CN110008526A - The analogy method of Shallow-water Flow containing source item based on large time step format - Google Patents
The analogy method of Shallow-water Flow containing source item based on large time step format Download PDFInfo
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Abstract
The present invention discloses a kind of analogy method of Shallow-water Flow containing source item based on large time step format, includes the following steps: that (10) river initial parameter obtains: obtaining river and stream parameters；(20) channel unit divides: river being divided into multiple units along its length, and using streamflow original state as state value in each channel unit；(30) channel unit Shallow-water Flow is simulated: according to state in channel unit, state updates state in channel unit, obtains each channel unit subsequent time Shallow-water Flow state according to state between unit between computing unit；(40) convergence judges: subsequent time Shallow-water Flow state is compared with last moment Shallow-water Flow state, when error meets convergence threshold, and end simulation；Otherwise, subsequent time Shallow-water Flow state is set as last moment Shallow-water Flow state, goes to state computation step between (30) unit.Shallow-water Flow of the invention determines method, and computational efficiency is high, result convergence is good.
Description
Technical field
The invention belongs to shallow water hydrodynamics technical field, be a kind of computational efficiency is high, result convergence it is good based on it is big when
Between step-length format the analogy method of Shallow-water Flow containing source item.
Background technique
Shallow-water Flow refer to horizontal movement scale much larger than vertical movement scale flowing, it is characterized in that vertical flow velocity and add
Speed is negligible, so that water pressure has free surface close to static pressure distribution, using gravity as main drive.In usual river
Water flow movement may be considered Shallow-water Flow.
Shallow water equation is the important mathematical model that Shallow-water Flow is described in hydraulics.Therefore the simulation to Shallow-water Flow state
It is main to be realized by solving shallow water equation.
Shallow water equation belongs to partial differential equation, it is difficult to direct solution.It is first to ask at present for the numerical simulation of this class equation
Take it is discrete after between adjacent cells interface Riemann Solution, then two units on interface both sides are updated.However, due to by
To the limitation of CFL condition, the method computational efficiency is low.
To improve computational efficiency, industry proposes the large time step for being considered as simulation non-linear hyperbolic partial differential equation
Format breaches the limitation of CFL number, so that computational efficiency has obtained significant increase by changing original update method.
However, this method is when undergone to the unicast unit of application large time step format is updated, big time step
Unicast can obtain disobeying entropy across multiple units in a time step to dealing with improperly for the last one unit in long format
Solution, will appear oscillation, so that the shallow water equation of large time step format is difficult to accurate description Shallow-water Flow shape at platform
State limits it and is determining the application in Shallow-water Flow.
Summary of the invention
The purpose of the present invention is to provide a kind of determination sides of Shallow-water Flow containing source item based on large time step shallow water equation
Method, computational efficiency is high, result convergence is good.
The technical solution for realizing the aim of the invention is as follows:
A kind of analogy method of Shallow-water Flow containing source item based on large time step format, includes the following steps:
(10) river initial parameter obtains: obtaining river parameter, length, width including river, streamflow initial shape
State, including the initial time depth of water, flow velocity, upstream inlet flow and the level of tail water；
(20) channel unit divides: river being divided into multiple units along its length, and by streamflow original state
As state value in each channel unit, river total length obtains each channel unit length divided by channel unit number；
(30) channel unit Shallow-water Flow is simulated: according to state in channel unit, state between computing unit, according between unit
State updates state in channel unit, obtains each channel unit subsequent time Shallow-water Flow state；
(40) convergence judges: subsequent time Shallow-water Flow state is compared with last moment Shallow-water Flow state,
When error meets convergence threshold, end simulation；Otherwise, subsequent time Shallow-water Flow state is set as last moment Shallow-water Flow
State goes to state computation step between (30) unit.
Compared with prior art, the present invention its remarkable advantage are as follows:
1, result convergence is good: due to using fixed back-and-forth method, increasing numerical viscosity, it is suppressed that concussion, obtain compared with
Good convergence effect.
2, computational efficiency is high: the present invention is carried out more simultaneously using multiple units of the large time step format to interface two sides
Newly, the limitation for breaching CFL condition, greatly improves computational efficiency.
The present invention is described in further detail with reference to the accompanying drawings and detailed description.
Detailed description of the invention
Fig. 1 is that the present invention is based on the main flow charts of the Shallow-water Flow containing source item of large time step format analogy method.
Fig. 2 is river initial water level and bed level of the river.
Fig. 3 is convergence solution calculated value figure compared with true solution.
Fig. 4 is the flow chart of channel unit Shallow-water Flow simulation steps in Fig. 1.
Fig. 5 is that state updates the flow chart of step in unit in Fig. 4.
Fig. 6 is that unicast passes through multiple cell schematics.
Fig. 7 is the result being calculated according to the method for the present invention.
Specific embodiment
As shown in Figure 1, the present invention is based on the Shallow-water Flow containing source item of large time step format analogy methods, including walk as follows
It is rapid:
(10) river initial parameter obtains: obtaining river parameter, length, width including river, streamflow initial shape
State, including the initial time depth of water, flow velocity, upstream inlet flow and the level of tail water；
Embodiment chooses the equal width of an a length of 25m, and bed level of the river is longitudinal (in the z-direction) equal, is distributed in the x-direction
As shown in Fig. 2, its functional expression meets following relationship:
It carves at the beginning, water level is unified for as 0.33m, as shown in Figure 2.Upstream inlet flow is 0.18m3/ s is constant, under
Swim out of that saliva position 0.33m is constant, the water surface profile in Fig. 2 can change, and eventually become the appearance in Fig. 3.
(20) channel unit divides: river being divided into multiple units along its length, and by streamflow original state
As state value in each channel unit, river total length obtains each channel unit length divided by channel unit number；
River is divided into 250 units by embodiment, and each element length is 0.1m.Calculate each unit flow velocity u1,
u2…, u250, and depth of water h1,h2,…,h250.By formula (1) it is found that when x is less than 8 or is greater than 12:
When x is between 8 to 12:
(30) channel unit Shallow-water Flow is simulated: according to state in channel unit, state between computing unit, according between unit
State updates state in channel unit, obtains each channel unit subsequent time Shallow-water Flow state；
As shown in figure 4, (30) the channel unit Shallow-water Flow simulation steps include:
(31) interface state calculates between unit: according to state in channel unit, to the Roe of the adjacent channel unit of every two
Average value is characterized, and it is strong to obtain boundary wave speed and wave between channel unit, and determine time step according to CFL value；
(311) it is average that Roe is on the interface between every section, such as in Fig. 6Interface, Unit (i-1)-th on the left side,
I-th cell on the right, is indicated with L and R respectively.So forInterface:
(312) it calculates velocity of wave and wave is strong.Interface issues two waves, and velocity of wave is respectively as follows:
Wave is strong are as follows:
Wherein:
(32) state updates in unit: it is strong according to boundary wave speed and wave between unit, using fixed back-and-forth method, to shape in unit
State is updated, and subsequent time Shallow-water Flow state is obtained；
As shown in figure 5, state update step includes: in (32) unit
(321) it calculates and involves unit number: boundary wave speed between unit being multiplied into time step, divided by element length, is worth
A, integer part b；
Such as in Fig. 6,Interface, by formula (6) it is found that this interface can issue small one and large one two waves of speed,
The velocity of wave for taking one of them big is λ2For, if it calculates:
The value that so value of a is 2.5, b is 2.
(322) completely involve the update of unit velocity of wave: when boundary wave speed is greater than 0 between unit, indicating the right propagation of wave direction, it will be single
It is strong all to add a wave for b unit on the right side of first interface；When boundary wave speed is less than 0 between unit, the left propagation of wave direction is indicated, by unit
It is strong all to add a wave for b unit on the left of interface；In the example of Fig. 6 more to 2 units (i unit and i+1 unit) on the right of interface
New method are as follows:
Un+1=Un+ΔU (13)
(323) partially involve the update of unit velocity of wave: for the b+1 unit partially involved, setting one between 0 to 1
Between numerical value, if | a-b | be less than this numerical value, the b+1 unit remain unchanged, if | a-b | more than or equal to this
A numerical value, then the unit is strong plus a wave.
In the example of Fig. 6, such as to the update method of namely the 3rd unit (i+2 unit) of the b+1 unit on the right of interface
Under:
| a-b | it is 0.5, sets a number (this example takes 0.9) between 0 to 1,0.5 less than 0.9, therefore the 3rd
Unit remains unchanged.
(33) interface traversal examine: judge the updating unit whether the last one interface, if not, going to (31) step, such as
It is ending said process.
(40) convergence judges: subsequent time Shallow-water Flow state is compared with last moment Shallow-water Flow state,
When error meets convergence threshold values, end simulation；Otherwise, subsequent time Shallow-water Flow state is set as last moment Shallow-water Flow
State goes to state computation step between (30) unit.
Calculated result is as shown in Figure 7.From calculated result as can be seen that using fixed back-and-forth method due to taking, increase
Numerical viscosity, it is suppressed that concussion；Simultaneously as being carried out simultaneously using multiple units of the large time step format to interface two sides
It updates, breaches the limitation of CFL condition, greatly improve computational efficiency.
Claims (3)
1. a kind of analogy method of Shallow-water Flow containing source item based on large time step format, which comprises the steps of:
(10) river initial parameter obtains: obtaining river parameter, length, width including river, streamflow original state, packet
Include the initial time depth of water, flow velocity, upstream inlet flow and the level of tail water；
(20) channel unit divides: river is divided into multiple units along its length, and using streamflow original state as
State value in each channel unit, river total length obtain each channel unit length divided by channel unit number；
(30) channel unit Shallow-water Flow is simulated: according to state in channel unit, state between computing unit, according to shape between unit
State updates state in channel unit, obtains each channel unit subsequent time Shallow-water Flow state；
(40) convergence judges: subsequent time Shallow-water Flow state being compared with last moment Shallow-water Flow state, when accidentally
When difference meets convergence threshold, end simulation；Otherwise, subsequent time Shallow-water Flow state is set as last moment Shallow-water Flow shape
State goes to state computation step between (30) unit.
2. Shallow-water Flow analogy method according to claim 1, which is characterized in that (30) the channel unit Shallow-water Flow
Simulation steps include:
(31) interface state calculates between unit: according to state in channel unit, to the Roe average value of the adjacent channel unit of every two
It is characterized, it is strong to obtain boundary wave speed and wave between channel unit, and time step is determined according to CFL value；
(32) state updates in unit: it is strong according to boundary wave speed and wave between unit, using fixed back-and-forth method, state in unit is added
To update, subsequent time Shallow-water Flow state is obtained；
(33) interface traversal is examined: judge the updating unit whether the last one interface, if not, go to (31) step, if so, knot
This process of beam.
3. Shallow-water Flow analogy method according to claim 2, which is characterized in that state updates step in (32) unit
Suddenly include:
(321) it calculates and involves unit number: boundary wave speed between unit being multiplied into time step, divided by element length, obtains value a,
Integer part is b；
(322) completely involve the update of unit velocity of wave: when boundary wave speed is greater than 0 between unit, the right propagation of wave direction is indicated, by unit circle
It is strong that b unit of right side of face all adds a wave；When boundary wave speed is less than 0 between unit, the left propagation of wave direction is indicated, by unit interface
It is strong that b, left side unit all adds a wave；
(323) partially involve the update of unit velocity of wave: for the b+1 unit partially involved, setting one between 0 to 1
Numerical value, if | a-b | be less than this numerical value, the b+1 unit remain unchanged, if | a-b | more than or equal to this number
Value, then the unit is strong plus a wave.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR101487846B1 (en) * | 2014-01-24 | 2015-02-02 | 서울대학교산학협력단 | Method for analyzing 2D shallow water flow through assignment of wetting/drying condition using critical drying depth method |
| CN108229083A (en) * | 2018-04-11 | 2018-06-29 | 南京航空航天大学 | A kind of Flow Numerical Simulation method based on improved finite difference scheme |
| CN108256177A (en) * | 2017-12-28 | 2018-07-06 | 中国水利水电科学研究院 | A kind of parameter optimization method and system of river Water-sand model |
-
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- 2019-03-14 CN CN201910190895.2A patent/CN110008526B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR101487846B1 (en) * | 2014-01-24 | 2015-02-02 | 서울대학교산학협력단 | Method for analyzing 2D shallow water flow through assignment of wetting/drying condition using critical drying depth method |
| CN108256177A (en) * | 2017-12-28 | 2018-07-06 | 中国水利水电科学研究院 | A kind of parameter optimization method and system of river Water-sand model |
| CN108229083A (en) * | 2018-04-11 | 2018-06-29 | 南京航空航天大学 | A kind of Flow Numerical Simulation method based on improved finite difference scheme |
Non-Patent Citations (1)
| Title |
|---|
| 许仁义: "浅水流动的大时间步长格式及其在沙坝模拟中的应用", 《博士电子期刊》 * |
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