water flow velocity and density parameters in the control equation, and input the downstream ADCP measured water level data into the water depth, coordinate and other control equation parameters together with the initially set terrain boundary condition. Through the model dimension reduction algorithm calculation, finally output the flow velocity field of the calculation domain, so as to obtain the dimension reduction simulation result fused with the measured data, realize the dimension reduction of three-dimensional hydrodynamic structure to two-dimensional efficient calculation.

[0098] In step S2, the expression of the modified shallow water equation is:

[0099]

[0100]

[0101]

[0102] wherein, represents the material derivative, represents the x-axis component of the velocity along the water depth integration, represents the equivalent water depth, i.e. the water volume per unit area, represents the x-direction Reynolds turbulent stress on the horizontal plane, represents the horizontal coordinate axis parallel to the main flow direction of the river channel (usually positive in the downstream direction), represents the shear component of the Reynolds turbulent stress on the horizontal plane, represents the horizontal coordinate axis perpendicular to the main flow direction of the river channel, represents the x-axis direction flow velocity fluctuation kinetic energy of vertical integration, which has the physical meaning of x-direction additional normal stress caused by uneven vertical flow velocity distribution, represents the vertical coordinate axis along the water depth direction (z=0 for the riverbed and z=Y for the water surface), represents the difference between the real value and the water depth average value of the x-axis direction velocity component, represents the vertical distribution of the x-direction instantaneous flow velocity, represents the x-direction water depth average velocity; both represent the x-y direction flow velocity fluctuation correlation term of vertical integration, which has the physical meaning of reflecting the momentum exchange caused by vertical shear, and represents the difference between the real value and the water depth average value of the y-axis direction velocity component, ​​​​​​​​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.

[0103] 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:

[0104] ,

[0105] ,

[0106] ,

[0107] 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:

[0108] ,

[0109] ,

[0110] ,

[0111] where, represents the friction parameter; represents the radius of curvature of the streamline averaged over the water depth, R is positive when the flow is bending in the clockwise direction and negative otherwise; represents the dimensionless transverse velocity at the free surface, reflecting the strength of the secondary flow. It can be calculated by the vorticity transport method, the specific steps are as follows:

[0112] First, the general form of the streamwise vorticity transport equation on the horizontal plane can be written as:

[0113] ,

[0114] where, represents the streamwise component of vorticity; represents the production term, which depends on the imbalance of the centrifugal acceleration and the transverse pressure gradient; represents the dissipation term;

[0115] The streamwise component of vorticity is expressed as:

[0116] ,

[0117] where, represents the angular velocity, represents the transverse velocity at the free surface;

[0118] The streamwise vorticity transport equation on the horizontal plane can be directly rewritten as:

[0119] ,

[0120] where, represents the coefficient of the production term; represents the von Karman constant, ; represents the coefficient of the dissipation term;

[0121] The dimensionless transverse velocity at the free surface can be expressed as:

[0122] .

[0123] In step S3, the expression of the angular momentum equation considering the density gradient is:

[0124] ,

[0125] where, all represent empirical coefficients, ​denotes the friction parameter, denotes the lateral coordinate pointing to the inner side of the bend;

[0126] Based on the assumption that the water depth varies slowly, the angular momentum equation considering the density gradient is modified as:

[0127] .

[0128] In step S4, the advection-diffusion equation describes the evolution of the vertical-averaged concentration of the tracer and the material moving with the flow in time and space. The original advection-diffusion equation is expressed as:

[0129] ,

[0130] where, denotes the concentration; denotes the two-dimensional divergence operator; denotes the convection term of the material flux; denotes the two-dimensional gradient of the concentration; denotes the turbulent diffusivity, , denotes the turbulent eddy viscosity, denotes the Schmidt number, which is generally taken as 1; denotes the anisotropic diffusivity tensor, which is used to explain the longitudinal and lateral dispersion; denotes the source term.

