CN114547869B - Method for processing flow boundary under two-dimensional non-structural dry beach condition - Google Patents
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Abstract
The invention discloses a method for processing a flow boundary under a two-dimensional non-structural dry beach condition. And aiming at the initial anhydrous dry beach state in the calculation area, selecting inlet sides corresponding to all inflow units to form a control section, and iteratively calculating the water level value of the inlet at the initial calculation moment according to the critical flow condition so as to obtain the water depth value corresponding to all the inlet units. And according to the corresponding relation between the water depth and the flow speed in the Manning formula, calculating the water depth value and the inflow of each inlet unit to obtain the normal flow speed at the inlet side corresponding to the inlet unit, and further obtaining the normal numerical flux passing through each inlet side. The method can accurately determine the number of inlet units of real inflow under the dry beach condition, reasonably distribute the flow value of the inlet into each inlet unit of a calculation area, improve the processing precision of the flow boundary under the two-dimensional non-structural dry beach condition, further improve the overall calculation precision of the flood evolution process, and effectively make up the defects of the traditional processing method.
Description
Technical Field
The invention belongs to the technical field of hydraulic engineering, and particularly relates to a method for processing a flow boundary under a two-dimensional non-structural dry beach condition.
Background
The two-dimensional flood routing calculation is an important service in the field of flood control and disaster reduction, and a hydrodynamic model capable of accurately simulating the flood routing process is an important tool in the field. Since the twenty-first century, the Godunov format based on solving the Riemann approximate solution is a main calculation format in the field of flood evolution analysis and calculation due to the strong shock wave capturing and large gradient water surface simulation capability of the Godunov format. In order to adapt to the complex calculation region boundary, the solution of the model is usually to perform non-structural discretization on a two-dimensional shallow water control equation by using a finite volume method with good conservative performance.
In engineering application, a two-dimensional flood routing model is often used for simulating the routing condition of downstream flood after flood discharge in a stagnant flood area or dam break. Under the situation, the calculation area is usually free of water flow in an initial state, namely belongs to a dry beach state, a flow boundary condition is usually given at a flood diversion opening position or a dam break opening position of a stagnant flood storage area, and then a flood evolution process is simulated through a two-dimensional flood evolution model. Under dry beach conditions, how to make the water flow accurately enter each inlet unit is a difficult problem. It is now common practice to give a very small water depth value in the inlet unit in advance, and assign the inflow value according to the weight of the total length of the inlet edge occupied by the corresponding edge of the inlet unit, so that each inlet unit has water entering. The method has two defects that firstly, the real inflow scene is damaged by the given initial water depth value of the inlet unit, because the bottom elevations of all the inlet units are usually greatly different, and in the initial state of calculation, not all the inlet units can have water flow to enter at the beginning; another drawback is that when the inlet flow distribution is performed, the flow entering each unit is related to the existing water depth of the unit, and the larger the water depth of the corresponding unit is, the larger the entering flow is. How to more accurately process the flow boundary under the condition of the two-dimensional non-structural dry beach is still a hotspot and difficult problem in the current field.
Disclosure of Invention
The invention aims to provide a method for processing a flow boundary under a two-dimensional non-structural dry beach condition, which can accurately distribute a flow value of an inlet into each inlet unit of a calculation area, improve the processing precision of the flow boundary under the two-dimensional non-structural dry beach condition and further improve the overall calculation precision of a flood evolution process.
