CN109918821A - A kind of conservation form river windward overflows flows method for numerical simulation out - Google Patents
A kind of conservation form river windward overflows flows method for numerical simulation out Download PDFInfo
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Abstract
It overflows the invention discloses a kind of conservation form river windward and flows method for numerical simulation out.To give full play to the advantage that one-dimensional model computational efficiency is fast and two dimensional model computational accuracy is high, the water flow in river is simulated using one-dimensional model, and river is simulated after overflowing overflow stream using two-dimensional numerical model.The finite volume method that one-dimensional model and two dimensional model are all made of cell centered scheme carrys out the Shallow Water Equations of discrete conservation form, boundary flux is calculated using the Godunov numerical value computational format of conservation form windward, the class model has good numerical value conservation property and extensive adaptability, it can be used for great rivers area, can be used for middle and small river area.Using the water flow interactive process inside and outside the property invariant theoretical calculation river with strict physical mathematical meaning, this kind of processing method can overcome conventional method using the defect of weir formula progress water flow interactive computing, the precision of water flow interactive computing between raising one, two dimensional model, guarantees the conservation of mass characteristic of mathematical model entirety.
Description
Technical field
The present invention relates to hydraulic engineering field more particularly to flood control and disaster reduction field, specially a kind of conservation form river windward
It overflows and flows method for numerical simulation out.
Background technique
With the variation of global climate model, extreme heavy rainfall event frequently occurs, and occurs river super standard flood often
The phenomenon that overflowing after flood overflows, can bring serious Loss of Life and property to the resident of flooding area.Mathematical model is as one
The useful tool of kind, can provide valuable decision information with the process of overflowing of simulating riverway flood for flood decision department.One
Mathematical model is tieed up, there is very high computational efficiency, good calculated result can be provided in streamflow simulation, but flood
Once overflowed, apparent two dimensional motion feature is presented in water flow outside river, and one-dimensional model is difficult to be applicable in again at this time.If in river
The simulation of outer water flow process is used uniformly two-dimensional numerical model progress, can undoubtedly obtain very high computational accuracy, but conditions present
Under, the computational efficiency of two dimensional model is difficult meet the needs of real-time analytical calculation in engineering.In consideration of it, by one-dimensional model and two dimension
Model coupling gets up, and can make full use of the computational efficiency of one-dimensional model and the computational accuracy of two dimensional model.
Currently, common one, two dimensional model coupled modes are calculated in river in the form of weir formula in engineering
The interaction of outer water flow, the momentum-exchange between one, two dimensional model however this method is beyond expression, while the calculating system in weir formula
Number, which is chosen, has very big uncertainty, these bring some errors to the simulation that flood overflows overflow stream, directly affect to overflow and flood
Do not have range and floods the order of accuarcy of process.In addition, in current engineering commonly used no Developing Shock-Capturing ability numerical discretization
Format, commonly used Preissmann format when such as river simulation, under conditions of mountain terrain and Complex Flow Status, Chang Buneng is obtained
Correct calculated result is obtained, it is preferable that effect is applicable in usually in the water flow simulation of great rivers, but is used for middle and small river river
The peb process that overflows usually fails when simulating.
Summary of the invention
It overflows the purpose of the present invention is to provide a kind of high applicability, high-precision river and flows method for numerical simulation out, both
The flow field simulation out that overflows that can be used for great rivers can be used for the simulation that heavy grade hilly area river overflows overflow stream,
Water flow interactive computing inside and outside river uses the property invariant theory with strict physical mathematical meaning to complete, and improves tradition
One, the precision of two dimensional model coupling process.
The present invention is achieved by the following technical solutions:
A kind of conservation form river windward overflows flows method for numerical simulation out, streamflow using One dimensional Mathematical Model simulation,
River water, which overflows, is simulated using two-dimensional numerical model after slot out, and One dimensional Mathematical Model and two-dimensional numerical model are all made of based on limited body
The numeric format of conservation form windward of area method is discrete, and waterpower variable is stored in unit center, and the water flow interaction inside and outside river passes through spy
Sign invariant theory is solved, to guarantee that a whole set of numerical discretization schemes have good precision sum number value conservation property；It has
The method and step of body is as follows:
1) basic data obtains: obtaining detailed river cross-section data and river plane geometric shape data；Obtain river
The outer detailed terrain data in flooding area.
2) zoning is discrete: using the discrete river of One Dimensional Finite elementary volume, volume element；It is discrete using non-structural triangular element
Flooded area outside river；In section of overflowing, the topology that need to establish one-dimensional channel unit and coupled triangular element is corresponding
Relationship.
3) model initialization: to one-dimensional channel unit setting roughness and hydraulics initial value；Interpolation grid node and net
The height value of lattice heart point, to two-dimensional grid unit setting roughness and hydraulics initial value.
4) acquisition time step-length dt: since one, two-dimensional numerical model is all made of explicit scheme numerical discretization schemes, because of this time
Step-length selection is limited by CFL condition, calculates separately the time step dt of one-dimensional model1With the time step dt of two dimensional model2,
To keep calculating monolithic stability, dt is taken1And dt2Numerical value smaller is the time step dt, i.e. dt=min (dt needed for calculating1,
dt2)。
5) overflow a section water flow interactive computing: whether there is water flow interaction inside and outside section river that first determines whether to overflow, if there is interaction,
By property invariant calculation formula, pass through the water level value of one-dimensional channel unit and the depth of water of two-dimensional grid unit adjacent thereto
The mass flux and momentum flux that side exterior normal direction is connected by each two-dimensional grid unit are calculated with flow speed value；If water flow without
Interactive then mass flux and momentum flux are 0.
6) one-dimensional model calculates: complete One-dimensional Shallow Water Equations group simulating riverway water flow movement is used, using based on limited body
The HLL format of conservation form windward of area method calculates one-dimensional channel unit interface numerical flux；The overflow interaction water of section of step 5) exists
Make source item processing in one-dimensional model；After the completion of calculating, the waterpower variable update of one-dimensional river each unit to t+dt moment；
7) two dimensional model calculates: using the outer water flow movement process of full two-dimensional Shallow Water Equations simulating riverway, using being based on
The Roe format of conservation form windward of finite volume method calculates the boundary flux of two-dimensional cell；What step 5) calculated passes through each two dimension
Grid cell connects the boundary condition of the mass flux and momentum flux on side as two dimensional model；After the completion of calculating, two-dimensional grid
The waterpower variable update of unit is to the t+dt moment.
8) t=t+dt is enabled, step 4) -7 is repeated), until completing entire calculating process.
Further, it in step 2), overflows section in river, one-dimensional channel unit is known as one-dimensional connection unit, single one-dimensional
Connection unit generally corresponds to multiple two-dimensional grid units, and the side that two-dimensional grid unit is connected with one-dimensional connection unit is known as connecting
Side, each two-dimensional grid unit being connected directly by connection side and channel unit are known as two-dimentional connection unit, and two dimension connection is single
Member cannot be equal to corresponding two-dimentional connection unit across two one-dimensional channel units, the i.e. length on one-dimensional channel unit connection side
Connect the sum of the length on side.
Further, it in step 2), overflows section in river, needs to encrypt one-dimensional channel unit number, while needing to encrypt two
Tie up connection unit number；
Further, a section channel unit length recommendation of overflowing in step 2) practical application takes to be advisable no more than 200m；
Further, two-dimensional grid unit connects side length depending on the topography and geomorphology at place of overflowing in step 2), if river
Without dyke, the two-dimensional grid unit connection side length at this recommends to take to be advisable less than the 1/3 of channel unit connection side length, if there is river
Road dyke, the connection side of two-dimensional grid unit are not preferably greater than the half of dyke top width.
Further, in step 5), when having water flow interaction inside and outside river, pass through the spy with strict physical Fundamentals of Mathematics
Sign invariant formula connects the mass flux and momentum flux on side, the calculating of property invariant to calculate by two-dimensional grid unit
Formula such as formula (1):
uLn+2cL=u*+2c* (1)
In formula: u*,c*The exterior normal direction flow velocity and velocity of wave on side, u are connected for two-dimensional grid unitLn,cLFor two-dimensional grid
Flow velocity and velocity of wave of the unit center hydraulic elements value in connection side exterior normal direction.
In above formula, uLnAnd cLIt is the known quantity of t moment, c*It can be acquired by the water level value of one-dimensional channel unit, according to
Formula (1) can directly find out the exterior normal direction flow velocity u on two dimension connection side*.Obtain u*Afterwards, in conjunction with the water level of one-dimensional channel unit
Value can immediately arrive at logical by the mass flux and momentum in two dimension connection side exterior normal direction according to two-dimensional shallow water equation group
Amount.
Further, in step 6), use complete One-dimensional Shallow Water Equations group for conservation form, specifically as shown in formula (2):
Wherein, x is space variable, and t is time variable, and D, U, F, S are the vector statement of each variable in equation group, specifically such as
Under:
In formula: B is water surface width, and Z is water level, and Q is section flow, and A is discharge section area, f1And f2Respectively represent to
Two components of F (U) are measured, g is acceleration of gravity, and J is friction loss, and expression formula is J=(n2Q|Q|)/(A2R4/3), R
For hydraulic radius, n is Manning roughness coefficien, qlFor quality source item.
Further, when having water flow interaction inside and outside one-dimensional channel unit, qlMethod for solving such as formula (3) shown in:
In formula: qjJ-th of two-dimensional cell to be connected with the one-dimensional channel unit connect the quality in side exterior normal direction
Flux, sjThe length on side is connected for j-th of two-dimensional cell, k is the number of the corresponding two-dimentional connection unit of the one-dimensional channel unit.
Further, river cross-section data and river plane geometric shape data, river cross-section spacing are obtained in step 1)
Less than 1km；Flooding area terrain data outside river is obtained, scale accuracy is greater than 1:10000.
The numerical value computational format of conservation form windward of Godunov format can be very good to adapt to various complicated landforms, accurately
Table is captured, traditional shallow water method for numerical simulation can be perfectly replaced.This conservation momentum equation windward is used for river
Road overflows the simulation of outflow process, has wider applicability, is on the one hand suitable for the great rivers flood mistake of gentle gradient
Journey simulation, while can be used for the simulation of the precipitous middle and small river peb process of the gradient.To overcome traditional use weir formula coupling
Unify, the defect of two dimensional model, one, two dimensional model is handled using the property invariant theory with strict physical Fundamentals of Mathematics
Between water flow interaction problems.This method stream calculation out that can overflow for river provides a kind of new high-adaptability and high-precision solution
Scheme.
Beneficial effects of the present invention:
When progress river overflows and flows analytical calculation out, using the numeric format of conservation form windward model is had wider
General applicability, the great rivers for being used not only for gentle gradient overflow the simulation of outflow process, can be used for mountain and hill
Area's heavy grade middle and small river overflows the simulation of process；In addition, theoretical using the property invariant with strict physical Fundamentals of Mathematics
The water flow interaction inside and outside river is handled, the defect of traditional coupled modes using weir formula can be overcome, improve simulation precision.
To sum up, this method can expand existing waterway overflow out flow mathematical model the scope of application, promoted numerical precision.
Detailed description of the invention
Fig. 1 is that overflow one kind of the invention fluxion value calculating method flow chart out in conservation form river windward；
Fig. 2 is that one, two-dimensional numerical model couples schematic diagram, and i is one-dimensional connection unit, k1、k2、k3For two-dimentional connection unit,
s1、s2、s3For the connection side of two-dimentional connection unit.
Specific embodiment
With reference to the accompanying drawing 1 and attached drawing 2 the invention will be further described.
The invention provides one kind, and overflow fluxion value calculating method out in conservation form river windward.On the one hand, conservation windward
The numerical computation method of type has very wide applicability, and the great rivers flood for being applicable not only to gentle gradient overflows process mould
Quasi-, the middle and small river for being also applied for heavy grade hilly area overflows peb process simulation；It on the other hand, is the whole of guarantee model
Body computational accuracy and conservation property, the water flow interactive process inside and outside river are calculated using the feature with strict physical Fundamentals of Mathematics
Invariant theory carries out.Detailed process is as follows for this method:
1) basic data obtains: obtaining detailed river cross-section data and river plane geometric shape data, river cross-section
Spacing need to be less than 1km；The detailed terrain data in flooding area outside river is obtained, scale accuracy need to be greater than 1:10000.