[0131] The advection-diffusion equation is generally based on the assumption that the passive scalar concentration is constant in the vertical direction. However, this assumption is often not true. When simulating the transport of suspended sediment, the highest concentration often approaches the riverbed bottom. This non-uniform vertical concentration distribution, combined with the flow direction helical flow, produces a net sediment flux in the lateral direction, which can be explained by a suitable dispersion term in the equation. Given the vertical distribution of the spanwise velocity and the concentration distribution, the dispersion stress is calculated by integrating the difference between the water depth-dependent flux and its water depth average. The advection-diffusion equation describing the transport of suspended sediment can be rewritten as:

[0132] ,

[0133] where, denotes the vertical integrated dispersion flux component in the x direction, denotes the vertical integrated dispersion flux component in the y direction, denotes the erosion flux, denotes the deposition flux;

[0134] ,

[0135] ,

[0136] where, 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.

[0137] 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:

[0138] ,

[0139] in, Represents the normalization coefficient. , Indicates the height of the bedrock; Represents the Routh number;

[0140] Thus, dispersed stress and It can be represented as:

[0141] ,

[0142] ,

[0143] 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:

[0144] ,

[0145] ;

[0146] 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.

[0147] In step S5, the expression for the two-dimensional planar hydrodynamic-mass transport finite element model is:

[0148] ,

[0149] ,

[0150] ,

[0151]

[0152]

[0153] S6, input the satellite remote sensing topographic data or the water depth data measured by ADCP into the plane two-dimensional hydrodynamic-mass transport finite element model as the topographic boundary condition, complete the drawing and meshing of the study area. Based on the calculation domain, input the flow and water temperature data of the upstream branch into the water flow velocity and density parameters in the control equation, and input the downstream ADCP measured water level data into the water depth, coordinate and other control equation parameters together with the initially set topographic boundary conditions. Through the model dimension reduction algorithm calculation, finally output the flow velocity field of the calculation domain, so as to obtain the dimension reduction simulation result fused with the measured data, realize the dimension reduction of three-dimensional hydrodynamic structure to two-dimensional efficient calculation.

[0154] Next, taking the fixed bed simulation of a confluence area in A River Basin as an example, through two field monitoring in 2018, the acoustic Doppler current profiler (ADCP) was used to measure the data of multiple river section, the measurement section layout is shown in Figure 2 , the monitoring range covers 7 km of A River section and 4 km of B Lake river section, detailed hydrological and topographic data of A River branch, B Lake branch and confluence area are collected, the basic hydraulic parameters of two working conditions are shown in Table 1.

[0155] Table 1 Basic hydraulic parameters of measured working conditions

[0156]

[0157] In order to consider the contribution of bend circulation to momentum equation, the dispersion stress corresponding to the curvature induced secondary flow in two-dimensional shallow water equation is expressed by dimensionless transverse velocity at free surface, and is calculated by vorticity transport method. Further, the contribution of density gradient to angular momentum is introduced into the angular momentum conservation equation, and the interaction between density gradient and bend circulation and its net effect on momentum equation are considered by the relative direction of curvature and density gradient. Then, the convection-diffusion equation of dispersion stress is coupled, and the plane two-dimensional hydrodynamic-mass transport finite element model is established. The specific derivation process of the control equation and formula is described before, which is not repeated here.

[0158] ​​The constructed plane two-dimensional hydrodynamic-mass transport finite element model considering the interaction of density gradient and bend circulation is applied to the fixed bed simulation of a confluence area in A River Basin, and two working conditions are simulated. In the high flow working condition 1, the flow of a branch of A River is much larger than that of a branch of B Lake, and the average flow velocity of the branch of A River is almost 4 times that of the branch of B Lake. In the confluence area, the water flow of the branch of A River and the branch of B Lake deflects to the left and right respectively. Due to the bending of the flow line, the spiral flow is generated in the transverse plane, and it is two counter-rotating secondary flows. From the confluence vertex, the two counter-rotating secondary flows interact with each other. In the simulation considering only the influence of curvature-induced secondary flow, the intensity of the clockwise secondary flow on the side of the branch of A River is much larger than that on the side of the branch of B Lake Figure 3 ), however, the field measurement data show that the counterclockwise secondary flow formed on the side of the branch of B Lake is not inhibited, because under this working condition, the water temperature on the side of the branch of A River is lower than that on the side of the branch of B Lake, a horizontal density gradient is formed at the mixing interface, and a counterclockwise transverse circulation driven by density is generated, which helps to inhibit the clockwise circulation on the side of the branch of A River and enhance the counterclockwise circulation on the side of the branch of B Lake, so that two counter-rotating circulations with similar intensity are formed.

