CN108345964B - Water quality prediction method and system based on water quality model - Google Patents
Water quality prediction method and system based on water quality model Download PDFInfo
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Abstract
The invention discloses a water quality prediction method and a water quality prediction system based on a water quality model. The method comprises the following steps: establishing a one-dimensional water quality model for a river network or a river reach area of a water quality area to be predicted according to a lattice Boltzmann method; establishing a two-dimensional water quality model for a key prediction area in a water quality area to be predicted according to a lattice Boltzmann method; the grid width at the boundary of the two-dimensional water quality model is equal to the river section width at the boundary of the one-dimensional water quality model; coupling the boundaries of the one-dimensional water quality model and the two-dimensional water quality model according to the mass and momentum conservation of solute particles to obtain a coupled water quality model; the coupled water quality model is a model formed by coupling the one-dimensional water quality model and the two-dimensional water quality model; and predicting the water quality area to be predicted according to the coupled model to obtain a parameter prediction result of the area to be predicted. The method and the system improve the calculation precision and efficiency of the model and improve the precision and efficiency of water quality prediction.
Description
Technical Field
The invention relates to the field of water quality prediction, in particular to a water quality prediction method and a water quality prediction system based on a water quality model.
Background
Water quality predictions include predictions of solute (contaminant) concentration distributions in the water quality. The existing water quality prediction is generally carried out by adopting a one-dimensional water quality model or a two-dimensional water quality model, the calculation speed of the one-dimensional water quality model is high, the calculation precision of the two-dimensional water quality model is high, but the one-dimensional water quality model or the two-dimensional water quality model can not meet the simulation requirement of water quality near a complex water network intersection and a sea entrance.
Therefore, the invention provides a water quality model with a one-dimensional water quality model and a two-dimensional water quality model coupled, wherein the one-dimensional water quality model is adopted at a river channel close to a straight river, the two-dimensional water quality model is adopted at a river bend with a larger horizontal scale and near a lake or an entrance, the two-dimensional water quality model and the river bend are subjected to boundary coupling calculation, and the concentration of pollutants or solutes in water is predicted through the coupled water quality model, so that the calculation precision and efficiency of the model can be improved, and the precision and efficiency of water quality prediction can be improved.
Disclosure of Invention
The invention aims to provide a water quality prediction method and a water quality prediction system based on a water quality model so as to improve the accuracy and efficiency of water quality prediction.
In order to achieve the purpose, the invention provides the following scheme:
a water quality prediction method based on a water quality model, the method comprising:
establishing a one-dimensional water quality model for a river network or a river reach area of a water quality area to be predicted according to a lattice Boltzmann method;
establishing a two-dimensional water quality model for a key prediction area in a water quality area to be predicted according to a lattice Boltzmann method; the grid width at the boundary of the two-dimensional water quality model is equal to the river section width at the boundary of the one-dimensional water quality model;
coupling the boundaries of the one-dimensional water quality model and the two-dimensional water quality model according to the mass and momentum conservation of solute particles to obtain a coupled water quality model; the coupled water quality model is a model formed by coupling the one-dimensional water quality model and the two-dimensional water quality model;
and predicting the water quality area to be predicted according to the coupled model to obtain a parameter prediction result of the area to be predicted.
Optionally, the method of coupling the one-dimensional water quality model and the two-dimensional water quality model according to the mass and momentum conservation of solute particles to obtain a coupled water quality model specifically includes:
obtaining a particle distribution function of the downstream flow in the water quality area to be predicted to the direction of the one-dimensional water quality model according to the one-dimensional water quality model
Wherein
A particle distribution function M representing the direction of the one-dimensional water quality model flowing to the two-dimensional water quality model in the water quality area to be predicted1D(end) represents the single wide solute mass, u, of the last mesh in the one-dimensional water quality model1D(end) representing a flow velocity of a last mesh in the one-dimensional water quality model;s1Drepresenting particle velocities of solute particles in the one-dimensional water quality model;
obtaining a particle distribution function of the upstream flow in the water quality area to be predicted to the direction of the two-dimensional water quality model according to the two-dimensional water quality model
Wherein
A particle distribution function M representing the direction of the two-dimensional water quality model flowing to the one-dimensional water quality model in the water quality area to be predicted2D(1) Representing the single wide solute mass, u, of the first row of meshes in the two-dimensional water quality model2D(1) Representing the longitudinal flow velocity of the first row of meshes in the two-dimensional water quality model, u2D(1) And u1D(end) the directions are parallel; s2DRepresenting particle velocities of solute particles of a first row of meshes in the two-dimensional water quality model;
according to the conservation of mass of solute particles
Wherein
Representing a single wide solute mass average of a first row of grids in the two-dimensional water quality model; wherein
Wherein
Representing a particle distribution function of a static direction in the last grid in the one-dimensional water quality model;
representing a first drainage net in the two-dimensional water quality modelParticle distribution function of transverse flow forward direction in the water quality area to be predicted in the grid;
representing a particle distribution function of a transverse flow reverse direction in the water quality area to be predicted in a first row of grids in the two-dimensional water quality model;
representing a particle distribution function of a static direction in a first row of grids in the two-dimensional water quality model;
according to conservation of momentum of solute particles
Resolving momentum of solute particles according to conservation of mass and conservation of momentum
Obtaining a particle distribution function of the downstream flow in the water quality area to be predicted to the direction of the one-dimensional water quality model according to the momentum of the particles, wherein the particle distribution function is as follows:
obtaining a particle distribution function of the upstream flow to the direction of the two-dimensional water quality model in the water quality area to be predicted according to the momentum of the particles as follows:
and coupling the boundaries of the one-dimensional water quality model and the two-dimensional water quality model according to the formula to obtain a coupled water quality model.
