CN111046567B - Godunov format-based urban drainage pipe network water flow numerical simulation method - Google Patents
Godunov format-based urban drainage pipe network water flow numerical simulation method Download PDFInfo
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Abstract
The invention discloses a Godunov format-based numerical simulation method for water flow of a municipal drainage pipe network, which comprises the steps of firstly establishing corresponding relations between pipe sections and nodes, dispersing the pipe sections by adopting finite volume units, storing hydraulic elements in unit centers, selecting boundary condition types of the inner nodes according to the water level relations between the head and tail end unit water levels or pressure water heads of the pipe sections and the inner nodes connected with the pipe sections, calculating the numerical flux of the interface of each unit through H LL approximate Riemann solution with the outer boundary conditions and the hydraulic element values of the units at the moment, updating the hydraulic element values of all the pipe section units to the next moment, calculating the flow entering or leaving the inner nodes according to the boundary conditions of the inner nodes, and calculating the water level value of the inner nodes at the next moment by using a water balance equation at the inner nodes.
Description
Technical Field
The invention relates to the field of municipal engineering, in particular to the field of urban flood control, and specifically relates to a Godunov format-based urban drainage pipe network water flow numerical simulation method.
Background
The urban drainage pipe network is a unified whole with hydraulic connection formed by connecting a series of drainage pipe sections end to end, the pipe sections are connected through a rain grate, an inspection well, a rainwater well and the like, and the connection points are defined as nodes. In the urban drainage pipe network calculation, the nodes applied by the external boundary conditions are generally defined as external nodes, and other nodes are internal nodes.
Under the large background of rapid urbanization in China, with frequent extreme weather, the urban flood problem is increasingly prominent. The urban flood model is a useful tool and can provide technical support for the prevention and treatment work of urban flood problems. In the urban flood model, the simulation of the water flow of the urban drainage pipe network is an indispensable important ring. The current drain net model is dominated by internationally commercialized software products, with the SWMM (StormWaterManagementModel) model developed by the United states Environmental Protection Agency (EPA) being the most popular. The study of the field is also done by scholars in China, but no mature drainage pipe network product exists yet.
At present, the mainstream methods used in the field of computation of urban drainage pipe networks are limited difference methods which are popular after 70 years of the last century, and compared with classical swim models, mine-piping MOUSE models and the like, it should be said that the models are developed and perfected for many years, and are relatively mature in application.
Disclosure of Invention
The invention aims to provide a Godunov finite volume format-based urban drainage pipe network water flow numerical simulation method, which overcomes the defects of the conventional method.
The Godunov format, which is based on solving the Riemann approximate solution, is referred to as a new generation hydrodynamic model format, and the Godunov format can simulate a smooth classical solution and well simulate large-gradient water surface flow. The form is applied to river network water flow simulation, but is not applied to urban drainage pipe network water flow simulation. The urban drainage pipe network and the river network have two outstanding differences: 1) the river network water flow is all open channel water flow, but the open channel flow and the pressure flow in the drainage pipe network are alternately generated; 2) the node range of the river network is not clear, in the solution of the river network, the water level of the river reach connected with the nodes is generally assumed to be equal, but the nodes of the drainage pipe network are very clear and are inspection wells, rainwater wells and the like, but the water flow form in the nodes is more complex, the height of the embedded bottom of the pipe section is not necessarily consistent with the height of the node bottom, and the difficulty in processing the nodes is increased. In view of this, in order to break through the difficulty encountered when the traditional urban drainage pipe network model is applied to the finite difference method, the Godunov format is popularized and applied to the field of urban drainage pipe network water flow numerical simulation, and the Godunov format has important academic significance and engineering application significance.
The invention is realized by the following technical scheme:
a Godunov format-based urban drainage pipe network water flow numerical simulation method adopts a narrow slit method to simulate the change process of open channel flow and pressure flow, adopts H LL format to calculate the interface flux of pipe section units, and determines the specific boundary condition type used by an inner node according to the relation between the water level or pressure head of the head and tail end unit of each pipe section and the water level of the inner node of the pipe network connected with the pipe section, thereby calculating the flow rate flowing into or flowing out of the pipe network node, and providing the inner boundary water level at the next moment for each pipe section after solving the water balance equation of the pipe network node.
