A hydrodynamic simulation method considering the lodging of tall plants

Abstract

The present invention relates to a hydrodynamic simulation method considering the lodging of tall vegetation, including: data collection; determining the generalization mode of the studied vegetation in the model; establishing a hydrodynamic model based on the shallow water equation; judging the lodging mode of upright vegetation; and calculating the evolution of floods in tall vegetation. The present invention adds the vegetation resistance term into the shallow water equation in the form of a source term, and analyzes the resistance difference of the two modal changes of upright and lodging of tall vegetation in the vegetation resistance prediction model, determines the upright or lodging state of the vegetation by the flow velocity and water depth threshold, and then repeatedly iterates to perform explicit time advancement, calculates the process of flood evolution in the vegetation, and realizes the scientific and accurate prediction of the resistance of tall vegetation in the river channel.

Description

Technical Field

[0001] The invention relates to a two-dimensional hydrodynamic simulation method considering the lodging of tall vegetation, a hydraulic engineering design analysis method and an analysis and calculation method for the influence of vegetation on flood evolution in hydraulic engineering design. Background Art

[0002] Flood disasters often cause huge economic losses, and with the accelerated warming of the global climate, the frequency of flood disasters has increased significantly. In order to prevent and reduce disasters, it is necessary to study and analyze the flow laws of floods and provide a scientific basis for responding to disasters. A large number of naturally grown or artificially planted vegetation often appear in flood-passing areas, among which tall vegetation has a more significant flow-blocking effect than short vegetation. At present, the roughness coefficient of flood evolution simulation calculation in the field of water conservancy projects is often based on the degree of flow obstruction of land objects, and a constant roughness coefficient is set for each zone. The calculation process lacks adaptive dynamic adjustment that changes with the change of hydraulic elements. Tall vegetation has a phenomenon of lodging during the evolution of large floods, and the flood-blocking effect of the lodging vegetation is significantly reduced. The existing resistance prediction model lacks consideration of the vegetation lodging mode, resulting in deviations between the flood model prediction results and the flood measurement results. How to scientifically and accurately predict the resistance of tall vegetation in the river channel is a problem that needs to be solved. Summary of the invention

[0003] In order to overcome the problems of the prior art, the present invention proposes a hydrodynamic simulation method that takes into account the lodging of tall vegetation. The method fully considers the water blocking effect of tall vegetation during the evolution of large floods and the existence of lodging phenomenon, and the flood barrier effect of lodging vegetation is significantly reduced, thereby achieving accurate simulation of the evolution process of floods in vegetation floodplains.

[0004] The object of the present invention is achieved by: a hydrodynamic simulation method considering the lodging of tall plants, the steps of the method are as follows:

[0005] Step 1, data collection: collect data on hydrology, topography, plant species, and plant distribution in the study area as model input, and set initial conditions and boundary conditions;

[0006] Step 2, determine the generalization method of the vegetation under study in the model: determine the parameters representing plants in the vegetation, including: vegetation height, stem diameter, and vegetation density;

[0007] Step 3: Establish a hydrodynamic model based on the shallow water equation: The control equation based on the two-dimensional shallow water equation is shown in the following formula:

[0008] U t +F x +G y =S

[0009] U=[h,hu,hv]T

[0010]

[0011] S=[0,S x -f x ,S y -f y ] T

[0012] Among them: U is the conserved quantity; t is time; U t is the time partial derivative of the conserved quantity U at time t; x and y are Cartesian coordinates; u is the water flow velocity in the x direction; v is the water flow velocity in the y direction; F and G represent numerical fluxes; F x is the numerical flux in the x direction; G y is the numerical flux in the y direction; S is the terrain source term; S x is the terrain source term in the x direction, f x is the resistance of vegetation in the x direction; S y is the terrain source term in the y direction, f y is the resistance of vegetation in the y direction; h is the water depth at the current moment; g is the acceleration of gravity; T is the matrix transposition sign;

[0013] Step 4: Determine the lodging mode of upright vegetation: Determine whether some vegetation has fallen over based on the water flow conditions in the entire area, and calculate the resistance when the vegetation is in an upright state:

[0014]

[0015] Where: N is the number of vegetation per unit area; C D is the drag coefficient within the vegetation group; b v is the diameter of the vegetation stem; h v is the height of the vegetation stem;

[0016] When the product of flow velocity and water depth exceeds the threshold value Cr of vegetation lodging, the tall stalks will lodging, and the water blocking effect of vegetation is the resistance value in the upright state which is reduced according to the reduction coefficient k1;

[0017] Step 5, calculation of flood evolution in tall vegetation: Discretize the control equation based on the finite volume method, use square grids to discretize the calculation area, use the approximate Riemann solution to calculate the grid flux, and perform iterative calculations when the time step meets the CFL condition:

[0018]

[0019] Among them: U i,jis the conservation quantity of the i-th and j-th grid cells; i and j represent the grid cell number or the number of the boundary in a certain grid cell; Δt is the time step; F E 、F W , G N , G S are the flux vectors of the east, west, north and south interfaces respectively; k is the kth time step; Δx is the change in x in time step Δt; Δy is the change in y in time step Δt;

[0020] Step 6: In each time step, all grids are traversed to perform the calculations in steps 4 and 5, and then time is advanced. In subsequent time steps, each grid is tested for the upright or fallen modal state of vegetation, and the resistance source term is updated before time stepping calculation.