The invention is realized by the following technical scheme:
a method for processing a flow boundary under a two-dimensional non-structural dry beach condition comprises the steps of connecting all inlet sides corresponding to water flow inlet units to form a one-dimensional inlet control section at the initial stage of calculation, calculating a water level value corresponding to an inflow flow value under the section at the initial moment according to a critical flow condition, wherein the water level value minus the bottom elevation of the inlet units is the water depth value of each inlet unit, and distributing the inflow of each inlet unit according to the corresponding relation between the water depth value of each inlet unit and the flow speed of the inlet sides in the normal direction;
the method comprises the following specific steps:
1) Acquiring basic data required by calculation, wherein the basic data mainly comprises topographic data, land utilization type data and inflow flow process data;
2) Dividing a calculation area by adopting a quadrilateral or triangular non-structural grid, and after division is finished, assigning a grid elevation value by adopting a flat-bottom model mode, namely assigning a bottom elevation value to a central point of a non-structural grid unit by adopting terrain data of the area, wherein the terrain is flat in each calculation unit; assigning roughness values to the grid cells according to the land utilization type data of the calculation region; the calculated initial water depth and the flow velocity value are both set to be 0, and the dry beach calculation condition is met;
3) Selecting the upper boundary of the calculation area as a flow boundary, wherein a unit corresponding to the boundary is called an inlet unit, and a boundary edge corresponding to each inlet unit is an inlet edge; selecting the lower boundary of the calculation area as a free outflow boundary, wherein a unit corresponding to the boundary is called an outlet unit; the units inside the calculation region, except for the inlet unit and the outlet unit, are called conventional units;
4) Obtaining the inlet flow value Q corresponding to the t moment t Obtaining and calculating time step dt according to the CFL condition;
5) Without loss of generality, at the start of the calculation step t =0, Q is assumed 0 The value of (A) is not 0, the inlet edges corresponding to the inlet units are connected to form a one-dimensional inlet control section, and the iterative solution Q is obtained according to the critical flow condition 0 Corresponding control section water level Z 0 (ii) a The water level value Z 0 If it is higher than the bottom elevation Z of the ith inlet unit i Then use Z 0 Minus Z i A water depth value, denoted H, of the inlet cell may be obtained i On the contrary, the water level value Z 0 If it is lower than or equal to the bottom elevation Z of the ith inlet unit i Then the water depth H of the unit i Is 0;
6) According to the Manning formula, the proportional correlation relationship exists between the flow velocity and the 2/3 power of the water depth at each position in the calculation area, and according to the correlation relationship, the flow velocity in the normal direction of the inlet side corresponding to the inlet unit is calculated according to the water depth value and the flow value at the inlet of each inlet unit;
7) According to the water depth value of the inlet unit and the normal direction flow speed of the inlet edge corresponding to the inlet unit, calculating a normal numerical flux value passing through the inlet edge corresponding to each inlet unit;
8) Describing the flood motion process by adopting a complete two-dimensional shallow water equation set, and calculating the numerical flux between the conventional units in the region by adopting an approximate Riemann solution in a Roe format; calculating the numerical flux of the boundary edge of the lower boundary free outflow; summing the numerical flux passing through each unit, and updating the central hydraulic element value of each unit to the t + dt moment;
9) Let t = t + dt, repeat steps 4) -8) until the calculation is finished;
further, the critical flow conditions in step 5) are shown as follows:
in the formula, A (Z) 0 ) For controlling the water level of the cross-section at the inlet to be Z 0 Corresponding area of water passage, H (Z) 0 ) For controlling the water level of the cross-section at the inlet to be Z 0 Time corresponding control section averagingThe water depth g is the acceleration of gravity.
Further, the flow velocity in the normal direction of the inlet edge corresponding to each inlet unit in the step 6) is as follows:
in the formula of U i The flow velocity in the normal direction of the ith inlet edge, L i Is the length of the ith inlet edge, and n is the total number of inlet units at the flow boundary.
Further, the numerical flux through the ith inlet edge of the flow boundary in step 7) is shown as follows:
in the formula, F i ＊ Is the numerical flux of the ith entry edge normal direction, n x ，n y The component of the unit vector of the normal direction of the ith inlet edge in the x direction and the component of the unit vector in the y direction are respectively, and g is the gravity acceleration.
The invention has the advantages and beneficial effects that:
the method can accurately determine the number of the real inlet units under the dry beach condition, can accurately and effectively distribute the inlet flow value under the two-dimensional non-structural dry beach condition into each inflow unit, more reasonably considers the movement characteristics of water flow at the inlet of the dry beach under the condition of ensuring the conservation of the inlet flow at the inlet, and provides a new solution for the inflow boundary treatment of the dry beach situation under the numerical frame of the two-dimensional non-structural finite volume method.
Drawings
FIG. 1 is a flow chart of a method for processing a flow boundary under a two-dimensional unstructured beach condition according to the present invention;
FIG. 2 is a schematic view of an inlet control section formed by connecting inlet sides of inlet units;
in the figure Z 0 Is the initial flow rate Q 0 Iterative computation through critical flow conditionsThe water level value obtained later;
FIG. 3 is a comparison graph of calculation results of the Toce river arithmetic example;
in the figure, (a) is a water depth distribution calculation result of the conventional flow boundary processing method, and in the figure, (b) is a water depth distribution calculation result of the flow boundary processing method proposed by the present invention.
Detailed Description
The first embodiment is as follows:
the invention will be further described with reference to fig. 1 and the examples.
The invention relates to a method for processing a flow boundary under a two-dimensional non-structural dry beach condition. Considering the characteristic of water-free distribution of the inlet units during initial calculation, in order to correctly determine the water flow distribution of the inlet units, connecting the corresponding inlet edges of the water flow inlet units to form a one-dimensional inlet control section, calculating the water level value corresponding to the inflow flow value under the section at the initial moment according to the critical flow condition, and subtracting the bottom elevation of the inlet units from the water level value to obtain the water depth value of each inlet unit. And distributing the inflow of each inlet unit according to the corresponding relation between the water depth value of the inlet unit and the flow speed in the normal direction of the inlet edge. The method comprises the following specific processes:
1) Acquiring basic data required by calculation, wherein the basic data mainly comprises DLG topographic data with a scale not less than 1 ten thousand, and the data is mainly used for extracting geometric boundaries of a calculation area and performing elevation interpolation on a subdivided two-dimensional grid; land use type DOM data having a resolution of not less than 10m, the data being used mainly to set a roughness value required for calculating the area; and inflow flow process data.
2) Dividing a calculation area by adopting a quadrilateral or triangular non-structural grid, and after division is finished, assigning a grid elevation value by adopting a flat-bottom model mode, namely assigning a bottom elevation value to a central point of a non-structural grid unit by adopting terrain data of the area, wherein the terrain is flat in each calculation unit; assigning roughness values to the grid cells according to the land use type data of the calculation area; the calculated hydraulic power element values are all set at the central nodes of the grid units, the initial water depth and the flow rate value are all set to be 0, and the calculation condition that the initial water depth is the dry beach is met;
3) Selecting the upper boundary of the calculation area as a flow boundary, wherein a unit corresponding to the boundary is called an inlet unit, and a boundary edge corresponding to each inlet unit is an inlet edge; selecting the lower boundary of the calculation area as a free outflow boundary, wherein a unit corresponding to the boundary is called an outlet unit; the units inside the calculation region, except for the inlet unit and the outlet unit, are called conventional units;
4) Obtaining the inlet flow value Q corresponding to the t moment t Obtaining and calculating time step dt according to the CFL condition;
wherein u and v are flow velocity components of the center x and y directions of the grid unit, h is the depth of the center water of the grid unit, g is the gravity acceleration, and N is cfl Is the CFL number, dt is the calculation time step, L L,LR The distance between the center of the grid cell to the midpoint of the corresponding edge.
5) Without loss of generality, at the initial step t =0 of the calculation, Q is assumed 0 Is not 0, connecting the corresponding inlet edges of the inlet units to form a one-dimensional inlet control section, the schematic diagram of the control section is shown in figure 2, and iteratively solving Q according to the critical flow conditions 0 Corresponding control section water level Z 0 The critical flow conditions are shown below:
in the formula, Q 0 Is the value of the flow at the inlet at the initial moment, Z 0 Is Q under the critical flow condition 0 Corresponding water level value, A (Z) 0 ) Controlling the water level of the cross-section for the inlet to be Z 0 Corresponding area of water passage, H (Z) 0 ) Controlling the water level of the cross-section for the inlet to be Z 0 The average water depth of the corresponding inlet control section is measured, and g is the gravity acceleration.
The water level value Z 0 If it is higher than the bottom elevation Z of the ith inlet unit i Then use Z 0 Minus Z i The water depth value of the inlet unit can be obtained and is recorded as H i Otherwise, the water level value Z 0 If it is lower than or equal to the bottom elevation Z of the ith inlet unit i Then the water depth H of the unit i Is 0.
6) According to the Manning formula, there is a proportional correlation between the flow velocity and the water depth at each position in the calculation area to the power of 2/3, and according to the correlation, the water depth value H of each inlet unit i And the inflow rate Q t The normal direction flow speed U at the inlet edge corresponding to the inlet unit can be obtained i The specific formula is shown as the following formula:
in the formula, Q t Is the flow value at the inlet at time t, U i Flow velocity in the direction of the normal to the ith entry side, H i Is the water depth value, L, in the ith inlet unit i Is the length of the ith inlet edge, and n is the total number of inlet units at the flow boundary.
7) According to H at the inlet i And U i The value can be calculated through the normal numerical flux value of each inflow unit corresponding to the inflow edge, and the specific formula is as follows:
in the formula, F i ＊ Numerical flux, n, in the normal direction of the inlet edge of the ith strip x ，n y The component of the unit vector of the normal direction of the ith entry side in the x direction and the component of the unit vector of the normal direction of the ith entry side in the y direction are respectively, and g is the gravity acceleration.
8) Describing the flood motion process by adopting a complete two-dimensional shallow water equation set, and calculating the numerical flux between the conventional units in the region by adopting an approximate Riemann solution in a Roe format; calculating the numerical flux of the free outflow boundary edge of the lower boundary; summing the numerical flux passing through each unit, and updating the central hydraulic element value of each unit to the t + dt moment; the specific numerical solving process in this section can be seen in the following works (zhangda. Dam breach water flow numerical simulation based on Godunov format [ M ],2014, chinese water conservancy and hydropower press).
9) Let t = t + dt, repeat steps 4) -8) until the computation is finished.
FIG. 3 is a comparison chart of the calculation results of the Toce river calculation example. The basic case of this example is as follows: the ENEL-HYDRO established a physical model of about 5km upstream of the Rice city Toce river in Milan, italy, according to a scale of 1. The physical model is about 50m 11m in size. The model gives the distribution of elevation points of the river channel according to the space step length of 5cm, and accurately depicts the real topography of the Toce river. The test material of the physical model is concrete, so the roughness is calculated by 0.0162 recommended by CADAM. The upper end of the physical model is a flow inflow boundary, the lower end of the physical model is a free outflow boundary, the water depth in the calculation area under the initial condition is 0, and the dry beach calculation condition is met. Specific inflow boundary values and other detailed descriptions can be found in the following literature (zhangda, mathematical model of dam breach flow and its application study [ D ], university of qinghua, 2008.). During calculation, space step length of 0.2m is adopted to uniformly disperse calculation areas, and 21176 triangular grid units are formed. Fig. 3 (a) is a water depth distribution calculation result obtained by a conventional inflow boundary processing method, and fig. 3 (b) is a water depth distribution calculation result obtained by the method provided by the present invention, it can be seen through comparison that, in the conventional processing method, inlet currents are not distributed reasonably, and currents are distributed at higher positions of the terrains at the two ends of the inlet, but the motion condition of the inlet currents obtained by the method provided by the present invention is better matched with the real condition, and the defect caused by the conventional processing method that small water depths are directly assigned to all inlet units at the initial stage to distribute inlet flows is successfully avoided. In conclusion, the method for processing the flow boundary under the two-dimensional non-structural dry beach condition provided by the invention is successful.
The above-mentioned embodiments are only part of the present invention, and do not cover the whole of the present invention, and on the basis of the above-mentioned embodiments and the attached drawings, those skilled in the art can obtain more embodiments without creative efforts, so that the embodiments obtained without creative efforts are all included in the protection scope of the present invention.
Claims (4)
1. A method for processing a flow boundary under a two-dimensional non-structural dry beach condition is characterized by comprising the following steps: in the initial stage of calculation, connecting all inlet sides corresponding to the inlet units to form a one-dimensional inlet control section, iteratively calculating a water level value corresponding to an inflow flow value at the initial moment under the one-dimensional inlet control section according to a critical flow condition, wherein the water level value minus the bottom elevation of the inlet units is the water depth value of each inlet unit, and distributing the inflow of each inlet unit according to the corresponding relation between the water depth value of the inlet unit and the flow speed in the normal direction of the inlet sides; the method comprises the following specific steps:
1) Acquiring basic data required by calculation, wherein the basic data comprises topographic data, land utilization type data and inflow flow process data;
2) Dividing a calculation area by adopting a quadrilateral or triangular non-structural grid, after dividing, assigning a bottom elevation value to the central point of a non-structural grid unit by adopting a flat-bottom model mode and utilizing terrain data of the area, wherein in each calculation unit, the terrain is flat; assigning roughness values to the grid cells according to the land use type data of the calculation area; the calculated initial water depth and the flow velocity value are both set to be 0, and the dry beach calculation condition is met;
3) Selecting the upper boundary of the calculation area as a flow boundary, wherein a unit corresponding to the flow boundary is called an inlet unit, and a boundary edge corresponding to each inlet unit is an inlet edge; selecting the lower boundary of the calculation area as a free outflow boundary, wherein a unit corresponding to the free outflow boundary is called an outlet unit; the units inside the calculation region, except for the inlet unit and the outlet unit, are called conventional units;
4) Obtaining the inlet flow value Q corresponding to the t moment t Obtaining and calculating time step dt according to the CFL condition;
5) At the initial step t =0 of the calculation, the flow value Q at the initial moment at the inlet is assumed 0 Is not 0, will eachThe inlet sides corresponding to the inlet units are connected to form a one-dimensional inlet control section, and under the flat-bottom model mode, the central elevation of each inlet unit is the elevation of the corresponding inlet side; iterative solution of Q from critical flow conditions 0 Corresponding control section water level Z 0 ；Z 0 If it is higher than the bottom elevation Z of the ith inlet unit i Then use Z 0 Minus Z i The water depth value of the inlet unit is obtained and recorded as H i On the contrary, Z 0 If less than or equal to Z i Then H is i Is 0;
6) Calculating the flow velocity in the normal direction of the inlet edge corresponding to each inlet unit according to the water depth value and the flow value at the inlet of each inlet unit;
7) Calculating a normal numerical flux value passing through the inlet edge corresponding to each inlet unit according to the water depth value of the inlet unit and the inlet edge normal flow rate corresponding to the inlet unit;
8) Describing a flood motion process by adopting a complete two-dimensional shallow water equation set, and calculating the numerical flux between the conventional units in the region by adopting an approximate Riemann solution in a Roe format; calculating the numerical flux of the free outflow boundary edge; summing the numerical flux passing through each unit, and updating the central hydraulic element value of each unit to the t + dt moment;
9) Let t = t + dt, repeat steps 4) -8) until the computation is finished.
2. The method of claim 1, wherein the method comprises the following steps: the critical flow conditions in step 5) are shown below:
in the formula, A (Z) 0 ) For controlling the water level of the cross-section at the inlet to be Z 0 Corresponding area of water passage, H (Z) 0 ) For controlling the water level of the cross-section at the inlet to be Z 0 The average water depth of the corresponding inlet control section is measured, and g is the gravity acceleration.
3. The method of claim 1, wherein the method comprises the following steps: the flow velocity in the normal direction of the inlet edge corresponding to each inlet unit in the step 6) is shown as the following formula:
in the formula of U i The flow velocity in the normal direction of the ith inlet edge, L i Is the length of the ith inlet edge, and n is the total number of inlet units at the flow boundary.
4. The method of claim 3, wherein the method comprises the following steps: the numerical flux across the ith inlet edge of the flow boundary in step 7) is shown by the following equation:
in the formula, F i * Is the numerical flux of the ith entry edge normal direction, n x ，n y The component of the unit vector of the normal direction of the ith inlet edge in the x direction and the component of the unit vector in the y direction are respectively, and g is the gravity acceleration.
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