1) And acquiring urban drainage pipe network data in a calculation range, wherein the urban drainage pipe network data comprises data such as pipe network plane geometric topological data, pipe diameter size of each pipe section, pipe bottom elevation of the head end and the tail end of each pipe section, pipe network node bottom elevation, maximum water depth and overload water depth of each pipe network node, area of each pipe network node and the like.
2) Numbering each pipe section and each node, establishing a corresponding relation between each pipe section and each node, appointing that water flow flows from one end with high elevation of the node bottom to one end with low elevation of the node bottom to be a positive direction, dispersing each drainage pipe section by adopting a finite volume unit, and sequentially numbering the discrete units of each pipe section along the positive direction; the hydraulic variable is stored in the central point of each unit; and determining an inflow boundary and an outflow boundary of the drainage pipe network, wherein the inflow boundary and the outflow boundary are collectively called as an outer boundary, a node applying an outer boundary condition is called as an outer node, and the other nodes are called as inner nodes.
3) Initializing a municipal drainage pipe network model: setting roughness and initial values of hydraulic conditions for one-dimensional finite volume units of each pipe section; and setting initial hydraulic conditions for nodes in the pipe network.
4) And determining and calculating a time step dt, namely solving the urban drainage pipe network model by adopting a finite volume method in a display format, wherein the time step acquisition is limited by a CF L (Courant-Friedrichs-L ewy) condition, and acquiring the outer boundary condition of each pipe section at the current moment, wherein the current moment is represented by the moment t.
5) The method adopts an equation set with unified pipeline open channel flow and pressure flow to describe the motion of pipeline water flow, and comprises the following specific forms:
the continuous equation:
the momentum equation:
in the formula, Q is the flow of the cross section, A is the area of the cross section, g is the gravity acceleration, t is the time variable, sfFor on-way drag loss, the expression is sf＝(n2Q|Q|)/(A2R4/3) R is hydraulic radius, n is a Manning roughness coefficient, when the pipeline is open flow, B is water surface width, and H is water level value; when pressure flow exists in the pipeline, B is gA/a2A is the wave velocity of the pressure wave, B is assigned a very small narrow slit width during actual calculation, and H is the pressureA force head.
6) The method comprises the following steps of judging and using different boundary conditions of the inner nodes according to the relation between the water level of the inner nodes and the water level value (pressure water head value) of the head (tail) end unit of each pipe section connected with the inner nodes, and calculating the water quantity flowing into or out of the inner nodes, wherein the specific process comprises the following steps:
a) when the flow of an upstream pipe section connected with the internal node flowing into the internal node is calculated, the following situations are divided:
① if the last unit of the upstream pipe section has water and the water level value of the inner node is less than the bottom height value of the unit, then the flow entering the inner node is calculated according to the boundary condition of free outflow;
② if the last unit of the upstream pipe section has water and the water level of the inner node is larger than or equal to the bottom elevation value of the unit, then the flow entering the inner node is calculated according to the boundary condition of the water level;
③ if the last unit of the upstream pipe section has no water and the water level of the inner node is larger than the height value of the bottom of the unit, then the flow entering the inner node is calculated according to the boundary condition of the water level, under the condition, the water flow flows backwards, and the flow entering the inner node is a negative value;
④ if the last unit of the upstream pipe section has no water and the water level of the inner node is less than or equal to the bottom height value of the unit, then the flow entering the inner node is calculated according to the boundary condition of the fixed wall, and the flow entering the inner node is 0;
b) when the flow of the downstream pipe section connected with the internal node flowing out of the internal node is calculated, the following situations are divided:
① if the first unit of the downstream pipe section has water and the water level of the inner node is larger than or equal to the height value of the bottom of the unit, then the flow out of the inner node is calculated according to the boundary condition of the water level;
② if the first unit of the downstream pipe has water and the water level of the inner node is less than the height of the bottom of the unit, then the flow leaving the inner node is calculated according to the boundary condition of free outflow, in this case, the water flow flows backwards, and the flow flowing out of the inner node is negative;
③ if the first unit of the downstream pipe section has no water and the water level of the inner node is larger than the bottom elevation value of the unit, then the flow leaving the inner node is calculated according to the water level boundary condition;
④ if the first unit of the downstream pipe section has no water and the water level of the inner node is less than or equal to the bottom elevation value of the unit, then the flow leaving the inner node is calculated according to the solid wall boundary condition, and the flow is 0.
