Hydrodynamic modeling method for flood control four-pre-platform construction

Abstract

The invention discloses a hydrodynamic modeling method for flood control four-pre-platform construction, and particularly relates to the technical field of hydrodynamic model and flood forecast deduction, and the method comprises the steps: obtaining drainage basin basic data and flow data simulated by a hydrological model, and carrying out the preprocessing; the method comprises the following steps: constructing a drainage basin one-dimensional hydrodynamic model, extracting boundary conditions based on drainage basin basic data and flow data simulated by a hydrological model, arranging a drainage basin topological relation, carding a corresponding relation of the boundary conditions, taking one-dimensional section data contained in the boundary conditions as time sequence input, and sketching a modeling range of the drainage basin two-dimensional hydrodynamic model; and according to the drainage basin modeling range, constructing a drainage basin two-dimensional hydrodynamic model with a closed and independent partition scheme so as to facilitate parallel calculation of flood routing and realize evaluation and optimization of different flood control schemes.

Description

Technical Field

[0001] This invention relates to the field of hydrodynamic modeling and flood forecasting, specifically to a hydrodynamic modeling method for constructing a flood control four-prevention platform. Background Technology

[0002] In recent years, flood disasters have become increasingly frequent due to the combined effects of intensified climate change, natural environmental factors, and the negative impacts of human activities. These disasters are characterized by complex causes, distinct features, and high destructiveness, necessitating mature flood forecasting technologies to address their shortcomings. While the "four early warnings" (early warning, early warning, early warning, and early warning systems) for flood control have seen significant development and application, traditional hydrodynamic modeling methods for building digital platforms face challenges in terms of computational complexity, modeling complexity, and adaptability to complex scenarios. Furthermore, related fusion models present significant challenges in data fusion and model stability. Digital twin watershed technology, on the other hand, is limited by insufficient technological maturity, difficulties in data acquisition and processing, and problems with model coupling and integration. Current research needs to further focus on the application of digital twin watershed technologies for flood control to fully realize real-time monitoring, early warning, and simulation of flood disasters. Summary of the Invention

[0003] To overcome the shortcomings of existing digital simulations for flood forecasting, this invention provides a hydrodynamic modeling method for constructing a flood control four-prevention platform. This method can not only realize one-dimensional river flood evolution simulation and two-dimensional flood inundation simulation, but also be put into operation in the flood control four-prevention platform system to assist in high-precision digital forecasting across the entire basin. It provides technical support for real-time monitoring, early warning, and simulation of flood disasters, thereby solving the problems mentioned in the background art.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a hydrodynamic modeling method for the construction of a flood control four-prevention platform, comprising the following steps:

[0005] Step 1: Obtain basic watershed data and flow data simulated by hydrological models, and perform preprocessing;

[0006] Step 2: Extract boundary conditions from the flow data simulated by the hydrological model in Step 1, generalize the river network situation through basic watershed data, organize the watershed topology, and sort out the corresponding relationships of the boundary conditions;

[0007] Step 3: Construct a one-dimensional hydrodynamic model of the watershed, using the time series data of the one-dimensional cross-section as the boundary condition input, run the basic watershed data and the flow data simulated by the hydrological model, and delineate the modeling scope of the two-dimensional hydrodynamic model of the watershed.

[0008] Step 4: Based on the modeling scope of the two-dimensional hydrodynamic model of the watershed, construct a two-dimensional hydrodynamic model of the watershed with an independent partitioning scheme, and use the finite volume method to discretize and solve the two-dimensional unsteady shallow water control equations. By solving the depth-averaged two-dimensional shallow water equations, the unsteady evolution and inundation process of water flow within the watershed can be effectively simulated.

[0009] Preferably, the basic watershed data includes high-precision remote sensing images of the watershed, the centerline of the watershed river network, river cross-section data, and high-precision DEM data of the watershed. The flow data simulated by the hydrological model includes hourly measured flow and water level at hydrological stations.