[0159] Figure 4 The transverse velocity component (i.e. secondary flow intensity) at the free surface of the cross section CYP2-CYP7 predicted by the fixed bed simulation of the high flow working condition 1 in the embodiment of the present application The effect comparison chart, in which the red dotted line represents the ADCP measured data result, the green line represents the simulation result considering only the influence of curvature-induced secondary flow, and the blue line represents the simulation result considering the interaction of density gradient and bend circulation. Figure 4 (a) is a comparison chart of the secondary flow intensity simulation result and the measured result of the cross section CYP2 in the working condition 1, Figure 4 (b) is a comparison chart of the secondary flow intensity simulation result and the measured result of the cross section CYP3 in the working condition 1, Figure 4 (c) is a comparison chart of the secondary flow intensity simulation result and the measured result of the cross section CYP4 in the working condition 1, Figure 4 (d) is a comparison chart of the secondary flow intensity simulation result and the measured result of the cross section CYP5 in the working condition 1, Figure 4 (e) is a comparison chart of the secondary flow intensity simulation result and the measured result of the cross section CYP6 in the working condition 1, Figure 4 (f) is a comparison chart of the secondary flow intensity simulation result and the measured result of the cross section CYP7 in the working condition 1. As shown in Figure 3 and Figure 4 the plane two-dimensional hydrodynamic-mass transport finite element model considering the interaction of density gradient and bend circulation proposed in the present application accurately predicts the formation of the two counter-rotating secondary flows, and has good consistency and high precision with the measured data result.

[0160] In the low flow condition 2, the flow of a branch of A river is about 2 times of the flow of a branch of B lake, the average flow velocity of the branch of A river and the branch of B lake is close, and the water temperature of one side of the branch of B lake is lower than that of one side of the branch of A river. Due to the reverse bending of the flow lines on both sides, two reverse rotating spiral flows are formed at the beginning of the intersection, and the intensity is relatively weak. Figure 5 After the intersection of the flow on both sides, the clockwise rotating secondary flow generated on one side of the branch of A river gradually dominates, and is stronger than the counterclockwise rotating secondary flow of the branch of B lake, mainly because the flow line deflects to the left downstream of the intersection, thereby enhancing the secondary flow of the branch of A river and weakening the reverse rotating secondary flow of the branch of B lake. The existence of the horizontal temperature gradient further enhances the clockwise secondary flow of the branch of A river, which can be clearly seen at the intersection vertex (see Figure 5 ).

[0161] Figure 6 The transverse velocity component (i.e., the secondary flow intensity) of the free surface of the cross section CYP2-CYP7 predicted by the fixed bed simulation of the low flow condition 2 in the embodiment of the application The effect comparison chart of the transverse velocity component (i.e., the secondary flow intensity) of the free surface of the cross section CYP2-CYP7 predicted by the fixed bed simulation of the low flow condition 2 in the embodiment of the application, wherein the red dotted line represents the ADCP measured data result, the green line represents the result of considering only the curvature induced secondary flow effect, and the blue line represents the result of considering the density gradient and the bend circulation interaction. Figure 6 (a) of FIG. 1 is a comparison chart of the secondary flow intensity simulation result and the measured result of the cross section CYP2 in the condition 2, Figure 6 (b) of FIG. 1 is a comparison chart of the secondary flow intensity simulation result and the measured result of the cross section CYP3 in the condition 2, Figure 6 (c) of FIG. 1 is a comparison chart of the secondary flow intensity simulation result and the measured result of the cross section CYP4 in the condition 2, Figure 6 (d) of FIG. 1 is a comparison chart of the secondary flow intensity simulation result and the measured result of the cross section CYP5 in the condition 2, Figure 6 (e) of FIG. 1 is a comparison chart of the secondary flow intensity simulation result and the measured result of the cross section CYP6 in the condition 2, Figure 6 (f) of FIG. 1 is a comparison chart of the secondary flow intensity simulation result and the measured result of the cross section CYP7 in the condition 2. It can be seen from Figure 6 that compared with the two-dimensional model considering only the curvature induced secondary flow effect, the planar two-dimensional hydrodynamic-matter transport finite element model considering the density gradient and the bend circulation interaction is more matched with the measured data result.