7) And calculating the numerical flux passing through the unit interface by adopting an H LL explicit format according to the hydraulic element value, the outer boundary condition and the inner node boundary condition of each pipe section unit at the time t, calculating to obtain the hydraulic element value of each unit at the time t + dt of each pipe section, and if the newly calculated water depth value of a certain unit is greater than the pipe diameter, changing the water flow into a pressure flow state, and setting the water surface width of the pipe section as the narrow slit width.
8) Establishing a water quantity balance equation of each internal node, and obtaining the water level value of each internal node at the t + dt moment according to the balance equation;
in the formula (I), the compound is shown in the specification,
indicating the flow rate of the ith upstream pipe segment connected to the internal node k into the internal node,
indicating the flow out of the internal node of the jth downstream pipe section connected to the internal node k, AkIs the area of the kth internal node,
is the water level of the kth internal node at time t,
in order to solve the water level of the kth internal node at the time of t + dt, m is the number of upstream pipe sections connected with the kth internal node, and n is the number of downstream pipe sections connected with the kth internal node; q. q.skFor water flow between the kth inner node and the groundInteraction volume, q when flowing from the inner node to the groundkNegative values, and vice versa, positive values.
9) Let t be t + dt, repeat steps 4) -8) until the computation is finished.
Further, the dt in step 4) is limited by the condition of CF L (cournt-Friedrichs-L ewy), as shown in formula (4):
in the formula: u is the flow rate;
c is wave velocity, g is gravity acceleration, A is flow area, B is water surface width, and B adopts narrow slit width after water flow is changed into pressure flow; Δ x is the unit space step; dt is the time step.
Further, in step 5), when the water flow is in a pressure flow state, the water surface width is set as a narrow slit width, theoretically, the smaller the narrow slit width is, the more accurate the numerical solution is, but the smaller the narrow slit value is, the stability of the calculation becomes worse, and the requirements of numerical accuracy and stability are comprehensively considered, and the value range of the narrow slit is recommended to be 0.01 m-0.001 m.
Further, the step 6) of calculating the flow rate flowing into or out of the internal node through the internal node boundary condition is completed by setting a virtual unit after the last unit of the upstream pipe section or before the first unit of the downstream pipe section, the characteristics of the virtual unit are consistent with the characteristics of the units connected with the virtual unit, and setting the hydraulic variables of the virtual unit according to different types of the internal node boundary condition, wherein in the case of the free outflow boundary condition, the flow rate and the water level of the virtual unit are equal to those of the units adjacent to the virtual unit, in the case of the water level boundary condition, the flow rate of the virtual unit is equal to that of the units adjacent to the virtual unit, and the water level is equal to that of the units adjacent to the virtual unit, in the case of the fixed wall boundary condition, the flow rate of the virtual unit is equal to the negative value of the flow rate of the units adjacent to the virtual unit, and the mass flow rate value and the flow rate value at the interface between the virtual unit and the unit adjacent to the virtual unit can be calculated according to the approximate Riemann solution of H LL, and the mass.
Drawings
FIG. 1 is a flow chart of a Godunov format-based urban drainage pipe network water flow numerical simulation method of the present invention;
FIG. 2 is a schematic diagram of boundary condition types of interior nodes;
FIG. 3 is an exemplary schematic view of a municipal drainage pipe network;
C1-C21 in the figure are finite volume unit numbers of each pipe section;
fig. 4 is a numerical calculation result of an example of the municipal drainage pipe network.
Detailed Description
The invention will be further described with reference to fig. 1 and the examples.
The invention provides a Godunov format-based urban drainage pipe network water flow numerical simulation method. The method adopts a slit method to unify control equations of open channel flow and pressure flow, adopts a Godunov finite volume method format with good shock wave capture capacity to calculate interface flux, judges the boundary conditions of the adopted inner nodes according to the water level relation between the water level or the pressure water head of the head and tail end unit of the drainage pipe section and the inner nodes connected with the water level relation, and obtains the water level of the inner nodes at the next moment by solving the water quantity balance equation of the inner nodes. The method can effectively make up for the inherent defects of the traditional finite difference method and improve the numerical calculation precision of the drainage pipe network. The method comprises the following specific steps:
1) and acquiring urban drainage pipe network data in a calculation range, wherein the urban drainage pipe network data comprises data such as pipe network plane geometric topological data, pipe diameter size of each pipe section, pipe bottom elevation of the head end and the tail end of each pipe section, pipe network node bottom elevation, maximum water depth and overload water depth of each pipe network node, area of each pipe network node and the like.
2) Numbering each pipe section and each node, establishing a corresponding relation between each node and each pipe section, appointing that water flows from one end with high node bottom elevation to one end with low node bottom elevation to be a positive direction, and numbering discrete units of each pipe section in sequence along the positive direction; dispersing each drainage pipe section by adopting a finite volume unit, and storing hydraulic variables at the central point of each unit; and determining an inflow boundary and an outflow boundary of the drainage pipe network, wherein the inflow boundary and the outflow boundary are collectively called as an outer boundary, a node applying an outer boundary condition is called as an outer node, and the other nodes are called as inner nodes.
3) Initializing a municipal drainage pipe network model: setting roughness and initial values of hydraulic conditions for one-dimensional finite volume units of each pipe section; and setting initial hydraulic conditions for nodes in the pipe network.
4) Determining and calculating a time step dt, namely solving the urban drainage pipe network model by adopting a finite volume method in a display format, wherein the time step acquisition is limited by a CF L (Courant-Friedrichs-L ewy) condition, and the specific formula is shown as a formula (4):
in the formula: u is the flow rate;
c is wave velocity, g is gravity acceleration, A is flow area, B is water surface width, and B adopts narrow slit width after water flow is changed into pressure flow; Δ x is the unit space step; dt is the time step.
And acquiring the outer boundary conditions of each pipe section at the current moment, wherein the current moment is represented by the time t.
5) The method adopts an equation set with unified pipeline open channel flow and pressure flow to describe the motion of pipeline water flow, and comprises the following specific forms:
the continuous equation:
the momentum equation:
in the formula: q is the cross-sectional flow, A is the cross-sectional area of water, g is the gravitational acceleration, t is the time variable, sfFor on-way drag loss, the expression is sf＝(n2Q|Q|)/(A2R4/3) R is hydraulic radius, n is a Manning roughness coefficient, when the pipeline is open flow, B is water surface width, and H is water level value; when pressure flow exists in the pipeline, B is gA/a2And a is the wave velocity of the pressure wave, in the actual calculation, B is assigned with a small narrow slit width, theoretically, the smaller the narrow slit width is, the more accurate the numerical solution is, but the smaller the narrow slit value is, the calculation stability is deteriorated, the requirements of numerical precision and stability are comprehensively considered, and the value range of the narrow slit is suggested to be B0.01-0.001 m, and H is the pressure head.
6) The method comprises the following steps of judging and using different boundary conditions of the inner nodes according to the relation between the water level of the inner nodes and the water level value (pressure water head value) of the head (tail) end unit of each pipe section connected with the inner nodes, and calculating the water quantity flowing into or out of the inner nodes, wherein the specific process comprises the following steps:
a) when the flow of an upstream pipe section connected with the internal node flowing into the internal node is calculated, the following situations are divided:
① if the last unit of the upstream pipe section has water and the water level value of the inner node is less than the bottom height value of the unit, then the flow entering the inner node is calculated according to the boundary condition of free outflow;
② if the last unit of the upstream pipe section has water and the water level of the inner node is larger than or equal to the bottom elevation value of the unit, then the flow entering the inner node is calculated according to the boundary condition of the water level;
③ if the last unit of the upstream pipe section has no water and the water level of the inner node is larger than the height value of the bottom of the unit, then the flow entering the inner node is calculated according to the boundary condition of the water level, under the condition, the water flow flows backwards, and the flow entering the inner node is a negative value;
④ if the last unit of the upstream pipe section has no water and the water level of the inner node is less than or equal to the bottom elevation value of the unit, then the flow entering the inner node is calculated according to the boundary condition of the fixed wall, and the flow entering the inner node is 0.
b) When the flow of the downstream pipe section connected with the internal node flowing out of the internal node is calculated, the following situations are divided:
① if the first unit of the downstream pipe section has water and the water level of the inner node is larger than or equal to the height value of the bottom of the unit, then the flow out of the inner node is calculated according to the boundary condition of the water level;
② if the first unit of the downstream pipe has water and the water level of the inner node is less than the height of the bottom of the unit, then the flow leaving the inner node is calculated according to the boundary condition of free outflow, in this case, the water flow flows backwards, and the flow flowing out of the inner node is negative;
③ if the first unit of the downstream pipe section has no water and the water level of the inner node is larger than the bottom elevation value of the unit, then the flow leaving the inner node is calculated according to the water level boundary condition;
④ if the first unit of the downstream pipe section has no water and the water level of the inner node is less than or equal to the bottom elevation value of the unit, then the flow leaving the inner node is calculated according to the solid wall boundary condition, and the flow is 0.