[0010] Preferably, the one-dimensional hydrodynamic model of the watershed is controlled by the Saint-Venant equations, as follows:

[0011] The continuity equation reflects the water balance in the waterway, that is, the rate of change of storage capacity (first term) should be equal to the rate of change of flow rate along the channel (second term):

[0012] (1);

[0013] The equation of motion consists of two terms: the first term reflects the local acceleration at a fixed point; the second term reflects the convective acceleration caused by the uneven spatial distribution of the flow velocity; these two terms are called the inertial terms; the third term reflects the gravitational effect caused by the bottom slope; the fourth term reflects the influence of water depth; the third and fourth terms can be combined into one term, namely the water surface gradient; and the fifth term represents the frictional losses within and at the boundaries of the flow. This equation expresses how the combined action of gravity and pressure enables the flow to overcome the energy losses caused by inertial forces and frictional resistance, thereby achieving acceleration.

[0014] (2);

[0015] In the formula, and All are independent variables; For time; h is the distance along the flow path from a fixed cross-section of the waterway; both h and v are dependent variables. , , Corresponding to The water depth, average flow velocity, and bottom elevation at the cross-section of the water passage; This refers to the energy drop caused by frictional losses; It is the acceleration due to gravity; , Depend on , and Sure.

[0016] Preferably, the boundary conditions are determined by the interaction of water volume and momentum between the river boundary or the outside world along the river, and the watershed is modeled by a given flow process upstream and a given water level process or water level-flow relationship downstream.

[0017] (3);

[0018] Based on the water level at the first node of the river channel and the water level at the end of the river channel As free variables, the water level and flow rate at intermediate cross-sections are eliminated using the three-coefficient pursuit method. Finally, two equations are obtained relating the flow rates at the first and last cross-sections to the water levels at the first and last nodes. That is, the flow rates at the first and last cross-sections are expressed as a linear relationship between the water levels at the first and last nodes. The specific equations are as follows:

[0019] (4);

[0020] Where: α, β, ζ, θ, and η are all catch-up coefficients;

[0021] Express the cross-sectional flow rate as cross-sectional water level and the water level at the end of the river channel, sequentially from back to front. The linear function is given by the following recurrence relation:

[0022] (5);

[0023] ;

[0024] Similarly, starting from the first river section, we should try to express the cross-sectional flow rate as the water level at that cross-section and the water level at the first node of the river channel. Linear functions:

[0025] (6);

[0026] ;

[0027] After obtaining the water levels at the beginning and end of the river channel, the flow rates at the same cross-section can be calculated using equations (5) and (6):

[0028] (7);

[0029] Solving the system of equations simultaneously, we get:

[0030] (8);

[0031] Seek Then, substituting it into equation (7) yields the result. .

[0032] Preferably, the two-dimensional hydrodynamic model of the watershed is solved discretically using the finite volume method based on unstructured grids, as shown in the following formula:

[0033] (9);

[0034] The two-dimensional shallow water equation with average water depth is abbreviated as:

[0035] (10);

[0036] (11);

[0037] (12);

[0038] In the formula, For water depth; for Flow velocity in the direction; for Flow velocity in the direction; , For the source term, the expression is:

[0039] (13);

[0040] (14);

[0041] In the formula, The atmospheric pressure at the water surface; The elevation of the bottom of the bed surface; , The force exerted by the wind is expressed as:

[0042] (15);

[0043] (16);

[0044] In the formula, air density; , 10 above the water surface Wind speed at the location; This is the drag coefficient;

[0045] , The Coriolis force, in the Northern Hemisphere, is expressed as:

[0046] (17);

[0047] (18);

[0048] In the formula, Coriolis coefficient, ; Let be the angular velocity of Earth's rotation. ; Latitude;

[0049] , The riverbed resistance is expressed as:

[0050] (19);

[0051] (20);

[0052] In the formula, For roughness;

[0053] Equations (10), (11), and (12) can be written in vector form as follows:

[0054] (twenty one);

[0055] In the formula, , , They are respectively for time and space planes. , Partial derivatives in direction:

[0056] (twenty two).

[0057] The present invention has the following advantages:

[0058] (1) This invention uses high-precision geographic information basic data and real-time flood forecast data to construct a one-dimensional hydrodynamic model of the main river channel of the whole basin and construct a two-dimensional hydrodynamic model of the basin by considering the flood zone. It can realize the fine simulation of the flood process, including key links such as the generation, propagation and inundation of floods, which helps to more accurately predict the spatiotemporal distribution and intensity of floods and provide a scientific basis for flood control decision-making.