2) zoning is discrete: using the discrete river of One Dimensional Finite elementary volume, volume element；It is discrete using non-structural triangular element
Flooded area outside river.In section of overflowing, the topology that need to establish one-dimensional channel unit and coupled triangular element is corresponding
Relationship.The one-dimensional channel unit for section of overflowing is known as one-dimensional connection unit, and single one-dimensional connection unit generally corresponds to multiple two-dimensional mesh
Lattice unit, two-dimensional grid unit be connected with one-dimensional connection unit when being known as connecting, it is each to pass through connection side and river list
The two-dimensional grid unit that member is connected directly is known as two-dimentional connection unit, and two-dimentional connection unit cannot be across two one-dimensional channel units two
Tie up grid cell, i.e., the connection of one-dimensional channel unit while length be equal to corresponding two-dimentional connection unit connection while length it
With.In fig 2, it is one-dimensional connection unit that one-dimensional channel unit i, which is in section of overflowing, and coupled two-dimentional connection unit is
k1、k2And k3, corresponding connection side is respectively s1、s2And s3.To guarantee computational accuracy, overflows section in river, need to encrypt river
Unit number, while needing ciphering two-dimension connection unit number；Section channel unit length of overflowing in practical application is recommended no more than 200m
Left and right is advisable, and two-dimensional grid unit connects side length depending on the topography and geomorphology at place of overflowing, if two dimension of the river without dyke, at this
Grid cell connection side recommends to take to be advisable less than the 1/3 of channel unit side length, if there is River Embankment, the connection of triangular element
Side is not preferably greater than the half of dyke top width.
3) model initialization: to one-dimensional channel unit setting roughness and hydraulics initial value；Interpolation grid node and net
The height value of lattice heart point, to two-dimensional grid unit setting roughness and hydraulics initial value.
4) acquisition time step-length dt: since one, two-dimensional numerical model is all made of explicit scheme numerical discretization schemes, because of this time
Step-length selection is limited by CFL condition, calculates separately the time step dt of one-dimensional model1With the time step dt of two dimensional model2,
To keep calculating monolithic stability, dt is taken1And dt2Numerical value smaller is the time step dt, i.e. dt=min (dt needed for calculating1,
dt2)。
5) overflow a section water flow interactive computing: whether having water flow interaction inside and outside section river that first determines whether to overflow, if no interactions
Then mass flux and momentum flux are 0；If there is interaction, calculated by the property invariant with strict physical Fundamentals of Mathematics
Formula is calculated and is connected by each grid cell by the water level value of one-dimensional unit and the depth of water and flow speed value of grid cell adjacent thereto
The mass flux and momentum flux in edge fit exterior normal direction, calculation formula such as formula (1):
uLn+2cL=u*+2c* (1)
u*,c*The exterior normal direction flow velocity and velocity of wave on side, u are connected for two-dimensional grid unitLn,cLFor two-dimensional grid unit
Flow velocity and velocity of wave of the center hydraulic elements value in connection side exterior normal direction.
In above formula, uLnAnd cLIt is the known quantity of t moment, c*It can be acquired by the water level value of one-dimensional channel unit, according to
Formula 1) it can directly find out the two-dimentional exterior normal direction flow velocity u connected on side*.Obtain u*Afterwards, in conjunction with the water level value of one-dimensional channel unit
The mass flux and momentum flux that exterior normal direction in side is connected by two dimension can be immediately arrived at.
6) one-dimensional model calculates: using complete One-dimensional Shallow Water Equations group simulating riverway water flow movement, complete one-dimensional shallow water
Equation group is conservation form, specifically as shown in formula (2):
Wherein, x is space variable, and t is time variable, and D, U, F, S are the vector statement of each variable in equation group, specifically such as
Under:
In formula: B is water surface width, and Z is water level, and Q is section flow, and A is discharge section area, f1And f2Respectively represent to
Two components of F (U) are measured, g is acceleration of gravity, and J is friction loss, and expression formula is J=(n2Q|Q|)/(A2R4/3), R
For hydraulic radius, n is Manning roughness coefficien, qlFor quality source item.When having water flow interaction inside and outside one-dimensional channel unit, ql's
Shown in method for solving such as formula (3):
In formula: qjJ-th of two-dimensional cell to be connected with the one-dimensional channel unit connect the quality in side exterior normal direction
Flux, sjThe length on side is connected for j-th of two-dimensional cell, k is the number of the corresponding two-dimentional connection unit of the one-dimensional channel unit.
One-dimensional channel unit interface numerical flux is calculated using the HLL format of conservation form windward based on finite volume method, is adopted
The space values reconstruct that variable is carried out with TVD-MUSCL format, is improved time precision using Hancock predictor-corrector scheme
To second order, specific value departure process can refer to following document description, and (Zhang Dawei, the dykes and dams based on Godunov format burst water
Stream numerical simulation, 2014, Chinese Water Conservancy water power publishing house).
The overflow interaction water of section of step 5) makees source item processing in one-dimensional model；After the completion of calculating, the one-dimensional each list in river
The waterpower variable update of member is to the t+dt moment.
7) two dimensional model calculates: using the outer water flow movement process of full two-dimensional Shallow Water Equations simulating riverway, use it is complete
The conservation form such as formula (4) of whole two-dimensional shallow water equation:
In formula:H is the depth of water, u,
V is respectively x, and the flow velocity in the direction y, t is the time,X respectively, the gradient in the direction y, ZbFor ground
Elevation, g are acceleration of gravity,The frictional resistance item in the direction respectively x, y, wherein n
For Manning roughness coefficien.
Using the two-dimentional conservation form Roe format discrete two-dimensional Shallow Water Equations windward based on finite volume method, using triangle
Three vertex altitude data direct integrals of shape calculate source terms, using half hidden numerical discretization format analysis processing frictional resistance item, specific number
Value departure process can refer to following document description (Zhang Dawei, Quan Jin, Ma Jianming, basin of the Xiang Liyun based on Godunov format
Rainwash Two-dimensional numerical simulation Journal of Hydraulic Engineering, 2018,49 (7): 787-794.).
The mass flux for connecting side by each two-dimensional grid unit and momentum flux that step 5) calculates are as two-dimentional mould
The boundary condition of type；After the completion of calculating, the waterpower variable update of two-dimensional grid unit to t+dt moment.
8) t=t+dt is enabled, step 4) -7 is repeated), until completing entire calculating process.
The above embodiments are only that part of the invention is embodied, and can not cover whole of the invention, in above-described embodiment
And on the basis of attached drawing, those skilled in the art can get more embodiment party without creative efforts
Formula, therefore the embodiment obtained under the premise of these do not make the creative labor should be included in protection scope of the present invention
It is interior.
Claims (10)
1. a kind of conservation form river windward overflows flows method for numerical simulation out, it is characterised in that: streamflow uses one-dimensional mathematics
Modeling, river water, which overflows, is simulated using two-dimensional numerical model after slot out, and One dimensional Mathematical Model and two-dimensional numerical model are all made of
The numeric format of conservation form windward based on finite volume method is discrete, and waterpower variable is stored in unit center, the water flow inside and outside river
Interaction is solved by property invariant theory；Its specific method and step is as follows:
1) basic data obtains: obtaining river cross-section data and river plane geometric shape data；Obtain flooding area outside river
Graphic data；
2) zoning is discrete: using the discrete river of One Dimensional Finite elementary volume, volume element；Using the discrete river of non-structural triangular element
Outer flooded area；In section of overflowing, the topological corresponding relationship of one-dimensional channel unit and coupled triangular element need to be established；
3) model initialization: to one-dimensional channel unit setting roughness and hydraulics initial value；Interpolation grid node and grid type
The height value of heart point, to two-dimensional grid unit setting roughness and hydraulics initial value；
4) acquisition time step-length dt: the time step dt of one-dimensional model is calculated separately1With the time step dt of two dimensional model2, take
dt1And dt2Numerical value smaller is the time step dt needed for calculating；
5) overflow a section water flow interactive computing: whether there is water flow interaction inside and outside section river that first determines whether to overflow, if there is interaction, by
Property invariant calculation formula passes through the water level value of one-dimensional channel unit and the depth of water and stream of two-dimensional grid unit adjacent thereto
Speed value calculates the mass flux and momentum flux that exterior normal direction in side is connected by each two-dimensional grid unit；If non-water flow interaction
Then mass flux and momentum flux are 0；
6) one-dimensional model calculates: complete One-dimensional Shallow Water Equations group simulating riverway water flow movement is used, using based on finite volume method
The HLL format of conservation form windward calculate one-dimensional channel unit interface numerical flux；Step 5) overflow section interaction water one-dimensional
Make source item processing in model；After the completion of calculating, the waterpower variable update of one-dimensional river each unit to t+dt moment；
7) two dimensional model calculates: using the outer water flow movement process of full two-dimensional Shallow Water Equations simulating riverway, using based on limited
The Roe format of conservation form windward of volumetric method calculates the boundary flux of two-dimensional cell；What step 5) calculated passes through each two-dimensional grid
Unit connects the boundary condition of the mass flux and momentum flux on side as two dimensional model；After the completion of calculating, two-dimensional grid unit
Waterpower variable update to the t+dt moment；
8) t=t+dt is enabled, step 4) -7 is repeated), until completing entire calculating process.
