CN110008526B - Source-item-containing shallow water flow simulation method based on large time step format - Google Patents
Source-item-containing shallow water flow simulation method based on large time step format Download PDFInfo
- Publication number
- CN110008526B CN110008526B CN201910190895.2A CN201910190895A CN110008526B CN 110008526 B CN110008526 B CN 110008526B CN 201910190895 A CN201910190895 A CN 201910190895A CN 110008526 B CN110008526 B CN 110008526B
- Authority
- CN
- China
- Prior art keywords
- river channel
- state
- unit
- shallow water
- units
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The invention discloses a source item-containing shallow water flow simulation method based on a large time step format, which comprises the following steps: (10) acquiring initial parameters of the river channel: acquiring parameters of a river channel and water flow; (20) River channel unit division, namely dividing a river channel into a plurality of units along the length direction, and taking the initial state of river channel water flow as a state value in each river channel unit; (30) shallow water flow simulation of the river channel unit: calculating the inter-unit state according to the intra-unit state of the river channel, and updating the intra-unit state of the river channel according to the inter-unit state to obtain the shallow water flowing state of each river channel unit at the next moment; (40) convergence judgment: comparing the shallow water flowing state at the next moment with the shallow water flowing state at the previous moment, and finishing the simulation when the error meets the convergence threshold; otherwise, setting the shallow water flowing state at the next moment as the shallow water flowing state at the previous moment, and turning to (30) the inter-unit state calculating step. The shallow water flow determination method is high in calculation efficiency and good in result convergence.
Description
Technical Field
The invention belongs to the technical field of shallow water dynamics, and relates to a source item-containing shallow water flow simulation method based on a large time step format, which is high in calculation efficiency and good in result convergence.
Background
Shallow water flow is flow with horizontal movement scale far larger than vertical movement scale, and is characterized by negligible vertical flow velocity and acceleration, so that water pressure is close to static pressure distribution, free liquid level is provided, and gravity is used as main driving force. Typically the movement of water in a river can be considered as shallow water flow.
The shallow water equation is an important mathematical model in hydraulics describing shallow water flow. Therefore, the simulation of the shallow water flowing state is mainly realized by solving the shallow water equation.
The shallow water equation belongs to partial differential equation and is difficult to solve directly. At present, for numerical simulation of such equations, a riemann solution at an interface between adjacent discrete units is obtained, and then two units on two sides of the interface are updated. However, this method is computationally inefficient due to the limitations of CFL conditions.
In order to improve the calculation efficiency, the industry proposes to consider a large time step format adopting a simulated nonlinear hyperbolic partial differential equation, and breaks through the CFL number limitation by changing the original updating method, so that the calculation efficiency is greatly improved.
However, when the unit experienced by the single wave is updated by applying the large time step format, the single wave in the large time step format passes through a plurality of units within one time step, the last unit is improperly processed, a default solution is obtained, and oscillation occurs at a platform, so that the shallow water equation in the large time step format is difficult to accurately describe the flowing state of the shallow water, and the application of the shallow water equation in determining the flowing state of the shallow water is limited.
Disclosure of Invention
The invention aims to provide a method for determining shallow water flow containing source terms based on a large time step length shallow water equation, which has high calculation efficiency and good result convergence.
The technical solution for realizing the purpose of the invention is as follows:
a source item-containing shallow water flow simulation method based on a large time step format comprises the following steps:
(10) Acquiring initial parameters of a river channel: acquiring river channel parameters including the length and width of a river channel and the initial state of river channel water flow including the water depth, the flow speed, the upstream inlet flow and the downstream water level at the initial moment;
(20) River channel unit division, namely dividing a river channel into a plurality of units along the length direction, taking the initial state of river channel water flow as the state value in each river channel unit, and dividing the total length of the river channel by the number of the river channel units to obtain the length of each river channel unit;
(30) Simulating shallow water flow of a river channel unit: calculating the inter-unit state according to the intra-unit state of the river channel, and updating the intra-unit state of the river channel according to the inter-unit state to obtain the shallow water flowing state of each river channel unit at the next moment;
(40) And (3) convergence judgment: comparing the shallow water flowing state at the next moment with the shallow water flowing state at the previous moment, and finishing the simulation when the error meets the convergence threshold; otherwise, setting the shallow water flowing state at the next moment as the shallow water flowing state at the previous moment, and turning to (30) the inter-unit state calculating step.