Calculating flow into or out of an internal node by internal node boundary conditions is accomplished by setting a virtual cell after the last cell of the upstream pipe segment or before the first cell of the downstream pipe segment, the virtual cell having characteristics consistent with the characteristics of the cells connected thereto, setting hydraulic variables of the virtual cell according to different types of internal node boundary conditions, step 6) in the case of free outflow boundary conditions, the flow and level of the virtual cell being equal to the flow and level of the cell adjacent thereto, the flow of the virtual cell being equal to the flow of the cell adjacent thereto and the level being equal to the internal node level, the flow of the virtual cell being equal to the negative of the flow of the cell adjacent thereto and the level being equal to the level of the cell adjacent thereto, in the case of free outflow boundary conditions, the mass flow value and flow value at the interface between the virtual cell and the cell adjacent thereto can be calculated by approximating Riemann H LL after determining the hydraulic variables of the virtual cell, the approximate Riemann solution of the mass flow into or out of the internal node, i.e. H LL approximates the Riemann solution of the water conservancy process (zhang weimen, zhang (zhang math model 2010. the applicable math of water flow [ 2010. 536).
To facilitate understanding, FIG. 2 illustrates an example of an internal nodal boundary condition, as can be seen from FIG. 2, the last unit of the upstream pipe section has water and the internal nodal water level is less than the bottom elevation of that unit, so that the upstream pipe section now terminates in a free outflow boundary. Since the first unit of the downstream pipe section has water and the water level of the inner node is higher than the pipe bottom elevation of the unit, the head end of the downstream pipe section is the water level boundary at the moment.
7) And calculating the numerical flux passing through the unit interface by adopting an H LL explicit format according to the hydraulic element value, the outer boundary condition and the inner node boundary condition of each pipe section unit at the time t, calculating to obtain the hydraulic element value of each unit at the time t + dt of each pipe section, and if the newly calculated water depth value of a certain unit is greater than the pipe diameter, changing the water flow into a pressure flow state, and setting the water surface width of the pipe section as the narrow slit width.
8) Establishing a water quantity balance equation of each internal node, and obtaining the water level value of each internal node at the t + dt moment according to the balance equation;
in the formula (I), the compound is shown in the specification,
indicating the flow rate of the ith upstream pipe segment connected to the internal node k into the internal node,
indicating the flow out of the internal node of the jth downstream pipe section connected to the internal node k, AkIs the area of the kth internal node,
is the water level of the kth internal node at time t,
for the water level of the kth internal node needing to be solved at the moment of t + dt, m is the number of upstream pipe sections connected with the kth internal node, n is the number of upstream pipe sections connected with the kth internal nodeThe number of downstream pipe sections connected with the k internal nodes; q. q.skFor the water flow interaction quantity of the kth inner node and the ground, when the kth inner node flows to the ground, q iskNegative values, and vice versa, positive values.
9) Let t be t + dt, repeat steps 4) -8) until the computation is finished.
FIG. 3 is a schematic diagram of an example of an urban drainage Network, which was originally proposed by Zhong Ji (Zhong Zhi. general Hydrodynamic Model for Power/Channel Network Systems, Journal of hydralic Engineering (ASCE),1998,124(3):307-315.), for testing the ability of the Model to process complex drainage networks. The drainage pipe network consists of 6 pipe sections and 6 nodes, wherein the pipe diameter of the pipe section 1 is 0.8m, the pipe diameters of the rest pipe sections are 0.5m, the lengths of the pipe sections 1, 2 and 5 are 300m, the length of the pipe section 3 is 410m, the length of the pipe section 4 is 500m, the length of the pipe section 6 is 310m, and the number of dividing units of each pipe section is shown in figure 3. The nodes 1, 2 and 3 are external nodes where the external boundary conditions are located, wherein the node 1 is a flow external boundary, the nodes 2 and 3 are water level external boundaries, and the nodes 4, 5 and 6 are internal nodes, wherein the internal node 5 has an inflow process to be imported. The roughness of each pipe section is uniformly 0.0125, and the width of the narrow slit is 0.01 m.