[0162] Embodiment 2:

[0163] The computer readable storage medium of the embodiment, on which a computer program is stored, realizes the steps in the dimension reduction method for river hydrodynamic simulation of embodiment 1 when the program is executed by a processor.

[0164] The computer readable storage medium of the embodiment can be an internal storage unit of the terminal, such as a hard disk or a memory of the terminal; the computer readable storage medium of the embodiment can also be an external storage device of the terminal, such as a plug-in hard disk, a smart memory card, a secure digital card, a flash memory card, etc. equipped on the terminal; further, the computer readable storage medium can include both the internal storage unit and the external storage device of the terminal.

[0165] The computer readable storage medium of the embodiment is used to store a computer program and other programs and data required by the terminal, and can also be used to temporarily store data that has been output or will be output.

[0166] Embodiment 3:

[0167] The computer device of the embodiment includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the steps of the dimension reduction method for river hydrodynamic simulation of embodiment 1 when executing the program.

[0168] In the embodiment, the processor can be a central processing unit, and can also be other general-purpose processors, digital signal processors, application-specific integrated circuits, ready programmable gate arrays or other programmable logic devices, discrete gates 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 provide instructions and data for the processor. A part of the memory can also include non-volatile random access memory, for example, the memory can also store device type information.

[0169] Those skilled in the art should understand that the embodiments disclosed herein can be provided as a method, a system, or a computer program product. Therefore, the present solution can be in the form of a hardware embodiment, a software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present solution can be in the form of a computer program product implemented on one or more computer usable storage media (including but not limited to magnetic disk storage and optical storage, etc.) containing computer usable program code.

[0170] The present solution is described with reference to flowcharts and / or block diagrams of the method and computer program product according to the embodiments of the present solution, and it should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of the flows and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions; these computer program instructions can be provided to a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to produce a machine, so that the instructions executed by the computer or other programmable data processing devices produce a machine that implements the functions described in the flowcharts and / or block diagrams.Figure 1 one or more processes and / or blocks Figure 1 an apparatus for performing the functions specified in the flowchart

[0171] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the flowchart Figure 1 one or more processes and / or blocks Figure 1 an apparatus for performing the functions specified in the flowchart

[0172] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the flowchart Figure 1 one or more processes and / or blocks Figure 1 an apparatus for performing the functions specified in the flowchart

[0173] Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by computer programs instructing relevant hardware, and the programs can be stored in a computer-readable storage medium. When the programs are executed, they can include the processes of the above-mentioned embodiment methods. The storage medium can be a magnetic disc, an optical disc, a read-only memory (ROM), a random access memory (RAM), or the like.

[0174] The examples described in the present application are merely used to describe the preferred embodiments of the present application, and are not used to limit the concept and scope of the present application. Without departing from the design idea of the present application, various modifications and improvements of the technical solutions of the present application made by those of ordinary skill in the art should fall within the protection scope of the present application.

Claims

1. A method for dimensionality reduction of river hydrodynamics simulation, characterized in that, Comprise: Data collection; Construct a two-dimensional shallow water model based on shallow water equations, add the effect of curvature-induced secondary flow into the shallow water equations through the dispersion stress term to obtain modified shallow water equations; The expression of the modified shallow water equations is: ， ， ， where represents the material derivative, represents the x axis component of the velocity, represents the equivalent water depth, i.e. the volume of water per unit area, represents the x direction Reynolds stress, represents the horizontal coordinate axis parallel to the main flow direction of the river, represents the shear component of the Reynolds stress on the horizontal plane, represents the horizontal coordinate axis perpendicular to the main flow direction of the river, represents the vertically integrated x axis direction fluctuating kinetic energy of the velocity, , represents the vertical coordinate axis in the water depth direction, the river bed is z = 0, and the water surface is z = Y , represents the x axis direction velocity component true value and the water depth average value difference, , represents the x direction instantaneous velocity along the vertical direction distribution, represents the x direction water depth average velocity; , represents the vertically integrated x - y axis direction velocity fluctuation correlation term, due to symmetry, , represents the y axis direction velocity component true value and the water depth average value difference, , represents the y direction instantaneous velocity along the vertical direction distribution, represents the y direction water depth average velocity; represents the x axis component of the bed shear stress, represents the density of water, represents the gravitational acceleration, represents the free surface elevation relative to the horizontal datum plane, represents the y axis component of the velocity integrated along the water depth, represents the y direction Reynolds stress, represents the vertically integrated y axis direction fluctuating kinetic energy of the velocity, ; representing the bed shear stress y axial component, representing the wetted area fraction, is a storage coefficient related to the water depth, , representing time; Introduce the contribution of the density gradient to the angular momentum into the angular momentum conservation equation to obtain the angular momentum equation based on the influence of the density gradient; Couple the convection-diffusion equation considering the dispersion stress to construct a two-dimensional plane water power-matter transport finite element model; Calculate the average flow field of water depth and secondary flow intensity.

2. The method of claim 1, wherein, The data collection specifically includes: Obtain the parameter information of the river channel from the hydrological station, remote sensing monitoring system and historical measurement data, and the parameter information includes but is not limited to hydrological parameters, hydrodynamic parameters and topographic parameters.

3. The method of claim 2, wherein, A local reference frame is adopted, where s denotes the longitudinal direction, i.e. the main flow direction, n denotes the transverse direction; while it is assumed that the flow velocity has a simple vertical profile in s and n directions, and the velocity component in the main flow direction follows a power-law profile, the closed form expression of the dispersion stress term is obtained through coordinate transformation: ， ， ， wherein represents the magnitude of the mean current velocity, The three components of the dispersion stress represented in the local coordinate system are calculated as follows: ， ， ， where, represents the friction parameter; represents the radius of curvature of the streamline averaged over the water depth, which is positive when the flow is bending in the clockwise direction, R is positive, and negative otherwise; represents the dimensionless transverse velocity at the free surface; is calculated by the vorticity transport method.

4. The method of claim 3, wherein, The calculation step is as follows: First, the streamwise vorticity transport equation on the horizontal plane is: ， wherein, represents the streamwise component of the vorticity; represents the production term; represents the dissipation term; The streamwise component of vorticity is expressed as: ， wherein denotes the angular velocity, denotes the transverse velocity at the free surface; Assuming that the water depth changes slowly, the streamwise vorticity transport equation on the horizontal plane is directly given by which can be rewritten as: ， wherein, represents a coefficient of the production term; represents a von Karman constant, ; represents a coefficient of the dissipation term; The dimensionless transverse flow velocity at the free surface can be expressed as: 。 5. The method of claim 4, wherein, The expression of the angular momentum equation considering the density gradient is: ， wherein all represent empirical coefficients, represents a friction parameter, represents a 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 changed to: 。 6. The method of claim 5, wherein, Given the vertical distribution of the spanwise velocity and the concentration distribution, the dispersion stress is calculated by integrating the difference between the water depth related flux and the water depth average value; The convection-diffusion equation describing the transport of suspended sediment is rewritten as: wherein, denotes x the vertically integrated diffuse flux component in the direction of, denotes y the vertically integrated diffuse flux component in the direction of, denotes the erosion flux, denotes the deposition flux.

7. The method of claim 6, wherein, The expression of the two-dimensional plane water power-matter transport finite element model is: ， ， ， ， 。 8. A computer readable storage medium having stored thereon a computer program, characterized in that: The program is executed by the processor to realize the steps in the dimension reduction method for river water dynamics simulation in any one of claims 1-7.

9. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the program to realize the steps in the dimension reduction method for river water dynamics simulation in any one of claims 1-7.

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