2. a kind of conservation form river windward according to claim 1 overflows flows method for numerical simulation out, it is characterised in that: step
It is rapid 2) in, overflow section in river, one-dimensional channel unit is known as one-dimensional connection unit, and single one-dimensional connection unit is 1 corresponding or more
Two-dimensional grid unit, two-dimensional grid unit be connected with one-dimensional connection unit when being known as connecting, it is each to pass through connection side
The two-dimensional grid unit being connected directly with channel unit is known as two-dimentional connection unit, and the length on one-dimensional channel unit connection side is equal to
The sum of the length on corresponding two-dimentional connection unit connection side.
3. a kind of conservation form river windward according to claim 2 overflows flows method for numerical simulation out, it is characterised in that: step
It is rapid 2) in, overflow section in river, encrypt one-dimensional channel unit number, while ciphering two-dimension connection unit number.
4. a kind of conservation form river windward according to claim 2 overflows flows method for numerical simulation out, it is characterised in that: step
It is rapid 2) in overflow section channel unit length no more than 200m.
5. a kind of conservation form river windward according to claim 2 overflows flows method for numerical simulation out, it is characterised in that: step
It is rapid 2) in, without dyke, the two-dimensional grid unit at place of overflowing connection side length takes 1/3 less than channel unit connection side length in river.
6. a kind of conservation form river windward according to claim 2 overflows flows method for numerical simulation out, it is characterised in that: have
River Embankment, the connection side of two-dimensional grid unit are not more than the half of dyke top width.
7. a kind of conservation form river windward according to claim 1 overflows flows method for numerical simulation out, it is characterised in that: step
It is rapid 5) in, have inside and outside river water flow interaction when, calculated by property invariant formula by two-dimensional grid unit connect side
Mass flux and momentum flux, the calculation formula of property invariant such as formula (1):
uLn+2cL=u*+2c* (1)
In formula: u*,c*The exterior normal direction flow velocity and velocity of wave on side, u are connected for two-dimensional grid unitLn,cLFor two-dimensional grid unit
Flow velocity and velocity of wave of the center hydraulic elements value in connection side exterior normal direction.
8. a kind of conservation form river windward according to claim 1 overflows flows method for numerical simulation out, it is characterised in that: step
It is rapid 6) in, use complete One-dimensional Shallow Water Equations group for conservation form, specifically as shown in formula (2):
Wherein, x is space variable, and t is time variable, and D, U, F, S are the vector statement of each variable in equation group, specific as follows:
In formula: B is water surface width, and Z is water level, and Q is section flow, and A is discharge section area, f1And f2Respectively represent vector F
(U) two components, g are acceleration of gravity, and J is friction loss, and expression formula is J=(n2Q|Q|)/(A2R4/3), R is
Hydraulic radius, n are Manning roughness coefficien, and ql is quality source item.
9. a kind of conservation form river windward according to claim 8 overflows flows method for numerical simulation out, it is characterised in that:
When having water flow interaction inside and outside one-dimensional channel unit, qlMethod for solving such as formula (3) shown in:
In formula: qjJ-th of two-dimensional cell to be connected with the one-dimensional channel unit connect the mass flux in side exterior normal direction,
sjThe length on side is connected for j-th of two-dimensional cell, k is the number of the corresponding two-dimentional connection unit of the one-dimensional channel unit.
10. a kind of conservation form river windward according to claim 1 overflows flows method for numerical simulation out, it is characterised in that:
River cross-section data and river plane geometric shape data are obtained in step 1), river cross-section spacing is less than 1km；It obtains outside river
Flooding area terrain data, scale accuracy are greater than 1:10000.
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