In the initial stage, no water flow exists in each pipe section. In the embodiment, all pipe sections are subjected to a state from no water state to a state with water, and a part of pipe sections can have a state of alternating open and full flows and a state of reciprocating flow direction of water, so that the embodiment can effectively test the capability of the model for processing the alternation of dry and wet, the alternation of open and full flows and the reciprocating flow direction. Compared with the current most popular drainage pipe network water flow simulation model SWMM, the SWMM model adopts the latest 5.1.013 version. The results of the calculations of the method of the present invention were compared with the results calculated using the SWMM model, and the results are shown in FIG. 4. It can be seen from the figure that the calculation results of the present invention are substantially consistent with the SWMM calculation results. In addition, the method can segment the pipe sections at will, so that the description of the water flow of the pipe network is more detailed, and the capture of the water flow arrival time of the pipe section 3 is more accurate. The method for processing the simulation of the water flow of the drainage pipe network 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 (3)
1. A Godunov format-based urban drainage pipe network water flow numerical simulation method is characterized by comprising the following steps of: determining boundary conditions at the inner nodes according to the water level relation between the water level or the pressure head of the head and tail end unit of the pipe section and the water level of the inner nodes, simulating water flow movement in the pipeline by adopting a Godunov finite volume format, and treating the change process of open channel flow and pressure flow in the pipeline by adopting a narrow slit method; the method comprises the following specific steps:
1) acquiring urban drainage pipe network data in a calculation range, wherein the urban drainage pipe network data comprises pipe network plane geometric topological data, pipe diameter size of each pipe section, pipe bottom elevation of the head end and the tail end of each pipe section, pipe network node bottom elevation, maximum water depth and overload water depth of each pipe network node, and pipe network node area data;
2) numbering each pipe section and each node, establishing a corresponding relation between each pipe section and each node, setting the direction from one end with high elevation of the node bottom to one end with low elevation of the node bottom as a positive direction, dispersing each drainage pipe section by adopting a finite volume unit, and sequentially numbering the discrete units of each pipe section along the positive direction; the hydraulic variable is stored in the central point of each unit; determining an inflow boundary and an outflow boundary of a drainage pipe network, wherein the inflow boundary and the outflow boundary are collectively called as an outer boundary, a node applying an outer boundary condition is called as an outer node, and other nodes are called as inner nodes;
3) initializing a municipal drainage pipe network model: setting roughness and initial values of hydraulic conditions for one-dimensional finite volume units of each pipe section; setting initial hydraulic conditions for nodes in a pipe network;
4) determining and calculating time step dt, namely solving the urban drainage pipe network model by adopting a finite volume method in a display format, wherein the time step acquisition is limited by a CF L condition;
5) the method adopts an equation set with unified pipeline open channel flow and pressure flow to describe the motion of pipeline water flow, and comprises the following specific forms:
the continuous equation:
the momentum equation:
in the formula, Q is the flow of the cross section, A is the area of the cross section, g is the gravity acceleration, t is the time variable, sfFor on-way drag loss, the expression is sf＝(n2Q|Q|)/(A2R4/3) R is hydraulic radius, and n is a Manning roughness coefficient; when the channel flow is in the pipeline, B is the water surface width, and H is the water level; when pressure flow exists in the pipeline, B is gA/a2A is the pressure wave velocity and H is the pressure head;
6) the method comprises the following steps of judging and using different boundary conditions of the inner nodes according to the relation between the water level of the inner nodes and the water level or pressure water head of the head end unit and the tail end unit of each pipe section connected with the inner nodes, and calculating the water quantity flowing into or out of the inner nodes, wherein the specific process comprises the following steps:
a) when calculating the flow rate of the upstream pipe section connected with the internal node flowing into the internal node, the conditions are as follows:
if the last unit of the upstream pipe section contains water and the water level value of the inner node is smaller than the bottom height value of the unit, calculating the flow entering the inner node according to the boundary condition of free outflow at the moment;
if the last unit of the upstream pipe section contains water and the water level of the inner node is greater than or equal to the bottom height value of the unit, calculating the flow entering the inner node according to the boundary condition of the water level;
if the last unit of the upstream pipe section has no water and the water level of the inner node is greater than the bottom elevation value of the unit, calculating the flow entering the inner node according to the water level boundary condition, wherein under the condition, the water flow flows backwards, and the flow entering the inner node is a negative value;
if the last unit of the upstream pipe section has no water and the water level of the inner node is less than or equal to the bottom height value of the unit, calculating the flow entering the inner node according to the boundary condition of the fixed wall at the moment, wherein the flow entering the inner node is 0 at the moment;
b) when the flow of the downstream pipe section connected with the internal node flowing out of the internal node is calculated, the conditions are as follows:
if the first unit of the downstream pipe section contains water and the water level of the inner node is greater than or equal to the height value of the bottom of the unit, calculating the flow out of the inner node according to the boundary condition of the water level;
if the first unit of the downstream pipe section contains water and the water level of the inner node is smaller than the bottom elevation value of the unit, the flow leaving the inner node is calculated according to the boundary condition of free outflow at the moment, under the condition, the water flow flows backwards, and the flow flowing out of the inner node is a negative value;
if the first unit of the downstream pipe section has no water and the water level of the inner node is greater than the bottom elevation value of the unit, calculating the flow leaving the inner node according to the boundary condition of the water level;
if the first unit of the downstream pipe section has no water and the water level of the inner node is less than or equal to the bottom height value of the unit, calculating the flow leaving the inner node according to the boundary condition of the fixed wall, wherein the flow is 0;
the flow rate of the virtual unit is consistent with the characteristics of the units connected with the virtual unit, and hydraulic variables of the virtual unit are set according to different types of the boundary conditions of the internal nodes in the step 6), wherein in the case of the free outflow boundary condition, the flow rate and the water level of the virtual unit are equal to those of the units adjacent to the virtual unit, in the case of the boundary condition of the water level, the flow rate of the virtual unit is equal to the negative value of the flow rate of the unit adjacent to the virtual unit, and the water level is equal to that of the unit adjacent to the virtual unit, in the case of the boundary condition of the fixed wall, after the hydraulic variables of the virtual unit are determined, the mass flux value and the momentum flux value at the interface between the virtual unit and the unit adjacent to the virtual unit are calculated according to the similar Riemann solution of H LL, and the mass flux value is the flow rate flowing into or out of the internal nodes;
7) calculating the numerical flux passing through the unit interface by adopting an H LL display format according to the hydraulic element value, the outer boundary condition and the inner node boundary condition of each pipe section unit at the time t, and calculating to obtain the hydraulic element value of each unit at the time t + dt of each pipe section;
8) establishing a water quantity balance equation of each internal node, and obtaining the water level value of each internal node at the t + dt moment according to the balance equation;
in the formula (I), the compound is shown in the specification,
indicating the flow rate of the ith upstream pipe segment connected to the internal node k into the internal node,
indicating the flow out of the internal node of the jth downstream pipe section connected to the internal node k, AkIs the area of the kth internal node,
is the water level of the kth internal node at time t,
the water level of the kth internal node at the time of t + dt is shown, m is the number of upstream pipe sections connected with the kth internal node, and n is the number of downstream pipe sections connected with the kth internal node; q. q.skFor the water flow interaction quantity of the kth inner node and the ground, when the kth inner node flows to the ground, q iskNegative values, otherwise positive values;
9) let t be t + dt, repeat steps 4) -8) until the computation is finished.
2. The Godunov format-based urban drainage pipe network water flow numerical simulation method of claim 1 is characterized in that the selection of dt in the step 4) is limited by the CF L condition, and specifically shown in the formula (4):
in the formula: u is the flow rate;
c is wave velocity, g is gravity acceleration, A is flow area, B is water surface width, and B adopts narrow slit width after water flow is changed into pressure flow; Δ x is the unit space step; dt is the time step.
3. The Godunov format-based urban drainage pipe network water flow numerical simulation method of claim 1, wherein: and 5) when the water flow in the pipeline is in a pressure flow state, setting the water surface width as a narrow slit width, wherein the value range of the narrow slit width is B which is 0.01 m-0.001 m.
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