[0059] (2) Based on flood flow data and environmental data, the confluence evolution analysis is carried out to realize the multi-dimensional display and early warning of flood risk; various flood control simulation scenarios can be constructed based on the model, including different rainfall intensities and different terrain conditions, to realize the effective combination of the model and actual observation data, which improves the real-time performance, accuracy and adaptability of the hydrodynamic model. This helps to test and optimize the flood control plan in the simulation, and improve the pertinence and operability of the plan. Compared with the existing technology, the present invention considers the geographical characteristics of the basin and combines one-dimensional hydrodynamic model and two-dimensional hydrodynamic model to realize high-precision simulation and deduction of basin floods, providing technical innovation simulation and decision support for flood control and disaster reduction. Attached Figure Description

[0060] Figure 1 This invention provides a one-dimensional model of the river section above station a in river section A. Detailed Implementation

[0061] The following specific embodiments illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0062] Taking the AB watershed as the research object and the method of this invention as the specific implementation method;

[0063] Embodiments of the present invention provide a hydrodynamic modeling method for the construction of a flood control four-prevention platform, comprising the following steps:

[0064] Step 1: Obtain basic watershed data and flow data simulated by hydrological models, and perform preprocessing;

[0065] In one exemplary instance, the basic watershed data includes high-precision remote sensing images of the watershed, the centerline of the watershed river network, river cross-section data, and high-precision DEM data of the watershed, which together generalize the actual topographic undulations along the river course. The flow data simulated by the hydrological model includes hourly measured flow and water level at hydrological stations, which can be used as boundary conditions for the one-dimensional hydrodynamic model of the watershed.

[0066] Step 2: Construct a one-dimensional hydrodynamic model of the watershed. Multiple models are used to refine the flood process, allowing for the running of measured flow data and hydrological model simulation data. Based on the watershed basic data from Step 1 and the flow data simulated by the hydrological model, boundary conditions are extracted, watershed topological relationships are organized, the correspondence of boundary conditions is clarified, the river network situation is generalized, information on important stations is compiled, and optimal hydrodynamic cross-sectional data is selected to set the process data such as water level and flow at the cross-sections. A total of 191 cross-sections are included in the boundary conditions, with three types: flow boundary, concentrated inflow boundary, and water level boundary. The one-dimensional cross-sectional data included in the boundary conditions serves as time series input, outlining the modeling scope of the two-dimensional hydrodynamic model of the watershed.

[0067] Using ArcGIS tools, based on the interpretation of 2m precision remote sensing images and 5m precision DEM data, the two-dimensional modeling range of the AB watershed is delineated. The river boundary needs to be drawn in accordance with the top of the river embankment in the remote sensing image to ensure model coverage.

[0068] In one exemplary instance, the domestic IFMS hydrodynamic model software is selected, and the hourly flow hydrological data of the basin is used as the time series input to construct a one-dimensional hydrodynamic model of the main river channel of the basin. It can cover the operation of the entire basin, as well as the operation of the main and tributary channels in different areas. The measured flow data and hydrological model simulation data are used to realize the refined simulation and deduction of the whole process.

[0069] The one-dimensional hydrodynamic model of the watershed is controlled by the Saint-Venant equations and describes the river flow motion with typical one-dimensional properties, as follows:

[0070] The continuity equation reflects the water balance in the waterway, that is, the rate of change of storage capacity (first term) should be equal to the rate of change of flow rate along the channel (second term):

[0071] (1);

[0072] The equation of motion consists of two terms: the first term reflects the local acceleration at a fixed point; the second term reflects the convective acceleration caused by the uneven spatial distribution of the flow velocity; these two terms are called the inertial terms; the third term reflects the gravitational effect caused by the bottom slope; the fourth term reflects the influence of water depth; the third and fourth terms can be combined into one term, namely the water surface gradient; and the fifth term represents the frictional losses within and at the boundaries of the flow. This equation expresses how the combined action of gravity and pressure enables the flow to overcome the energy losses caused by inertial forces and frictional resistance, thereby achieving acceleration.

[0073] (2);

[0074] In the formula, and All are independent variables; For time; h is the distance along the flow path from a fixed cross-section of the waterway; both h and v are dependent variables. , , Corresponding to The water depth, average flow velocity, and bottom elevation at the cross-section of the water passage; This is due to the energy drop caused by frictional losses; It is the acceleration due to gravity; , Depend on , and Sure.

[0075] In one exemplary instance, the boundary conditions are determined by the interaction of water volume and momentum between the river boundary or the outside world along the river, and a one-dimensional hydrodynamic model of the watershed is achieved by giving a flow process upstream and a water level process or water level-flow relationship downstream.

[0076] (3);

[0077] Based on the water level at the first node of the river channel and the water level at the end of the river channel As free variables, the water level and flow rate at intermediate cross-sections are eliminated using the three-coefficient pursuit method. Finally, two equations are obtained relating the flow rates at the first and last cross-sections to the water levels at the first and last nodes. That is, the flow rates at the first and last cross-sections are expressed as a linear relationship between the water levels at the first and last nodes. The specific equations are as follows:

[0078] (4);

[0079] Where: α, β, ζ, θ, and η are all catch-up coefficients;

[0080] Express the cross-sectional flow rate as cross-sectional water level and the water level at the end of the river channel, sequentially from back to front. The linear function is given by the following recurrence relation:

[0081] (5);

[0082] ;

[0083] Similarly, starting from the first river section, we should try to express the cross-sectional flow rate as the water level at that cross-section and the water level at the first node of the river channel. Linear functions:

[0084] (6);

[0085] ;

[0086] After obtaining the water levels at the beginning and end of the river channel, the flow rates at the same cross-section can be calculated using equations (5) and (6):

[0087] (7);

[0088] Solving the system of equations simultaneously, we get:

[0089] (8);

[0090] Seek Then, substituting it into equation (7) yields the result. .

[0091] One-dimensional hydrodynamic model of the watershed, such as Figure 1 As shown ( Figure 1 (Modeling of the river section above station a in river segment A).

[0092] The calculation order for the one-dimensional hydrodynamic model of the watershed is as follows:

[0093] 1) Calculate the flood evolution of the main stream in river segment A (using important stations a1, a2, a3 as dividing nodes to construct river segment partition models such as a1-a2, a2-a3, a3-main stream outlet, etc.) and river segment B (using important stations b1, b2, b3 as dividing nodes to construct river segment partition models such as b1-b2, b2-b3, b3-main stream outlet, etc.). Add all hydrological forecast flows to the main stream model and perform calculations. Replace the original tributary one-dimensional model with the corresponding hydrological model forecast flows at the confluence points.

[0094] 2) Calculate the flood evolution of tributaries, extract the water level process at the main stream section where the tributary flows into the main stream, and use it as the hydrological boundary condition at the outlet section of the tributary model. Perform the calculation. The tributary models are river segments C, D, E, F, and G.

[0095] 3) Based on the flow processes at stations a1 and b1, and according to the flood diversion scheduling rules, the flow is diverted, and the water diversion / inflow conditions are set at the corresponding boundaries. Calculate the flood evolution of the H diversion channel, the A river segment (below station a1), and the B river segment (below station b1).

[0096] The main channel of the one-dimensional hydrodynamic model of the watershed is used to calculate the evolution of floodwaters. After the water level exceeds the embankment and overflows, the water flows into the two-dimensional hydrodynamic model of the watershed. Based on the modeling scope of the AB watershed, n two-dimensional segmented models are constructed to enrich the demonstration of the flood evolution process. Based on the model calculation results, different flood control schemes can be evaluated and optimized.

[0097] The premise of parallel computation of the two-dimensional hydrodynamic model of the watershed is that each model is independent and there is no exchange of water volume. Therefore, the calculation range is divided into left and right banks with the one-dimensional river channel as the boundary. Then, adjacent areas are merged to form a closed and independent partitioning scheme. The flood inundation range only occurs within each model. After the calculation of the one-dimensional model is completed, the overflow section is retrieved, the overflow water level is converted into flow rate, and loaded into the corresponding two-dimensional hydrodynamic model of the watershed for calculation.