Compared with the prior art, the invention has the following remarkable advantages:
1. the result has good convergence: due to the adoption of a fixed selection method, the numerical value viscosity is increased, the oscillation is inhibited, and a better convergence effect is obtained.
2. The calculation efficiency is high: the invention adopts a large time step format to update a plurality of units at both sides of the interface simultaneously, breaks through the limit of CFL conditions and greatly improves the calculation efficiency.
The invention is described in further detail below with reference to the figures and the detailed description.
Drawings
Fig. 1 is a main flow chart of the source item-containing shallow water flow simulation method based on a large time step format.
Fig. 2 shows the initial water level and river bottom elevation of the river.
FIG. 3 is a graph comparing a convergence solution calculation value with a true solution.
Fig. 4 is a flow chart of the simulation steps of shallow water flow in the river channel unit in fig. 1.
FIG. 5 is a flowchart of the intra-cell status update step of FIG. 4.
FIG. 6 is a schematic diagram of a single wave passing through multiple cells.
Fig. 7 shows the results calculated according to the method of the invention.
Detailed Description
As shown in FIG. 1, the method for simulating the shallow water flow containing source items based on the large time step format comprises the following steps:
(10) Acquiring initial parameters of a river channel: acquiring river channel parameters including the length and width of a river channel and the initial state of river channel water flow including the water depth, the flow speed, the upstream inlet flow and the downstream water level at the initial moment;
in the embodiment, a channel with the same width and the length of 25m is selected, the river bottom elevations are equal longitudinally (along the z direction) and are distributed along the x direction as shown in fig. 2, and the functional formula of the channel satisfies the following relation:
at the initial moment, the water level is unified to 0.33m as shown in fig. 2. The upstream inlet flow rate is 0.18m 3 The water level curve in FIG. 2 changes and finally becomes the same as that in FIG. 3 when the/s is constant and the downstream outlet water level is constant at 0.33mAnd (4) adding the active ingredients.
(20) River channel unit division, namely dividing a river channel into a plurality of units along the length direction, taking the initial state of river channel water flow as the state value in each river channel unit, and dividing the total length of the river channel by the number of the river channel units to obtain the length of each river channel unit;
the example divides the channel into 250 units, each unit being 0.1m in length. Calculating the flow rate u of each unit 1 ,u 2 …,u 250 And depth of water h 1 ,h 2 ,…,h 250 . As can be seen from equation (1), when x is less than 8 or greater than 12:
when x is between 8 and 12:
(30) Simulating shallow water flow of a river channel unit: calculating the inter-unit state according to the intra-unit state of the river channel, and updating the intra-unit state of the river channel according to the inter-unit state to obtain the shallow water flowing state of each river channel unit at the next moment;
as shown in fig. 4, the (30) river course unit shallow water flow simulation step includes:
(31) Calculating the interface state between the units: characterizing the Roe average value of every two adjacent river channel units according to the state in the river channel units to obtain the interface wave velocity and wave intensity between the river channel units, and determining the time step length according to the CFL value;
(311) Roe averaging over the interfaces between each segment, such as in FIG. 6
The interface, with the i-1 th cell to the left and the i-th cell to the right, is denoted by L and R, respectively. Then for->
Interface:
(312) And calculating the wave speed and the wave intensity. Two waves are emitted from the interface, and the wave speeds are respectively as follows:
the wave intensity is:
wherein:
(32) Updating the state in the unit: updating the state in the unit by adopting a fixed selection method according to the wave velocity and the wave intensity of the interface between the units to obtain the flowing state of shallow water at the next moment;
as shown in fig. 5, the (32) intra-cell state updating step includes:
(321) Calculating the number of swept units: multiplying the inter-cell interface wave velocity by the time step length, and dividing the time step length by the cell length to obtain a value a, wherein the integer part of the value a is b;
such as in fig. 6, in
The interface can emit two waves with a big velocity and a small velocity according to the formula (6), and the big velocity is lambda 2 For example, if it is calculated that:
then the value of a is 2.5 and the value of b is 2.