[0021] The advantages and beneficial effects of the present invention are as follows: the present invention adds the vegetation resistance term into the shallow water equation in the form of a source term, and analyzes the resistance difference of the two modal changes of the tall vegetation, namely, upright and fallen, in the vegetation resistance prediction model, and determines the upright or fallen state of the vegetation by the flow velocity and water depth threshold, and then repeatedly iterates to advance the explicit time, calculates the process of the evolution of the flood in the vegetation, and realizes the scientific and accurate prediction of the resistance of the tall vegetation in the river. The present invention is suitable for the prediction of the resistance of the tall vegetation in the full mode from "upright" to "fallen" of the identifiable vegetation in the evolution of non-steady flood waves, which can not only deepen the theoretical basis of the water flow resistance of the vegetated river channel and improve the accuracy of the flood evolution model prediction, but also has important practical significance in realizing flood prevention and disaster reduction, flood management, and rational use of beach. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0023] Figure 1 is a flow chart of the method described in an embodiment of the present invention;

[0024] Figure 2 2 is a schematic diagram comparing the hydrodynamic simulation results of the application example described in the embodiment of the present invention. DETAILED DESCRIPTION

[0025] Example:

[0026] This embodiment is a hydrodynamic simulation method considering the lodging of tall plants, and the steps of the method are as follows:

[0027] Step 1, data collection: Collect data on hydrology, topography, plant species, and plant distribution in the study area as model input, and set initial conditions and boundary conditions.

[0028] Hydrology includes local rainfall, annual flood flow, and the water level that floods can reach. Topography mainly includes river channels, areas flooded by floods, and topography of flood-related areas. Plant species mainly focus on tall plants, including the height of tall plants before and after lodging.

[0029] Setting the initial conditions includes: selecting a specific research area, for example, selecting a river channel planted with dense tall corn stalks. The shape of the river channel, the width, depth, flood inundation, flood flow, and roughness of the river channel, and setting the relevant initial state of vegetation to be all upright.

[0030] Application example (the following steps are a continuation of this application example): For a river with tall vegetation, Figure 2 In the middle oblique line part, flood evolution simulation is carried out to compare the hydrodynamic simulation results taking vegetation lodging into account and the hydrodynamic simulation results with constant roughness without taking vegetation lodging into account. The steps of hydrodynamic simulation taking vegetation lodging into account are described as follows:

[0031] Step 2, determine the generalization method of the vegetation under study in the model: determine the parameters representing plants in the vegetation, including: vegetation height, stem diameter, and vegetation density.

[0032] The research object of the application example is tall lodging vegetation, the height of the vegetation stem is about h v = 1.2m, the diameter of the vegetation stem is about b v =0.04m, the vegetation density is about n=9 plants per square meter. For other types of vegetation, characteristic parameters such as vegetation height, stems, density, etc. need to be adjusted.

[0033] Step 3, establish a hydrodynamic model based on the shallow water equation: Flood evolution calculation is performed based on the two-dimensional shallow water equation, and the vegetation resistance term is added to the shallow water equation in the form of a source term. The control equation is discretized using the finite volume method, and the flow field is obtained by time advancement calculation based on the explicit time format. The control equation based on the two-dimensional shallow water equation is shown in the following formula:

[0034] U t +F x +G y =S

[0035] U=[h,hu,hv] T

[0036]

[0037] S=[0,S x -f x ,S y -f y ] T

[0038] Among them: U is the conserved quantity; t is time; U t is the time partial derivative of the conserved quantity U at time t; x and y are Cartesian coordinates; u is the water flow velocity in the x direction; v is the water flow velocity in the y direction; F and G represent numerical fluxes; F x is the numerical flux in the x direction; G y is the numerical flux in the y direction; S is the terrain source term; S x is the terrain source term in the x direction, f x is the resistance of vegetation in the x direction; S y is the terrain source term in the y direction, f y is the resistance of vegetation in the y direction; h is the water depth at the current moment, in meters; g is the acceleration due to gravity, which is 9.8m 2 / s; T is the matrix transposition symbol;

[0039] Step 4: Determine the lodging mode of upright vegetation: Determine whether some vegetation has fallen over based on the water flow conditions in the entire area, and calculate the resistance when the vegetation is in an upright state:

[0040]

[0041] Where: N is the number of vegetation per unit area; C D is the drag coefficient within the vegetation group, usually taken as 0.9; b v is the diameter of the vegetation stem; h v is the height of the vegetation stem.

[0042] When the product of flow velocity and water depth exceeds the threshold value Cr of vegetation lodging, the tall stalks will lodging, and the water resistance of the vegetation will be reduced by about 10% to 30% of the upright state. The reduction coefficient is k1, and the specific value is different for different types of vegetation and needs to be determined experimentally. Therefore, the resistance of the lodging vegetation will be considered by multiplying the resistance in the upright state by the reduction coefficient, and different types of vegetation will select different reduction coefficients.