Optionally, the particle distribution function of the downstream flow in the water quality area to be predicted flowing to the direction of the one-dimensional water quality model is obtained according to the one-dimensional water quality model
The method specifically comprises the following steps:
obtaining according to the one-dimensional water quality model:
obtaining a particle distribution function of the downstream flowing to the direction of the one-dimensional water quality model in the water quality area to be predicted according to the deformation of the formula (1) and the formula (2)
Optionally, the particle distribution function of the upstream flow in the water quality area to be predicted flowing to the direction of the two-dimensional water quality model is obtained according to the two-dimensional water quality model
The method specifically comprises the following steps:
obtaining according to the two-dimensional water quality model:
wherein u is2D(1) Representing the longitudinal flow velocity, v, of the first row of meshes in the two-dimensional water quality model2D(1) Representing the transverse flow velocity, v, of the first row of meshes in the two-dimensional water quality model2D(1)≈0；；
Obtaining a particle distribution function of the upstream flow direction to the two-dimensional water quality model direction in the water quality area to be predicted according to the formula (3), the formula (4) and the formula (5)
Optionally, the predicting the water quality area to be predicted according to the coupled model to obtain a parameter prediction result of the water quality area to be predicted specifically includes:
and solving a convection diffusion equation according to the coupled model to predict the water quality area to be predicted, and obtaining the solute concentration distribution of the area to be predicted.
A water quality model-based water quality prediction system, the system comprising:
the one-dimensional water quality model building module is used for building a one-dimensional water quality model for a river network or a river reach area of a water quality area to be predicted according to a lattice Boltzmann method;
the two-dimensional water quality model building module is used for building a two-dimensional water quality model for a key prediction area in a water quality area to be predicted according to a lattice Boltzmann method; the grid width at the boundary of the two-dimensional water quality model is equal to the river section width at the boundary of the one-dimensional water quality model;
the coupling module is used for coupling the boundaries of the one-dimensional water quality model and the two-dimensional water quality model according to the mass and momentum conservation of solute particles to obtain a coupled water quality model; the coupled water quality model is a model formed by coupling the one-dimensional water quality model and the two-dimensional water quality model;
and the water quality prediction module is used for predicting the water quality area to be predicted according to the coupled model to obtain a parameter prediction result of the area to be predicted.
Optionally, the coupling module specifically includes:
a first particle distribution function obtaining unit for obtaining the particle distribution function of the downstream flow in the water quality area to be predicted towards the direction of the one-dimensional water quality model according to the one-dimensional water quality model
Wherein
A particle distribution function M representing the direction of the one-dimensional water quality model flowing to the two-dimensional water quality model in the water quality area to be predicted1D(end) represents the single wide solute mass, u, of the last mesh in the one-dimensional water quality model1D(end) representing a flow velocity of a last mesh in the one-dimensional water quality model; s1DRepresenting particle velocities of solute particles in the one-dimensional water quality model;
a second particle distribution function obtaining unit for obtaining the particle distribution function of the upstream flow in the water quality area to be predicted to the direction of the two-dimensional water quality model according to the two-dimensional water quality model
Wherein
A particle distribution function M representing the direction of the two-dimensional water quality model flowing to the one-dimensional water quality model in the water quality area to be predicted2D(1) Representing the single wide solute mass, u, of the first row of meshes in the two-dimensional water quality model2D(1) Representing the longitudinal flow velocity of the first row of meshes in the two-dimensional water quality model, u2D(1) And u1D(end) the directions are parallel; s2DRepresenting particle velocities of solute particles of a first row of meshes in the two-dimensional water quality model;
a particle mass relation obtaining unit for obtaining the mass conservation of the solute particles
Wherein
Representing a single wide solute mass average of a first row of grids in the two-dimensional water quality model; wherein
Wherein
Representing a particle distribution function of a static direction in the last grid in the one-dimensional water quality model;
representing a particle distribution function in the transverse flow forward direction in the water quality area to be predicted in a first row of grids in the two-dimensional water quality model;
representing a particle distribution function of a transverse flow reverse direction in the water quality area to be predicted in a first row of grids in the two-dimensional water quality model;
representing a particle distribution function of a static direction in a first row of grids in the two-dimensional water quality model;
a particle momentum relationship obtaining unit for obtaining the momentum conservation of the solute particles
A particle momentum solving unit for solving the momentum of the particles according to the mass and momentum conservation of the solute particles
A first particle distribution function determining unit, configured to obtain, according to the momentum of the particles, a particle distribution function of a downstream flow in the water quality region to be predicted toward the one-dimensional water quality model as:
a second particle distribution function determining unit, configured to obtain, according to the momentum of the particles, a particle distribution function in an upstream flow direction of the water quality region to be predicted to the two-dimensional water quality model direction, where the particle distribution function is:
and the boundary coupling unit is used for coupling the boundaries of the one-dimensional water quality model and the two-dimensional water quality model according to the formula to obtain a coupled water quality model.
Optionally, the first particle distribution function obtaining unit specifically includes:
the one-dimensional water quality model subunit is used for obtaining the following water quality models according to the one-dimensional water quality model:
a first deformation subunit, configured to obtain, according to the deformation of the equations (1) and (2), a particle distribution function flowing downstream in the water quality region to be predicted toward the one-dimensional water quality model
Optionally, the second particle distribution function obtaining unit specifically includes:
the two-dimensional water quality model subunit is used for obtaining the water quality model according to the two-dimensional water quality model:
wherein u is2D(1) Representing the longitudinal flow velocity, v, of the first row of meshes in the two-dimensional water quality model2D(1) Representing the transverse flow velocity, v, of the first row of meshes in the two-dimensional water quality model2D(1)≈0；；
A second deformation subunit, configured to obtain a particle distribution function flowing to the two-dimensional water quality model direction upstream in the water quality area to be predicted according to equation (3), equation (4), and equation (5)
Optionally, the water quality prediction module is configured to solve a convection diffusion equation according to the coupled model to predict the water quality area to be predicted, so as to obtain solute concentration distribution of the water quality area to be predicted.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
regarding the concept of introducing the cross section solute flow into a river network or a river reach in an area to be predicted, regarding water flow as one-dimensional flow, establishing a one-dimensional water quality model, and giving play to the characteristic that the one-dimensional water quality model quickly and accurately simulates the transmission and diffusion process of pollutants or conserved solutes; because the horizontal space scale of a wide water area or a key prediction area in the area to be predicted is far larger than the vertical space scale, the transverse change of the water quality parameter is far smaller than the change in the horizontal direction, a planar two-dimensional water quality model is adopted for simulation, and then the one-dimensional water quality model and the two-dimensional water quality model are coupled from the angle of distribution of microscopic particles according to the mass and momentum conservation of solute particles, so that the water quality prediction process of the whole area to be predicted is realized. Compared with the single use of a one-dimensional water quality model, the method increases the detail precision of the concentration field; compared with the simulation by singly using a two-dimensional water quality model, the calculation efficiency of the coupling simulation is higher, so that the efficient and accurate water quality simulation prediction of water areas such as river and lake intersections, sea entrances and the like is realized.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a schematic flow chart of a water quality prediction method based on a water quality model according to the present invention;
FIG. 2 is a schematic diagram of the coupling of a one-dimensional water quality model and a two-dimensional water quality model in the water quality prediction method based on the water quality model of the present invention;
FIG. 3 is a schematic structural diagram of a water quality prediction system based on a water quality model according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
FIG. 1 is a schematic flow chart of a water quality prediction method based on a water quality model according to the present invention. As shown in fig. 1, the method includes:
step 100: and establishing a one-dimensional water quality model for a river network or river reach area of the water quality area to be predicted according to a lattice Boltzmann method. Before a one-dimensional water quality model is established, the time-space distribution and transmission characteristics of pollutants in typical research areas such as river and lake systems and delta need to be analyzed, necessary conditions such as topography, landform, flow, water level and pollutant concentration in the river and lake areas and the delta areas of the research areas are determined, an environment data database such as pollutant degradation, diffusion and transmission is established, and a foundation is laid for establishing a one-dimensional and two-dimensional water quality coupling model.
A one-dimensional water quality model is established by using a lattice Boltzmann method, and for the concept of introducing section solute flow into a river network or a river reach in an area to be predicted, water flow is regarded as one-dimensional flow, the one-dimensional water quality model is established, and the characteristic that the one-dimensional water quality model rapidly and accurately simulates the transmission and diffusion process of pollutants or conserved solutes is exerted.
Step 200: and establishing a two-dimensional water quality model for a key prediction area in the water quality area to be predicted according to a lattice Boltzmann method. For a wide water area or a key prediction area in the area to be predicted, because the horizontal space scale of the area to be predicted is far larger than the vertical space scale, the transverse change of the water quality parameter is far smaller than the change in the horizontal direction, and a two-dimensional water quality model is constructed for simulation.
From the perspective of solute or contaminant transport, a mathematical model based on one-dimensional and two-dimensional convection dispersion equations is used for description. For a one-dimensional river channel or an open channel, considering dispersion and dispersion effects of water flow gradients on solutes or pollutants, and establishing a one-dimensional lattice Boltzmann model based on a self-adaptive grid; for a wide water area, solute or pollutant degradation is considered, and a plurality of lattice Boltzmann models coupled with two-dimensional water quality are established so as to improve the stability and the calculation precision of the models.
Step 300: and coupling the boundaries of the one-dimensional water quality model and the two-dimensional water quality model according to the mass and momentum conservation of solute particles to obtain a coupled water quality model.
Because different calculation methods are adopted by different areas in the area to be predicted and have different accuracies, the fact that the one-dimensional and two-dimensional coupling water quality models are formed by adopting different coupling methods to cover the whole calculation domain needs to be considered. The characteristic that the solute concentration of the one-dimensional water quality model and the two-dimensional water quality model changes along with the regional boundary to form dynamic change is fully considered, and the basic principle and the method of the coupling boundary position are finally determined. When the coupling boundary problem is processed, the boundary coupling of a one-dimensional and two-dimensional simulation area can be completed more conveniently and reasonably on the basis of ensuring the conservation of pollutant mass and momentum by using the conditions of equal solute mass and same flux at the connection section of the coupling model and expressing the conditions by using a particle balance distribution function in a lattice Boltzmann method. Meanwhile, to maintain the operational stability of the lattice boltzmann method, the grid local correlation and stability condition are maintained when the processing boundaries are coupled.
The one-dimensional and two-dimensional lattice Boltzmann water quality models are both existing efficient and accurate water quality models, and can respectively simulate solute transmission processes in open channel river networks and lakes and reservoirs. The existing water quality model couples the flow velocity calculated by using the one-dimensional water quality model and the water depth calculated by using the two-dimensional water quality model, so that the dynamic correlation of the two dimensional models is ensured, but the zero-gradient boundary condition is used, and the calculation error is inevitably introduced. Therefore, in order to avoid calculation errors, the invention utilizes the distribution characteristics of the microscopic particles of the lattice Boltzmann to couple the one-dimensional and two-dimensional lattice Boltzmann models from the distribution angle of the microscopic particles, can avoid using a zero-gradient boundary, fundamentally solves the problem of calculation errors of other traditional coupling methods, better accords with the characteristics of calculating the microscopic dynamic distribution of the lattice Boltzmann, and keeps the unique property of the mesoscale numerical method of reflecting macroscopic variables by the microscopic particles. The invention relates to a particle coupling method for coupling one-dimensional and two-dimensional water quality models by utilizing the characteristic particle distribution characteristics of a lattice Boltzmann method, which is a brand-new attempt.
Specifically, the process of coupling the one-dimensional water quality model and the two-dimensional water quality model is shown in fig. 2, and fig. 2 is a schematic diagram of coupling the one-dimensional water quality model and the two-dimensional water quality model in the water quality prediction method based on the water quality model. As shown in fig. 2, assuming that the water flow flows from the one-dimensional water quality model to the two-dimensional water quality model area, and the width of 3 grids at the boundary of the two-dimensional water quality model is the same as the width of the cross section of the river at the boundary of the one-dimensional water quality model, the grids at the boundary of the one-dimensional water quality model and the two-dimensional water quality model can be seen from fig. 2, the grid at the left side is the last grid of the one-dimensional water quality model, and the 3 grids at the right side are the first grid at the most upstream of the two-dimensional water quality modelThe row grid, i.e. the first row grid. s0、s1、s2、s3… denote the particle velocity vectors in different directions in the grid. The particle distribution function of the one-dimensional water quality model flowing to the two-dimensional water quality model at the coupling boundary
Is known (1D represents a one-dimensional water quality model), and the particle distribution function of the downstream flow to the one-dimensional water quality model
Is unknown; and the particle distribution function of the upstream flow in the two-dimensional water quality model (i.e. the particle distribution function of the one-dimensional water quality model flowing to the two-dimensional water quality model)
Is unknown. Although it is used for
And
the transfer directions of the particle distribution are complementary, but the calculation directions and modes of the particle distribution are different due to different dimensions between the first-dimensional water quality model and the second-dimensional water quality model, and the mechanism of mutual transfer is difficult to master.
And determining the particle distribution in unknown direction by utilizing the micro particles in known direction, so that the boundary coupling of the one-dimensional water quality model and the two-dimensional water quality model can be realized.
Taking the mass conservation and momentum conservation conditions of solute particles at the boundary as continuous conditions of one-dimensional and two-dimensional water quality model coupling, namely
Wherein M is1D(end) represents the single wide solute mass of the last mesh of the one-dimensional water quality model,
the average of the single wide solute masses of the first row of grids of the two-dimensional water quality model is represented. u. of1D(end) flow velocity, u, of the last mesh in the one-dimensional water quality model2D(1) Representing the longitudinal flow velocity, u, of the first row of grids in a two-dimensional water quality model2D(1) And u1D(end) indicates the same flow direction.
The following formula can be obtained from the lattice Boltzmann one-dimensional water quality model
Wherein s is1DAnd the particle velocity of solute particles in the one-dimensional water quality model is represented.
Obtained by transforming the formula (3)
The formula can be used as the outflow boundary of a one-dimensional water quality model, and the substitution of (4) into (2) can obtain
The two-dimensional water quality model of lattice Boltzmann can be used for obtaining
When the flow velocity in the longitudinal direction (the flow direction from upstream to downstream or downstream to upstream) of the water flow is much smaller than the flow velocity in the transverse direction (the direction perpendicular to the longitudinal direction is called the transverse direction), i.e. v < u, v can be approximately considered2D(1)≈0 (9)
Then by the transformation of the formulae (7) and (8) to give
The above three formulas (6) to (8) are used as inflow boundary condition calculation formulas of the two-dimensional lattice boltzmann model. Substituting (9) and (10) into (6) to obtain
Substituting (5) and (11) into (1) to obtain
U in the above formula1DM1D(end) and
are equal and are the only unknown quantities, as used herein
Is represented by the micro-particles of other one-dimensional and two-dimensional boundaries and the movement speed of the particles
Will be provided with
Substituting (4) to obtain an unknown particle distribution function in the boundary of the one-dimensional lattice Boltzmann modelNumber of
Will be provided with
Substitution (10) also makes it possible to calculate the unknown particle distribution function in the two-dimensional lattice Boltzmann model boundary
Wherein
Representing a particle distribution function of a static direction in the last grid in the one-dimensional water quality model;
representing a particle distribution function in the transverse flow forward direction in the water quality area to be predicted in a first row of grids in the two-dimensional water quality model;
representing a particle distribution function of a transverse flow reverse direction in the water quality area to be predicted in a first row of grids in the two-dimensional water quality model;
representing a particle distribution function of a static direction in a first row of grids in the two-dimensional water quality model; u. of2D(1) Representing the longitudinal flow velocity, v, of the first row of meshes in the two-dimensional water quality model2D(1) Representing the transverse flow velocity of a first row of grids in the two-dimensional water quality model;
a particle distribution function representing the direction of the two-dimensional water quality model flowing to the one-dimensional water quality model in the water quality area to be predicted。
By using the formula, the unknown particle distribution at the boundaries of the one-dimensional water quality model and the two-dimensional water quality model is completely calculated and supplemented according to the known particle distribution, and the solute concentration and flux of the two-dimensional models at the coupling boundary are ensured to be equal, so that the law of conservation of mass and momentum is satisfied, and the coupling of the one-dimensional water quality model and the two-dimensional water quality model is realized.
Step 400: and predicting the water quality area to be predicted according to the coupled model to obtain a parameter prediction result of the area to be predicted. Taking the prediction of the concentration of the pollutant solute in the water quality as an example, the convection diffusion equation is solved according to the coupled model to predict the water quality area to be predicted, so as to obtain the solute concentration distribution of the area to be predicted, and other parameters of the toxic substances in the water area can be predicted by utilizing the coupled model.
FIG. 3 is a schematic structural diagram of a water quality prediction system based on a water quality model according to the present invention. As shown in fig. 3, the system includes:
the one-dimensional water quality model building module 301 is used for building a one-dimensional water quality model for a river network or a river reach area of a water quality area to be predicted according to a lattice boltzmann method;
the two-dimensional water quality model building module 302 is used for building a two-dimensional water quality model for a key prediction area in a water quality area to be predicted according to a lattice boltzmann method; the grid width at the boundary of the two-dimensional water quality model is equal to the river section width at the boundary of the one-dimensional water quality model;
the coupling module 303 is configured to couple the boundaries of the one-dimensional water quality model and the two-dimensional water quality model according to the mass and momentum conservation of solute particles to obtain a coupled water quality model; the coupled water quality model is a model formed by coupling the one-dimensional water quality model and the two-dimensional water quality model;
and the water quality prediction module 304 is configured to predict the water quality area to be predicted according to the coupled model, and obtain a parameter prediction result of the area to be predicted. For example, for predicting the water quality pollutant solute concentration, the water quality prediction module 304 may solve the convection diffusion equation according to the coupled model to predict the water quality area to be predicted, so as to obtain the solute concentration distribution of the area to be predicted.
The coupling module 303 specifically includes:
a first particle distribution function obtaining unit for obtaining the particle distribution function of the downstream flow in the water quality area to be predicted towards the direction of the one-dimensional water quality model according to the one-dimensional water quality model
Wherein
A particle distribution function M representing the direction of the one-dimensional water quality model flowing to the two-dimensional water quality model in the water quality area to be predicted1D(end) represents the single wide solute mass, u, of the last mesh in the one-dimensional water quality model1D(end) representing a flow velocity of a last mesh in the one-dimensional water quality model; s1DRepresenting particle velocities of solute particles in the one-dimensional water quality model;
a second particle distribution function obtaining unit for obtaining the particle distribution function of the upstream flow in the water quality area to be predicted to the direction of the two-dimensional water quality model according to the two-dimensional water quality model
Wherein
A particle distribution function M representing the direction of the two-dimensional water quality model flowing to the one-dimensional water quality model in the water quality area to be predicted2D(1) Representing the single wide solute mass, u, of the first row of meshes in the two-dimensional water quality model2D(1) Representing the longitudinal flow velocity of the first row of meshes in the two-dimensional water quality model, u2D(1) And u1D(end) the directions are parallel; s2DRepresenting particle velocities of solute particles of a first row of meshes in the two-dimensional water quality model;
a particle mass relation obtaining unit for obtaining the mass conservation of the solute particles
Wherein
Representing a single wide solute mass average of a first row of grids in the two-dimensional water quality model; wherein
Wherein
Representing a particle distribution function of a static direction in the last grid in the one-dimensional water quality model;
representing a particle distribution function in the transverse flow forward direction in the water quality area to be predicted in a first row of grids in the two-dimensional water quality model;
representing a particle distribution function of a transverse flow reverse direction in the water quality area to be predicted in a first row of grids in the two-dimensional water quality model;
representing a particle distribution function of a static direction in a first row of grids in the two-dimensional water quality model;
a particle momentum relationship obtaining unit for obtaining the momentum conservation of the solute particles
A particle momentum solving unit for solving the momentum of the particles according to the mass and momentum conservation of the solute particles
A first particle distribution function determining unit, configured to obtain, according to the momentum of the particles, a particle distribution function of a downstream flow in the water quality region to be predicted toward the one-dimensional water quality model as:
a second particle distribution function determining unit, configured to obtain, according to the momentum of the particles, a particle distribution function in an upstream flow direction of the water quality region to be predicted to the two-dimensional water quality model direction, where the particle distribution function is:
and the boundary coupling unit is used for coupling the boundaries of the one-dimensional water quality model and the two-dimensional water quality model according to the formula to obtain a coupled water quality model.
The first particle distribution function obtaining unit specifically includes:
the one-dimensional water quality model subunit is used for obtaining the following water quality models according to the one-dimensional water quality model:
a first deformation subunit, configured to obtain, according to the deformation of the equations (1) and (2), a particle distribution function flowing downstream in the water quality region to be predicted toward the one-dimensional water quality model
The second particle distribution function obtaining unit specifically includes:
the two-dimensional water quality model subunit is used for obtaining the water quality model according to the two-dimensional water quality model:
wherein u is2D(1) Representing the longitudinal flow velocity, v, of the first row of meshes in the two-dimensional water quality model2D(1) Representing the transverse flow velocity, v, of the first row of meshes in the two-dimensional water quality model2D(1)≈0；；
A second deformation subunit, configured to obtain a particle distribution function flowing to the two-dimensional water quality model direction upstream in the water quality area to be predicted according to equation (3), equation (4), and equation (5)
The invention determines the particle distribution of unknown directions of the one-dimensional water quality model and the two-dimensional water quality model, and obtains the particle distribution through the known micro-particle distribution calculation, thereby not only ensuring the mass conservation of micro-particles transmitted between the one-dimensional water quality model and the two-dimensional water quality model, but also ensuring the momentum conservation of substances, accurately reducing the interactive motion process of solute particles between the models, and being a coupling mode of the one-dimensional water quality model and the two-dimensional water quality model based on micro-particle solution. Different from other methods, the particle coupling method only supplements the particle distribution in an unknown direction, and does not need to recalculate the particle distribution in all directions of the boundary grid; the calculation is accurate without overlapping a section of area, a zero gradient boundary which can bring calculation errors is not introduced, the calculation is relatively independent, the models of two dimensions can be independently calculated, only the grids of the coupling boundary participate in the coupling calculation when the models are coupled, and the complexity of the coupling model is greatly reduced; and the coupling calculation can be completed in the same time step, which is beneficial to the reuse of the model and the implementation of parallel calculation. The particle method coupling one and two-dimensional lattice Boltzmann water quality model is an accurate, efficient and brand-new water quality model coupling mode. The coupling principle can also be applied to the coupling of the one-dimensional water quality model and the three-dimensional water quality model or the coupling of the two-dimensional water quality model and the three-dimensional water quality model, and has the universality of the principle.
The particle method is coupled with the one-dimensional and two-dimensional lattice Boltzmann water quality models, the coupled transfer mechanism of pollutants or solute particles between the one-dimensional and two-dimensional water quality models is solved on a microscopic level by utilizing the supplemented solute momentum conservation principle, the characteristic of the mesoscale method that the microscopic particles reflect the change of macroscopic parameters by the lattice Boltzmann method is utilized, the particle method has stronger practicability and universality, and a high-efficiency and accurate coupling solution scheme is provided for simulating the water quality transfer problem in different dimensions by the lattice Boltzmann method.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (8)
1. A water quality prediction method based on a water quality model is characterized by comprising the following steps:
treating the water quality area to be predicted according to a lattice Boltzmann methodEstablishing a one-dimensional water quality model in a river network or river reach area of the area; the particle distribution function of the downstream flow in the water quality area to be predicted to the direction of the one-dimensional water quality model is
Wherein
A particle distribution function M representing the direction of the one-dimensional water quality model flowing to the two-dimensional water quality model in the water quality area to be predicted1D(end) represents the single wide solute mass, u, of the last mesh in the one-dimensional water quality model1D(end) representing a flow velocity of a last mesh in the one-dimensional water quality model; s1DRepresenting particle velocities of solute particles in the one-dimensional water quality model;
establishing a two-dimensional water quality model for a key prediction area in a water quality area to be predicted according to a lattice Boltzmann method; the grid width at the boundary of the two-dimensional water quality model is equal to the river section width at the boundary of the one-dimensional water quality model; the particle distribution function of the upstream flow in the water quality area to be predicted to the direction of the two-dimensional water quality model is
Wherein
A particle distribution function M representing the direction of the two-dimensional water quality model flowing to the one-dimensional water quality model in the water quality area to be predicted2D(1) Representing the single wide solute mass, u, of the first row of meshes in the two-dimensional water quality model2D(1) Representing the longitudinal flow velocity of the first row of meshes in the two-dimensional water quality model, u2D(1) And u1D(end) the directions are parallel; s2DRepresenting particle velocities of solute particles of a first row of meshes in the two-dimensional water quality model;
coupling the boundaries of the one-dimensional water quality model and the two-dimensional water quality model according to the mass and momentum conservation of solute particles to obtain a coupled water quality model; the coupled water quality model is a model formed by coupling the one-dimensional water quality model and the two-dimensional water quality model;
predicting the water quality area to be predicted according to the coupled model to obtain a parameter prediction result of the water quality area to be predicted;
according to the mass and momentum conservation of solute particles, coupling the boundaries of the one-dimensional water quality model and the two-dimensional water quality model to obtain a coupled water quality model, and the method specifically comprises the following steps:
according to the conservation of mass of solute particles
Wherein
Representing a single wide solute mass average of a first row of grids in the two-dimensional water quality model; wherein
Wherein
Representing a particle distribution function of a static direction in the last grid in the one-dimensional water quality model;
representing a particle distribution function in the transverse flow forward direction in the water quality area to be predicted in a first row of grids in the two-dimensional water quality model;
representing a particle distribution function of a transverse flow reverse direction in the water quality area to be predicted in a first row of grids in the two-dimensional water quality model;
representing a particle distribution function of a static direction in a first row of grids in the two-dimensional water quality model;
according to conservation of momentum of solute particles
Resolving momentum of solute particles according to conservation of mass and conservation of momentum
Obtaining a particle distribution function of the downstream flow in the water quality area to be predicted to the direction of the one-dimensional water quality model according to the momentum of the particles, wherein the particle distribution function is as follows:
obtaining a particle distribution function of the upstream flow to the direction of the two-dimensional water quality model in the water quality area to be predicted according to the momentum of the particles as follows:
and coupling the boundaries of the one-dimensional water quality model and the two-dimensional water quality model according to the formula to obtain a coupled water quality model.
2. The water quality prediction method according to claim 1, wherein the one-dimensional water quality model is used to obtain the one-dimensional water quality of the downstream flow in the water quality area to be predictedParticle distribution function of model orientation
The method specifically comprises the following steps:
obtaining according to the one-dimensional water quality model:
obtaining a particle distribution function of the downstream flowing to the direction of the one-dimensional water quality model in the water quality area to be predicted according to the deformation of the formula (1) and the formula (2)
3. The water quality prediction method according to claim 1, wherein the particle distribution function of the upstream flow in the water quality area to be predicted flowing to the direction of the two-dimensional water quality model is obtained according to the two-dimensional water quality model
The method specifically comprises the following steps:
obtaining according to the two-dimensional water quality model:
wherein u is2D(1) Representing the longitudinal flow velocity, v, of the first row of meshes in the two-dimensional water quality model2D(1) Representing the transverse flow velocity, v, of the first row of meshes in the two-dimensional water quality model2D(1)≈0；；
Obtaining a particle distribution function of the upstream flow direction to the two-dimensional water quality model direction in the water quality area to be predicted according to the formula (3), the formula (4) and the formula (5)
4. The water quality prediction method according to claim 1, wherein the predicting the water quality area to be predicted according to the coupled model to obtain a parameter prediction result of the water quality area to be predicted specifically comprises:
and solving a convection diffusion equation according to the coupled model to predict the water quality area to be predicted, and obtaining the solute concentration distribution of the water quality area to be predicted.
5. A water quality prediction system based on a water quality model, the system comprising:
the one-dimensional water quality model building module is used for building a one-dimensional water quality model for a river network or a river reach area of a water quality area to be predicted according to a lattice Boltzmann method; the particle distribution function of the downstream flow in the water quality area to be predicted to the direction of the one-dimensional water quality model is
Wherein
A particle distribution function M representing the direction of the one-dimensional water quality model flowing to the two-dimensional water quality model in the water quality area to be predicted1D(end) Single Wide solute quality representing the last mesh in the one-dimensional Water quality modelAmount u1D(end) representing a flow velocity of a last mesh in the one-dimensional water quality model; s1DRepresenting particle velocities of solute particles in the one-dimensional water quality model;
the two-dimensional water quality model building module is used for building a two-dimensional water quality model for a key prediction area in a water quality area to be predicted according to a lattice Boltzmann method; the grid width at the boundary of the two-dimensional water quality model is equal to the river section width at the boundary of the one-dimensional water quality model; the particle distribution function of the upstream flow in the water quality area to be predicted to the direction of the two-dimensional water quality model is
Wherein
A particle distribution function M representing the direction of the two-dimensional water quality model flowing to the one-dimensional water quality model in the water quality area to be predicted2D(1) Representing the single wide solute mass, u, of the first row of meshes in the two-dimensional water quality model2D(1) Representing the longitudinal flow velocity of the first row of meshes in the two-dimensional water quality model, u2D(1) And u1D(end) the directions are parallel; s2DRepresenting particle velocities of solute particles of a first row of meshes in the two-dimensional water quality model;
the coupling module is used for coupling the boundaries of the one-dimensional water quality model and the two-dimensional water quality model according to the mass and momentum conservation of solute particles to obtain a coupled water quality model; the coupled water quality model is a model formed by coupling the one-dimensional water quality model and the two-dimensional water quality model;
the water quality prediction module is used for predicting the water quality area to be predicted according to the coupled model to obtain a parameter prediction result of the water quality area to be predicted;
the coupling module specifically includes:
a particle mass relation obtaining unit for obtaining the mass conservation of the solute particles
Wherein
Representing a single wide solute mass average of a first row of grids in the two-dimensional water quality model; wherein
Wherein
Representing a particle distribution function of a static direction in the last grid in the one-dimensional water quality model;
representing a particle distribution function in the transverse flow forward direction in the water quality area to be predicted in a first row of grids in the two-dimensional water quality model;
representing a particle distribution function of a transverse flow reverse direction in the water quality area to be predicted in a first row of grids in the two-dimensional water quality model;
representing a particle distribution function of a static direction in a first row of grids in the two-dimensional water quality model;
a particle momentum relationship obtaining unit for obtaining the momentum conservation of the solute particles
A particle momentum solving unit for solving the momentum of the particles according to the mass and momentum conservation of the solute particles
A first particle distribution function determining unit, configured to obtain, according to the momentum of the particles, a particle distribution function of a downstream flow in the water quality region to be predicted toward the one-dimensional water quality model as:
a second particle distribution function determining unit, configured to obtain, according to the momentum of the particles, a particle distribution function in an upstream flow direction of the water quality region to be predicted to the two-dimensional water quality model direction, where the particle distribution function is:
and the boundary coupling unit is used for coupling the boundaries of the one-dimensional water quality model and the two-dimensional water quality model according to the formula to obtain a coupled water quality model.
6. The water quality prediction system of claim 5, wherein the coupling module further comprises:
the one-dimensional water quality model subunit is used for obtaining the following water quality models according to the one-dimensional water quality model:
a first deformation subunit, configured to obtain, according to the deformation of the equations (1) and (2), a particle distribution function flowing downstream in the water quality region to be predicted toward the one-dimensional water quality model
7. The water quality prediction system of claim 5, wherein the coupling module further comprises:
the two-dimensional water quality model subunit is used for obtaining the water quality model according to the two-dimensional water quality model:
wherein u is2D(1) Representing the longitudinal flow velocity, v, of the first row of meshes in the two-dimensional water quality model2D(1) Representing the transverse flow velocity, v, of the first row of meshes in the two-dimensional water quality model2D(1)≈0；；
A second deformation subunit, configured to obtain a particle distribution function flowing to the two-dimensional water quality model direction upstream in the water quality area to be predicted according to equation (3), equation (4), and equation (5)
8. The water quality prediction system of claim 5, wherein the water quality prediction module is configured to solve a convection diffusion equation according to the coupled model to predict the water quality area to be predicted, and obtain the solute concentration distribution of the water quality area to be predicted.
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