[0098] Step 3: Based on the watershed modeling scope, construct a two-dimensional hydrodynamic model of the watershed with closed and independent partitioning schemes to enable parallel computation of flood evolution and to evaluate and optimize different flood control schemes;

[0099] In one exemplary instance, the two-dimensional hydrodynamic model of the watershed is solved discretically using the finite volume method based on unstructured meshes, as shown in the following formula:

[0100] (9);

[0101] The two-dimensional shallow water equation with average water depth is abbreviated as:

[0102] (10);

[0103] (11);

[0104] (12);

[0105] In the formula, For water depth; for Flow velocity in the direction; for Flow velocity in the direction; , For the source term, the expression is:

[0106] (13);

[0107] (14);

[0108] In the formula, The atmospheric pressure at the water surface; The elevation of the bottom of the bed surface; , The force exerted by the wind is expressed as:

[0109] (15);

[0110] (16);

[0111] In the formula, air density; , 10 above the water surface Wind speed at the location; This is the drag coefficient;

[0112] , The Coriolis force, in the Northern Hemisphere, is expressed as:

[0113] (17);

[0114] (18);

[0115] In the formula, Coriolis coefficient, ; Let be the angular velocity of Earth's rotation. ; Latitude;

[0116] , The riverbed resistance is expressed as:

[0117] (19);

[0118] (20);

[0119] In the formula, For roughness;

[0120] Equations (10), (11), and (12) can be written in vector form as follows:

[0121] (twenty one);

[0122] In the formula, , , They are respectively for time and space planes. , Partial derivatives in direction:

[0123] (twenty two).

[0124] Step 4: Optimize the model simulation efficiency and the display effect of the "four predictions" platform, and analyze the characteristics of watershed floods and the applicability of the model;

[0125] In one exemplary instance, the method of this invention enables refined simulation of flood processes, ensuring that the model's calculation of the 7-day flood evolution takes no more than 5 minutes. It dynamically simulates the evolution of flow and integrates the four-prevention platform system for display, analyzing the characteristics of basin floods and the applicability of the model. This invention more accurately predicts the spatiotemporal distribution and intensity of floods, providing a scientific basis for flood control decisions; it significantly improves computational efficiency by utilizing distributed parallel acceleration algorithms; and it will enhance flood early warning capabilities, support flood control drills and contingency plan development, and promote the informatization and intelligentization of flood control.

[0126] Although the present invention has been described in detail above with general descriptions and specific embodiments, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

Claims

1. A hydrodynamic modeling method for the construction of a flood control four-prevention platform, characterized in that: Includes the following steps: Step 1: Obtain basic watershed data and flow data simulated by hydrological models, and perform preprocessing; Step 2: Extract boundary conditions from the flow data simulated by the hydrological model in Step 1, generalize the river network situation through basic watershed data, organize the watershed topology, and sort out the corresponding relationships of the boundary conditions; Step 3: Construct a one-dimensional hydrodynamic model of the watershed, using the time series data of the one-dimensional cross-section as the boundary condition input, run the basic watershed data and the flow data simulated by the hydrological model, and delineate the modeling scope of the two-dimensional hydrodynamic model of the watershed. Step 4: Based on the modeling scope of the two-dimensional hydrodynamic model of the watershed, construct a two-dimensional hydrodynamic model of the watershed with an independent partitioning scheme, and use the finite volume method to discretize and solve the two-dimensional unsteady shallow water control equations. By solving the depth-averaged two-dimensional shallow water equations, the unsteady evolution and inundation process of water flow within the watershed can be effectively simulated.

2. The hydrodynamic modeling method for constructing a flood control four-prevention platform according to claim 1, characterized in that: The basic data of the watershed includes high-precision remote sensing images of the watershed, the center line of the river network of the watershed, river cross-section data, and high-precision DEM data of the watershed. The flow data simulated by the hydrological model includes the flow and water level measured at hydrological stations every hour.

3. The hydrodynamic modeling method for constructing a flood control four-prevention platform according to claim 1, characterized in that: The specific one-dimensional hydrodynamic model of the watershed is as follows: The continuity equation reflects the water balance in the waterway, that is, the rate of change of storage capacity. Equal to the rate of change of flow along the path : （1）; Equations of motion The local acceleration at a fixed point is reflected, where A is the cross-sectional area of ​​the water passage. It reflects the convective acceleration caused by the uneven spatial distribution of flow velocity; It reflects the change in water depth along the flow path and is related to the effects of gravity and pressure; The friction loss inside and at the boundary of the water flow; Formula (2) expresses how the combined effect of gravity and pressure enables the water flow to overcome the energy loss caused by inertial force and friction to gain acceleration; （2）； In the formula, and All are independent variables. For time; Let h be the distance along the flow path from a fixed cross-section of the waterway; h and v are both dependent variables. , Corresponding to The water depth and average flow velocity at the cross-section; Let i be the acceleration due to gravity, and i be the cross-section.

4. The hydrodynamic modeling method for constructing a flood control four-prevention platform according to claim 1, characterized in that: The boundary conditions are determined by the interaction of water volume and momentum between the river boundary or along its course and the external environment. A one-dimensional hydrodynamic model of the watershed is achieved by providing an upstream flow process and a downstream water level process or water level-flow relationship. （3）； in, , The flow rate and water level at section i are respectively. , These represent the flow rate and water level at section i+1, respectively; C i D i E i G i F i φ i All are coefficients, derived from the cross-sectional flow rate at the previous time step j. , Determine; Based on the water level at the first node of the river channel and the water level at the end of the river channel As free variables, the water level and flow rate at intermediate cross-sections are eliminated using the three-coefficient pursuit method. Finally, two equations are obtained relating the flow rates at the first and last cross-sections to the water levels at the first and last nodes, i.e., the flow rates at the first and last cross-sections. , The linear relationship between the water levels at the first and last nodes is shown below: （4）； in: , β, ζ, θ, η, and γ are all catch-up coefficients; Express the cross-sectional flow rate as cross-sectional water level sequentially from back to front. and the water level at the end of the river channel The linear function is given by the following recurrence relation: （5）； ； Q i η represents the flow rate at each cross-section, and Zi represents the water level at that cross-section; i This represents the water level response coefficient at this cross-section, reflecting Z. i Changes on Q i Direct impact; γ i L1 represents the water level transfer coefficient at the end node, reflecting the indirect impact of the downstream end on the upstream Qi; L2 represents the final cross-section. Starting from the first river section, the cross-sectional flow rate is expressed as the cross-sectional water level and the water level at the first node of the river channel. Linear functions: （6）； ； After obtaining the water levels at the beginning and end of the river channel, the flow rates at the same cross-section can be calculated using equations (5) and (6): （7）； Solving the system of equations simultaneously, we get: （8）； θ i The constant term represents the comprehensive term, which is obtained through formula (8). Then, substituting it into equation (7) yields the result. .

5. The hydrodynamic modeling method for constructing a flood control four-prevention platform according to claim 1, characterized in that: The two-dimensional hydrodynamic model of the watershed is solved discretically using the finite volume method based on unstructured grids, and the governing equations for the two-dimensional unsteady flow are as follows: （9）； In the formula, U = [h, hu, hv] T As a conserved physical quantity, E=[hu,hu] 2 +gh 2 / 2,huv] T H=[hv,huv,hv] 2 +gh 2 / 2] T They are , The directional convection term, S0 is the bottom slope source term, S f For friction source term; The depth-averaged two-dimensional shallow water equation is a simplification of three-dimensional flow. It assumes uniform vertical velocity and retains only the horizontal flow characteristics. The depth-averaged two-dimensional shallow water equation can be simplified as follows: （10）； （11）； (12); In the formula, For water depth; for Flow velocity in the direction; for Flow velocity in the direction; s x s y The source term contains the physical factors that drive the water flow and cause momentum changes, and its expression is: (13); (14); In the formula, The atmospheric pressure at the water surface; ρ is the elevation of the bottom of the bed; ρ is the density of water. , The force exerted by the wind is expressed as: (15); (16); In the formula, air density; , 10 above the water surface Wind speed at the location; This is the drag coefficient; , The Coriolis force, in the Northern Hemisphere, is expressed as: (17); (18); In the formula, Coriolis coefficient, ; Let be the angular velocity of Earth's rotation. ; Latitude; Riverbed resistance characterizes the energy loss caused by friction between water flow and the riverbed, and is usually expressed by Manning coefficient or roughness coefficient; , The riverbed resistance is expressed as: (19); (20); In the formula, For roughness; Equations (10), (11), and (12) can be written in vector form as follows: (21); In the formula, , , They are respectively for time and space planes. , The partial derivative in direction and the time derivative represent the change of a physical quantity over time, capturing the characteristics of unsteady flow; the spatial derivative describes the differences in the distribution of a physical quantity in a planar direction, reflecting the diffusion, convergence, or directional changes of water flow. (22)。 In the formula, h is the water depth; u is the flow velocity in the x direction; and v is the flow velocity in the y direction. , For source terms; The atmospheric pressure at the water surface; The elevation of the bottom of the bed surface; , The force exerted by wind; , For riverbed resistance; .

Images