[0043]

[0044] Step 5, calculation of flood evolution in tall vegetation: Discrete the control equation based on the finite volume method, use square grids to discretize the calculation area, use the approximate Riemann solution to calculate the grid flux, and the time step meets the CFL (Courant-Friedrichs-Lewy) condition for iterative calculation:

[0045]

[0046] Among them: U i,jis the conservation quantity of the i-th and j-th grid cells; i and j represent the grid cell number or the number of the boundary in a certain grid cell; Δt is the time step; F E 、F W , G N , G S are the flux vectors of the east, west, north and south interfaces respectively; k is the kth time step; Δx is the change in x in time step Δt; Δy is the change in y in time step Δt.

[0047] Step 6: In each time step, all grids are traversed to perform the calculations in steps 4 and 5, and then time is advanced. In subsequent time steps, each grid is tested for the upright or fallen modal state of vegetation, and the resistance source term is updated before time stepping calculation.

[0048] The above simulation can be used to determine the water depth and velocity threshold of some areas where vegetation has fallen, through hydrodynamic calculation, to reach the threshold Cr of characteristic vegetation falling, and update the resistance size in this area. The water resistance of vegetation is k1 = 0.2 times that of the upright state. Therefore, the resistance of the fallen vegetation will be considered by multiplying the resistance of the upright state by the reduction coefficient. On this basis, the hydrodynamic evolution calculation will continue.

[0049] Figure 2 Shown is a comparison between the hydrodynamic simulation results of considering vegetation lodging (dark part) and not considering vegetation lodging (light part) in the application example. The results show that the maximum flood inundation range of the hydrodynamic simulation method considering vegetation lodging is slightly larger than the maximum flood inundation area of ​​the flood inundation range not considering the characteristics of vegetation lodging, which is closer to the actual inundation situation.

[0050] Finally, it should be noted that the above is only used to illustrate the technical solution of the present invention and is not intended to limit it. Although the present invention has been described in detail with reference to the preferred arrangement scheme, a person skilled in the art should understand that the technical solution of the present invention (such as the environment of the river channel, the application of various formulas, the sequence of steps, etc.) may be modified or replaced by equivalents without departing from the spirit and scope of the technical solution of the present invention.

Claims

1. A hydrodynamic simulation method considering the lodging of tall plants, characterized in that: The steps of the method are as follows: Step 1, data collection: collect data on hydrology, topography, plant species, and plant distribution in the study area as model input, and set initial conditions and boundary conditions; Step 2, determine the generalization method of the studied vegetation in the model: determine the parameters representing plants in the vegetation, including: vegetation height, stem diameter, and vegetation density; Step 3: Establish a hydrodynamic model based on the shallow water equation: The control equation based on the two-dimensional shallow water equation is shown in the following formula: U t +F x +G y =S U=[h,hu,hv] T S=[0,S x -f x ,S y -f y ] T Among them: U is the conserved quantity; t is time; U t is the time partial derivative of the conserved quantity U at time t; x and y are Cartesian coordinates; u is the water flow velocity in the x direction; v is the water flow velocity in the y direction; F and G represent numerical fluxes; F x is the numerical flux in the x direction; G y is the numerical flux in the y direction; S is the terrain source term; S x is the terrain source term in the x direction, f x is the resistance of vegetation in the x direction; S y is the terrain source term in the y direction, f y is the resistance of vegetation in the y direction; h is the water depth at the current moment; g is the acceleration of gravity; T is the matrix transposition sign; Step 4: Determine the lodging mode of upright vegetation: Determine whether some vegetation has fallen over based on the water flow conditions in the entire area, and calculate the resistance when the vegetation is in an upright state: Where: N is the number of vegetation per unit area; C D is the drag coefficient within the vegetation group; b v is the diameter of the vegetation stem; h v is the height of the vegetation stem; When the product of flow velocity and water depth exceeds the threshold of vegetation lodging, tall stalks will fall over, and the water blocking effect of vegetation will be k1 times that of the upright state. Among them: Cr is the lodging threshold of vegetation; Step 5, calculation of flood evolution in tall vegetation: Discrete the control equation based on the finite volume method, use square grids to discretize the calculation area, use the approximate Riemann solution to calculate the grid flux, and perform iterative calculations when the time step meets the CFL condition: Among them: U i,j is the conservation quantity of the i-th and j-th grid cells; i and j represent the grid cell number or the number of the boundary in a certain grid cell; Δt is the time step; F E 、F W , G N , G S are the flux vectors of the east, west, north and south interfaces respectively; k is the kth time step; Δx is the change in x in time step Δt; Δy is the change in y in time step Δt; Step 6: In each time step, all grids are traversed to perform the calculations in steps 4 and 5 and then time is advanced; in subsequent time steps, each grid is tested for the upright or fallen modal state of vegetation, and the resistance source term is updated before time stepping calculation.

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