(322) Updating the wave velocity of the complete sweep unit: when the wave velocity of the interface between the units is greater than 0, the wave is transmitted to the right, and b units on the right side of the interface of the units are added with one wave intensity; when the wave velocity of the interface between the units is less than 0, the wave is transmitted to the left, and b units on the left side of the interface of the units are added with one wave intensity; in the example of fig. 6, the method for updating the right 2 cells (i cell and i +1 cell) of the interface is as follows:
U n+l ＝U n +ΔU (13)
(323) And (3) updating the wave velocity of the partial sweep unit: for the b +1 th cell of the partial sum, a value between 0 and 1 is set, if | a-b | is less than this value, the b +1 th cell remains unchanged, if | a-b | is greater than or equal to this value, the cell is added with a wave strength.
In the example of fig. 6, the updating method for the b +1 th cell, i.e. the 3 rd cell (i +2 cell) on the right side of the interface is as follows:
| a-b | is 0.5, a number between 0 and 1 (0.9 in this example) is set, and 0.5 is less than 0.9, so the 3 rd cell remains unchanged.
(33) And (3) interface traversal inspection: and (4) judging whether the interface of the internal state updating unit is the last interface or not, if not, turning to the step (31), and if so, ending the process.
(40) And (3) convergence judgment: comparing the shallow water flowing state at the next moment with the shallow water flowing state at the previous moment, and finishing the simulation when the error meets the convergence threshold; otherwise, setting the shallow water flowing state at the next moment as the shallow water flowing state at the previous moment, and turning to (30) the inter-unit state calculating step.
The calculation results are shown in fig. 7. The calculation result shows that the numerical viscosity is increased and the oscillation is inhibited due to the adoption of a fixed selection method; meanwhile, the plurality of units on two sides of the interface are updated simultaneously by adopting a large time step format, so that the limit of CFL conditions is broken through, and the calculation efficiency is greatly improved.
Claims (1)
1. A source item-containing shallow water flow simulation method based on a large time step format is characterized by comprising the following steps:
(10) Acquiring initial parameters of a river channel: acquiring river channel parameters including the length and width of a river channel and the initial state of river channel water flow including the water depth, the flow speed, the upstream inlet flow and the downstream water level at the initial moment;
(20) River channel unit division, namely dividing a river channel into a plurality of units along the length direction, taking the initial state of river channel water flow as the state value in each river channel unit, and dividing the total length of the river channel by the number of the river channel units to obtain the length of each river channel unit;
(30) Simulating shallow water flow of a river channel unit: calculating the inter-unit state according to the intra-unit state of the river channel, and updating the intra-unit state of the river channel according to the inter-unit state to obtain the shallow water flowing state of each river channel unit at the next moment;
(40) And (3) convergence judgment: comparing the shallow water flowing state at the next moment with the shallow water flowing state at the last moment, and ending the simulation when the error meets the convergence threshold value; otherwise, setting the shallow water flowing state at the next moment as the shallow water flowing state at the previous moment, and turning to (30) the inter-unit state calculating step;
the (30) river course unit shallow water flow simulation step comprises:
(31) Calculating the interface state between the units: characterizing the Roe average value of every two adjacent river channel units according to the state in the river channel units to obtain the interface wave velocity and wave intensity between the river channel units, and determining the time step length according to the CFL value;
(32) Updating the state in the unit: updating the state in the unit by adopting a fixed selection method according to the wave velocity and the wave intensity of the interface between the units to obtain the flowing state of shallow water at the next moment;
(33) And (3) interface traversal inspection: judging whether the interface of the internal state updating unit is the last interface or not, if not, turning to the step (31), and if so, ending the process;
the (32) intra-cell state updating step includes:
(321) Calculating the number of swept units: multiplying the interfacial wave speed between the units by the time step length, and dividing the multiplied wave speed by the unit length to obtain a value a, wherein the integer part of the value a is b;
(322) Updating the wave velocity of the complete sweep unit: when the wave velocity of the interface between the units is greater than 0, the wave is transmitted to the right, and b units on the right side of the interface of the units are added with one wave intensity; when the wave velocity of the interface between the units is less than 0, the wave is transmitted to the left, and b units on the left side of the interface of the units are added with one wave intensity;
(323) And (3) updating the wave velocity of the partial sweep unit: for the b +1 th element of the partial sum, a value between 0 and 1 is set, if | a-b | is smaller than this value, the b +1 th element remains unchanged, if | a-b | is greater than or equal to this value, the element is added with a wave intensity.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910190895.2A CN110008526B (en) | 2019-03-14 | 2019-03-14 | Source-item-containing shallow water flow simulation method based on large time step format |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910190895.2A CN110008526B (en) | 2019-03-14 | 2019-03-14 | Source-item-containing shallow water flow simulation method based on large time step format |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110008526A CN110008526A (en) | 2019-07-12 |
| CN110008526B true CN110008526B (en) | 2023-04-07 |
Family
ID=67167008
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910190895.2A Active CN110008526B (en) | 2019-03-14 | 2019-03-14 | Source-item-containing shallow water flow simulation method based on large time step format |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110008526B (en) |
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 |
-
2019
- 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 |
|---|
| 浅水流动的大时间步长格式及其在沙坝模拟中的应用;许仁义;《博士电子期刊》;20150715;全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110008526A (en) | 2019-07-12 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN112464584B (en) | Method for estimating water level and flow of free surface flow | |
| Balabel et al. | On the performance of linear and nonlinear k–ε turbulence models in various jet flow applications | |
| CN109255160A (en) | Unit time delay prediction method and unit time-delay sensitivity calculation method neural network based | |
| CN110374047A (en) | Arch dam runtime real-time security monitoring Threshold based on deformation | |
| CN110955998B (en) | GIS-based large-scale debris flow numerical simulation and numerical processing method | |
| CN114065567A (en) | Method and device for optimizing structure of common manifold of fuel cell stack | |
| CN107464017A (en) | Based on the adaptive soft-sensor Forecasting Methodology with time difference Bayesian network | |
| Sauida | Calibration of submerged multi-sluice gates | |
| CN104091065A (en) | Intermittent flow numerical simulation method for solving shallow water problem | |
| CN110008526B (en) | Source-item-containing shallow water flow simulation method based on large time step format | |
| CN106372320A (en) | Method for performing large eddy simulation on highway tunnel turbulence by using sub-filtering scale model | |
| CN111311734A (en) | Three-dimensional numerical simulation method for hydraulic characteristics of flood discharge system of uranium tailing pond | |
| CN110410070B (en) | Method for determining water flooding reservoir flooding rule | |
| CN116562043A (en) | Data assimilation research method for three-dimensional hydrodynamic simulation of natural river reach | |
| CN107090798A (en) | Restoration ＆ saturation coefficient computational methods under a kind of reservoir over-saturation sediment transport state | |
| CN116956660A (en) | Dam safety monitoring medium-long term forecasting method | |
| CN105183965A (en) | Large eddy simulation method for predicting atomization process | |
| CN114757049A (en) | Method for analyzing and verifying necessity of upgrading and transforming drainage basin sewage treatment plant | |
| Budinski | Lattice Boltzmann method for 2D flows in curvilinear coordinates | |
| CN112307668B (en) | Mucus effect simulation method based on particles | |
| Jing et al. | Numerical modeling of flow in continuous bends from Daliushu to Shapotou in Yellow River | |
| CN109989747A (en) | A kind of oil field injection and extraction well group exploitation non-uniform degree quantitatively characterizing method | |
| CN116663223B (en) | Dam break flood evolution prediction method based on wave breaking principle | |
| CN110110455A (en) | The method of gatage is adjusted under given flow | |
| CN111695304B (en) | Weighted average calculation method for water level gradient |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |