CN116611274B - Visual numerical simulation method for groundwater pollution migration - Google Patents
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Abstract
The embodiment of the invention provides a visual numerical simulation method for groundwater pollution migration, which belongs to the technical field of data processing and specifically comprises the following steps: acquiring groundwater pollution data of a target area; constructing a conceptual model according to groundwater pollution data; constructing a geologic body structure model according to the conceptual model; constructing a three-dimensional grid model according to the spatial data, the conceptual model and the structural model; establishing an attribute field model according to the three-dimensional grid model; establishing a simulation numerical model of multiple solver types according to the three-dimensional grid model and the attribute field model, performing flow field simulation and pollutant diffusion simulation by using the simulation numerical model, and performing parameter correction by using a parameter correction module in the simulation process to construct a variable parameter model; and carrying out simulation according to the simulation numerical model and the variable parameter model iteration, and generating an analysis result and a data report. By the scheme provided by the invention, the prediction efficiency, adaptability and accuracy are improved.
Description
Technical Field
The embodiment of the invention relates to the technical field of data processing, in particular to a visual numerical simulation method for groundwater pollution migration.
Background
At present, with the rapid development of urban treatment and the continuous increase of industrial production, the problem of groundwater pollution is increasingly emphasized. In order to better understand and control groundwater pollution, a groundwater pollution visual simulation technology is adopted, namely, groundwater pollution conditions and solute transportation rules are visually presented through a three-dimensional visual technology. The groundwater pollution visual simulation technology combines groundwater flow with three-dimensional visualization of a groundwater pollution model, and combines actually collected hydrogeologic data with a calculation program, so that a complete groundwater flow and pollution transmission model is constructed. Through the simulation technology, the flow and pollution degree of the underground water can be observed in real time, so that the pollution diffusion of the underground water can be predicted and controlled better. The underground water pollution visual simulation technology needs to adopt a certain modeling method and algorithm, the prior art has complicated data input, and the prior art lacks a hydrogeological basic data management system, so that data cannot be stored in a centralized manner, inconvenience is caused for later research, and the data processing efficiency is low and the prediction precision is low.
Therefore, a visual numerical simulation method for groundwater pollution migration with high treatment efficiency, adaptability and accuracy is needed.
Disclosure of Invention
Therefore, the embodiment of the invention provides a visual numerical simulation method for groundwater pollution migration, which at least partially solves the problems of poor prediction efficiency, adaptability and accuracy in the prior art.
The embodiment of the invention provides a method for predicting efficiency, adaptability and accuracy, which comprises the following steps:
step 1, obtaining groundwater pollution data of a target area;
step 2, constructing a conceptual model according to groundwater pollution data;
the step 2 specifically includes:
according to the hydrogeological plan and the section in the groundwater pollution data, the frame modeling range on the basis of the subsequent construction of the site three-dimensional model is deduced, and a conceptual model is established;
step 3, constructing a geologic body structure model according to the conceptual model;
the step 3 specifically includes:
based on the conceptual model, establishing a geologic body structure model by combining an observation well distribution table, borehole lithology data and a geological profile;
step 4, constructing a three-dimensional grid model according to the space data, the conceptual model and the structural model;
the step 4 specifically includes:
based on the space data, the conceptual model and the structural model, dividing the three-dimensional space into unit bodies by utilizing a three-dimensional mesh subdivision algorithm, and forming a three-dimensional mesh model by all unit body sets;
step 5, establishing an attribute field model according to the three-dimensional grid model;
the step 5 specifically includes:
an interpolation method is adopted to distribute initial attributes to each grid cut by the three-dimensional grid model to form an attribute field model, wherein the initial attributes comprise an initial water level, an initial pollutant concentration, a water storage rate, a delay factor, effective porosity, a diffusion coefficient, a permeability coefficient and boundary conditions;
step 6, establishing a simulation numerical model of multiple solver types according to the three-dimensional grid model and the attribute field model, performing flow field simulation and pollutant diffusion simulation by using the simulation numerical model, and performing parameter correction by using a parameter correction module in the simulation process to construct a variable parameter model;
the step 6 specifically includes:
according to the three-dimensional grid model and the attribute field model, combining the influencing factors of underground water flow and solute migration, adopting a finite difference method to establish a mass conservation equation and a motion equation on nodes and units, establishing a simulation numerical model using multiple solver types, performing flow field simulation and pollutant diffusion simulation, and performing parameter correction by using a parameter correction model in the simulation process to construct a variable parameter model;
and 7, carrying out simulation iteration according to the simulation numerical model and the variable parameter model, and generating an analysis result and a data report.
According to a specific implementation manner of the embodiment of the present invention, the step of dividing the three-dimensional space into unit bodies by using the three-dimensional mesh subdivision algorithm includes:
establishing a bounding box, dividing cube elements in the range of the bounding box, and determining the function values of eight vertexes of each small cube, wherein the function values of the vertexesTernary function scalar value +.>The spatial position relation between the identification point and the implicit curved surface defined by the ternary function is that
；
And selecting a corresponding implicit function expression, and extracting an implicit function value of a cube element between every two stratum surfaces according to the equivalent surface function in the subdivision process to serve as a stratum identifier of the cube element to form a unit body.
According to a specific implementation manner of the embodiment of the invention, the expression of the initial attribute is
wherein ,representing grid cell->Interpolation function at the center point +.>Representing the attribute value at the cell center point, the interpolation function is conditioned on the maximum search radius and the maximum search point number by using an inverse distance weighting method.
According to a specific implementation of an embodiment of the present invention, the solver types include a conjugate gradient solver, a bistable conjugate gradient solver, and a multiple grid solver.
According to a specific implementation manner of the embodiment of the invention, the expression of the simulation numerical model is
wherein ,representing the number of finite element nodes, +.>Index subscript of representing voxel->Representation->Time->A head value of each node;
coefficients ofFor water head->Is expressed as:
wherein ,is->Permeability coefficient of direction, < >>Is a set of three-dimensional directions->For the current->The head estimate of a node is solved by this method>The change rate in the direction obtains the total water head change rate of the node;
coefficients ofFor water head->Is expressed as:
wherein the subscriptRepresenting the two-dimensional index of the node in the equation, +.>For water storage capacity, add>For time order->For the current->A head estimate of the node;
coefficients ofAs a source sink item, expressed as:
wherein ,is a fluid source sink item;
the percolation coupling equation and the convection-diffusion coupling equation of the variable parameter model are expressed as:
wherein ,for osmotic coefficient->For the source sink item->Is water head (or)>For effective porosity, ++>For blocking factor, ->Is of dispersion coefficient->For the source sink item->For adsorbate density, ++>For various chemical reactions, ++>For adsorption term rate constant, +.>Is dynamic adsorption rate coefficient, +.>Is the mass of the compound adsorbed per unit mass of adsorbate, < >>Is the solute concentration.
The processing efficiency, adaptability and accuracy scheme in the embodiment of the invention comprises the following steps: step 1, obtaining groundwater pollution data of a target area; step 2, constructing a conceptual model according to groundwater pollution data; step 3, constructing a geologic body structure model according to the conceptual model; step 4, constructing a three-dimensional grid model according to the space data, the conceptual model and the structural model; step 5, establishing an attribute field model according to the three-dimensional grid model; step 6, establishing a simulation numerical model of multiple solver types according to the three-dimensional grid model and the attribute field model, performing flow field simulation and pollutant diffusion simulation by using the simulation numerical model, and performing parameter correction by using a parameter correction module in the simulation process to construct a variable parameter model; and 7, carrying out simulation iteration according to the simulation numerical model and the variable parameter model, and generating an analysis result and a data report.
The embodiment of the invention has the beneficial effects that: according to the scheme, the data in different periods are checked and analyzed through setting and management of the data in the modeling process, the model is checked and modified, different simulation parameters and solvers are adopted for pollution migration under different conditions, a parameter feedback module is established, a parameter list is updated in real time, and the efficiency and accuracy of groundwater pollution numerical simulation are improved; the underground water pollution monitoring, collecting and simulating data and parameters are integrated and visualized, so that the simulation flow links can be intuitively known, and the comprehensive management, evaluation and prediction capabilities of site pollution are improved.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed 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 that other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow chart of a visual numerical simulation method for groundwater pollution migration provided by an embodiment of the invention;
FIG. 2 is a schematic diagram of a specific implementation process of a visual numerical simulation method for groundwater pollution migration provided by an embodiment of the invention;
FIG. 3 is a schematic diagram of a pollution site conceptual model established in an application example of an underground water pollution simulation method according to an embodiment of the present invention;
fig. 4 is a schematic diagram of a geologic body structure model established in an application example of a groundwater pollution simulation method according to an embodiment of the invention;
FIG. 5 is a schematic diagram of a three-dimensional mesh model obtained by mesh division in an application example of a groundwater pollution simulation method according to an embodiment of the invention;
FIG. 6 is a schematic diagram of a flow chart of assignment and numerical simulation solution of attribute parameters in an application example of an underground water pollution simulation method according to an embodiment of the present invention;
fig. 7 is a schematic diagram illustrating a structure diagram and a three-dimensional display of results in an integrated system in an application example of a groundwater pollution simulation method according to an embodiment of the invention.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
Other advantages and effects of the present invention will become apparent to those skilled in the art from the following disclosure, which describes the embodiments of the present invention with reference to specific examples. It will be apparent that the described embodiments are only some, but not all, embodiments of the invention. The invention may be practiced or carried out in other embodiments that depart from the specific details, and the details of the present description may be modified or varied from the spirit and scope of the present invention. It should be noted that the following embodiments and features in the embodiments may be combined with each other without conflict. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It is noted that various aspects of the embodiments are described below within the scope of the following claims. It should be apparent that the aspects described herein may be embodied in a wide variety of forms and that any specific structure and/or function described herein is merely illustrative. Based on the present disclosure, one skilled in the art will appreciate that one aspect described herein may be implemented independently of any other aspect, and that two or more of these aspects may be combined in various ways. For example, an apparatus may be implemented and/or a method practiced using any number of the aspects set forth herein. In addition, such apparatus may be implemented and/or such methods practiced using other structure and/or functionality in addition to one or more of the aspects set forth herein.
It should also be noted that the illustrations provided in the following embodiments merely illustrate the basic concept of the present invention by way of illustration, and only the components related to the present invention are shown in the drawings and are not drawn according to the number, shape and size of the components in actual implementation, and the form, number and proportion of the components in actual implementation may be arbitrarily changed, and the layout of the components may be more complicated.
In addition, in the following description, specific details are provided in order to provide a thorough understanding of the examples. However, it will be understood by those skilled in the art that the aspects may be practiced without these specific details.
The embodiment of the invention provides a visual numerical simulation method for migration of groundwater pollution, which can be applied to an analysis process of migration rules of groundwater pollutants.
Referring to fig. 1, a flow chart of a visual numerical simulation method for groundwater pollution migration is provided in an embodiment of the invention. As shown in fig. 1 and 2, the method mainly comprises the following steps:
step 1, obtaining groundwater pollution data of a target area;
in specific implementation, related data such as groundwater pollution sources, groundwater pollutant content, groundwater flow speed and the like are obtained through various data acquisition modes, and data source pretreatment is carried out for the input of analog data. The acquisition mode comprises site monitoring and sample experiment, and acquired data is analyzed and preprocessed and is arranged into a plurality of data sets according to data types and characteristics so as to be convenient for subsequent processing and analysis. And designing a plurality of data structure input programs supporting source data and comprising standard formats and custom formats, and ensuring the integrity of data reading.
For example, a geological plan, a geological profile, and an observation well profile are acquired: taking a certain heavy metal polluted site as an example, a detailed site survey report is used as a map source, and the coordinate distribution of observation wells is marked on a map of a plan view and a section view.
Further, the investigation report is analyzed, the obtained information data is classified, sorted and normalized, specifically, the space data is normalized in a form of coordinates plus stratum marks and is input into a data file, the non-space data is stored in a form of a sequence table as a general text or CSV table file, and a general index lookup table is established for the two data so as to facilitate subsequent indexes.
Step 2, constructing a conceptual model according to groundwater pollution data;
further, the step 2 specifically includes:
and according to the hydrogeological plan and the section in the groundwater pollution data, the modeling range of the frame on the basis of the follow-up construction of the site three-dimensional model is deduced, and a conceptual model is established.
In specific implementation, a conceptual model is constructed by defining modeling targets including a space coordinate system and parameter units, groundwater types, solute adsorption types, reaction types and the like; determining the space and time range of the model and the basic model scale according to collected and tidied geological, hydrologic, engineering and environmental data and information; a generalized global element system showing formation distribution, subsurface flow fields and pollution source diffusion migration trends is initially established, including boundary generalization and internal structure generalization.
For example, the rough simulation range is framed on the basis of the ground plane profile and the hydrogeological plan and the section in the survey report, the follow-up construction of the three-dimensional model of the ground is deduced, and the conceptual model of the ground is constructed as shown in fig. 3. In this example, as shown in fig. 3, the soil properties from the surface down are roughly classified into a heterofill, a silty clay, a round gravel, a strong wind mudstone and a wind mudstone, and the submerged layer is a 3 rd round gravel layer from the surface down, and the boundary range and the relative position of the pollution source and the diffusion migration process in the groundwater are roughly determined according to the groundwater flow field characteristics.
Step 3, constructing a geologic body structure model according to the conceptual model;
on the basis of the above embodiment, the step 3 specifically includes:
based on the conceptual model, a geologic body structure model is built by combining an observation well distribution table, borehole lithology data and a geological profile.
In specific implementation, a geologic body structure model is built based on the conceptual model and by combining the acquired drilling distribution table, drilling lithology data, geological section views and the like. The model comprises a hierarchical structure and a vector model of the entity object, wherein the hierarchical structure is used for describing the space distribution rule of the stratum, and the vector model of the entity object is used for describing the entity morphology and the vector attribute of the space element. Based on known rock formation information and lithology data, attribution judgment is carried out on the boundary parts of the stratum surface at the junctions of all vertical upper and lower strata, and a more reasonable structural model is constructed, as shown in fig. 4, which is a geologic body structural model in the example.
Further, for the vertical direction of the structural model, the hierarchical structure is generally represented by stratigraphic sequences, each stratigraphic sequence comprising its number, name and aquifer marking, provided thatLayer stratum->The spatial range of the layer on the plane is +.>The thickness in the vertical direction is +.>The hierarchy of the formation may be expressed as:
and satisfies the following:
。
step 4, constructing a three-dimensional grid model according to the space data, the conceptual model and the structural model;
on the basis of the above embodiment, the step 4 specifically includes:
based on the space data, the conceptual model and the structural model, the three-dimensional space is divided into unit bodies by utilizing a three-dimensional mesh subdivision algorithm, and all the unit bodies are assembled to form the three-dimensional mesh model.
Further, the step of dividing the three-dimensional space into unit bodies by using the three-dimensional mesh subdivision algorithm includes:
establishing a bounding box, dividing cube elements in the range of the bounding box, and determining the function values of eight vertexes of each small cube, wherein the function values of the vertexesTernary function scalar value +.>The spatial position relation between the identification point and the implicit curved surface defined by the ternary function is that
；
And selecting a corresponding implicit function expression, and extracting an implicit function value of a cube element between every two stratum surfaces according to the equivalent surface function in the subdivision process to serve as a stratum identifier of the cube element to form a unit body.
In specific implementation, in this example, encryption points are set on a model boundary and structured meshing is performed, and further stated that stratum marks need to be given to each obtained mesh element in the meshing process, and the three-dimensional model meshing is implemented by means of an implicit function, and the three-dimensional model meshing comprises structured meshes and unstructured meshes.
The structured grid subdivision establishes a bounding box space model according to the input field conceptual model and the structure information, and regularly cuts the space model, namely in spaceThe three directions are divided into a certain space step length) Controlling coordinates of three-dimensional points, each three-dimensional point can be abstracted into a cube (length, width and height are respectively) Model information, including spatial geographic location and node information, is stored using a regular grid data table.
The unstructured grid subdivision carries out irregular spatial cutting on the three-dimensional model according to the input field conceptual model and structure information, namely the three-dimensional model is divided into a set of irregular voxels, each irregular voxel represents spatial information of a voxel region, data interaction among the voxels is realized through common corner points, and an irregular grid data file is used for storing model spatial information, wherein the model spatial information comprises three-dimensional points (irregular voxel corner point coordinates) and three-dimensional volumes (irregular voxel corner point serial numbers).
Taking structured grid subdivision as an example, the embodiment of the invention specifically firstly establishes a bounding box, divides the cube elements within the scope of the bounding box, determines the function values of eight vertexes of each small cube, and the vertex functionsTernary function scalar value +.>Spatial positional relationship (internal, on-plane, external) of the identification point and the implicit surface defined by the ternary function:
further, according to the mode, a proper implicit function expression is selected, and in the splitting process, the implicit function value of the cube element between every two stratum surfaces is extracted according to the equivalent surface function and is used as the stratum identification. In this embodiment, the formation identifier 3 is labeled as an aquifer.
Further, in the present invention, the three-dimensional grid model is built by specifying the side length of the structured grid or the grid number in the three-dimensional direction to obtain the simulation accuracy meeting the requirement, in this embodiment, the resolution of the split plane is selected to be 10m, the vertical resolution is selected to be 0.5m, and the built three-dimensional grid model is shown in fig. 5.
Step 5, establishing an attribute field model according to the three-dimensional grid model;
further, the step 5 specifically includes:
and (3) distributing initial attributes to each grid cut by the three-dimensional grid model by adopting an interpolation method to form an attribute field model, wherein the initial attributes comprise an initial water level, an initial pollutant concentration, a water storage rate, a delay factor, effective porosity, a diffusion coefficient, a permeability coefficient and boundary conditions.
Further, the expression of the initial attribute is
wherein ,representing grid cell->Interpolation function at the center point +.>Representing the attribute value at the cell center point, the interpolation function is conditioned on the maximum search radius and the maximum search point number by using an inverse distance weighting method.
In particular implementations, the initial properties include initial water level, initial contaminant concentration, water storage rate, delay factor, effective porosity, diffusion coefficient, permeability coefficient, and boundary conditions.
Further, due to the limited number of observation wells, all attribute values of the 10m high-precision grid cannot be obtained, and in this example, the parameter values are extracted for each voxel by adopting an interpolation method:
further, for a certain attribute item, the attribute value is set asIt can be described in a discrete manner:
wherein ,representing grid cell->Interpolation function at the center point +.>Representing the attribute value at the cell center point. Similarly, permeability->Porosity->Underground water level->Isohydrologic indicators can also be described in discrete terms.
Further, thereinInterpolation function to apply Inverse Distance Weighting (IDW) to maximum search radiusAnd maximum search points +.>As a limiting condition:
wherein ,for the property value of the i-th point, +.>For the distance of the i-th point from the current point to be interpolated,for the current spatial coordinates of the point to be interpolated, +.>For the spatial coordinates of the ith interpolation point, +.>And the inverse distance weight of the ith interpolation point.
Further, through the steps, a three-dimensional grid model with stratum marks, attribute values and initial conditions is established, and the model can be used as an initial iterative input source of numerical simulation.
Meanwhile, boundary conditions are divided into Dirichlet boundary conditions and Norman boundary conditions according to types, and the setting of the boundary conditions is derived from field real detection data and is divided into seepage field boundary conditions and concentration field boundary conditions.
Let the boundary of the simulation area beThe boundary type parameter may be expressed as:
wherein For a set of regions specifying traffic boundaries +.>For a set of zones specifying a waterhead boundary, +.>For the set of areas affecting the water level change by isolation and pore elasticity effects +.>Is a collection of overflow areas.
Further, the four types of boundary conditions described above may be specified according to the actual site.
Step 6, establishing a simulation numerical model of multiple solver types according to the three-dimensional grid model and the attribute field model, performing flow field simulation and pollutant diffusion simulation by using the simulation numerical model, and performing parameter correction by using a parameter correction module in the simulation process to construct a variable parameter model;
on the basis of the above embodiment, the step 6 specifically includes:
according to the three-dimensional grid model and the attribute field model, the influence factors of underground water flow and solute migration are combined, a mass conservation equation and a motion equation are established on the nodes and the units by adopting a finite difference method, a simulation numerical model using multiple solver types is established, flow field simulation and pollutant diffusion simulation are carried out, parameter correction is carried out by using a parameter correction model in the simulation process, and a variable parameter model is established.
Optionally, the solver types include a conjugate gradient solver, a bistable conjugate gradient solver, and a multiple grid solver.
Further, the expression of the simulation numerical model is
wherein ,representing the number of finite element nodes, +.>Index subscript of representing voxel->Representation->Time->A head value of each node;
coefficients ofFor water head->Is expressed as:
wherein ,is->Permeability coefficient of direction, < >>Is a set of three-dimensional directions->For the current->The head estimate of a node is solved by this method>The change rate in the direction obtains the total water head change rate of the node;
coefficients ofFor water head->Is expressed as:
wherein the subscriptRepresenting the two-dimensional index of the node in the equation, +.>For water storage capacity, add>For time order->Is at presentA head estimate of the node;
coefficients ofAs a source sink item, expressed as:
wherein ,is a fluid source sink item;
the percolation coupling equation and the convection-diffusion coupling equation of the variable parameter model are expressed as:
wherein ,for osmotic coefficient->For the source sink item->Is water head (or)>For effective porosity, ++>In order for the blocking factor to be a factor,is of dispersion coefficient->For the source sink item->For adsorbate density, ++>For various chemical reactions, ++>For adsorption term rate constant, +.>Is dynamic adsorption rate coefficient, +.>Is the mass of the compound adsorbed per unit mass of adsorbate, < >>Is the solute concentration.
In specific implementation, fig. 6 is a schematic diagram of assignment of attribute parameters and numerical simulation solving process in an application example according to an embodiment of the present invention. The finite difference simulator adopts a regular grid space discrete and time approximation method to process a field model to form a large-scale sparse linear equation set, and takes a water head as an example, the solution scheme is as follows:
is provided withFor solving the Dirichlet problem of the seepage field model, according to a three-dimensional finite difference method, taking the values of t time steps of all water heads based on an implicit difference method, the method is +.>The method meets the following conditions:
wherein ,represents the head value at the center point of the t+1 time-scale finite difference grid, +.>Water head value representing t-1 time-scale finite difference grid central point, +.>Represents the water storage capacity of unit volume element and water head +.>And (5) correlation. Considering all finite difference grid nodes to obtain an integral seepage field model, the method can be approximated as:
wherein ,representing the number of finite element nodes, +.>Index subscript of representing voxel->Representation->Time->A head value of each node;
further, coefficientsFor water head->Is expressed as:
wherein ,is->Permeability coefficient of direction, < >>Is a set of three-dimensional directions->For the current->Nodes ofWater head estimation, by which the +.>The change rate in the direction obtains the total water head change rate of the node;
coefficients ofFor water head->Is expressed as:
wherein the subscriptRepresenting the two-dimensional index of the node in the equation, +.>For water storage capacity, add>For time order->Is at presentA head estimate of the node;
coefficients ofAs a source sink item, expressed as:
wherein ,is a fluid source sink item;
further, a final form of a sparse linear system of equations can be obtained, the implicit solution of which is:
wherein ,is a linear coefficient>Is->The linear system matrix of sub-regions, further, the finite difference voxel result set, may be expressed as:
wherein ,is->The water head value at the central point of the time-order finite difference grid.
As a further technical scheme of the invention, aiming at the problem of solving the large sparse linear equation set formed by the numerical model, a plurality of solving types such as conjugate gradient, bistable conjugate gradient, multiple grids and the like can be selected to be adopted for numerical operation:
optionally, the conjugate gradient method can be used for solving a discretized water flow equation, and the key numerical model is solved as follows:
for matrixSum vector->，Is->Estimated head or pollution concentration value at a moment that satisfies the residual vector +.> andThen satisfy the relationship->：
For the next iteration valueAnd the initial iteration value->The differences of (2) are:
；
wherein ,is->Step size of the iteration>Is->Conjugate direction of the next iteration, continue solving +.>There are;
repeating the steps until convergence or maximum iteration number is reached.
Alternatively, the stable bi-conjugate gradient method is for a resolution ofCoefficient matrix->Sum vector->Initializing the equation set->And parameters, calculate new residual vector +.>And left offset conjugate vector->The method comprises the following steps:
wherein ,for the iteration stop condition>For relaxation coefficient->Is->Conjugate direction of the next iteration,To->A vector calculated for the conjugate direction;
continuing to calculate new vectors:
；
wherein ,for the iteration step, the vector is updated with this step>And residual vector->：
Simultaneously calculating iteration conditions and relaxation coefficients:
；
satisfying the simulation iteration condition, i.e. returning to the solution。
Optionally, the multiple grid method performs iterative solution on multiple grids with different granularities, so as to obtain better solution speed and precision. The basic mathematical equation is expressed as:
wherein ,is a smooth operator, ++>For residual vector, ++>Represents the number of iterations, +.>Indicate->Solution vector for the next iteration,/->Representing the solution vector of the last iteration.
Further, the grid is restricted to the parent grid:
wherein ,representing the resolution of the parent grid, +.>Representing the resolution of the current grid, +.>The restriction operator is represented as a function of the restriction operator,representing residual vector of parent mesh obtained after limiting operation,/->Representing the residual vector of the original grid.
As a further technical scheme of the invention, a variable parameter model is constructed by utilizing a parameter correction module in the numerical solution iteration process, a variable parameter data set of the parameter correction module and a model variable parameter identifier are read, a simulation variable parameter is corrected, and the updated model variable parameter participates in the simulation of the next time step and is expressed as follows:
in the formula ,for parameter correction status, ++>Indicating that no parameter correction has been carried out,representing the implementation;For model variable parameter dataset, +.>Unique identifier set for model variable parameter, < ->For the total number of variable parameters of the model, +.>For a model variable parameter matrix +.>Unique identifier for model variable parameters.
Specifically, in this example, the simulation parameters are set to be for 2 years, the iteration step length is 15 days, the solute adsorption type is selected to be Frenchque equilibrium adsorption, the chemical reaction type is selected to be Dissolve chemical equilibrium, different linear equation sets solvers are respectively selected to carry out numerical operation for comparison, and a reasonable absolute error limit and a relative error limit are set according to the iteration process.
Further, the invention establishes a variable parameter model comprising a permeable reactive barrier and a pumping well:
the osmotic coupling equation and the convection-dispersion coupling equation of the osmotic reaction wall model are as follows:
wherein ,respectively indicate->Permeability coefficient in direction, qs as source sink term, h as head, ++>For effective porosity, ++>For blocking factor, ->Is of dispersion coefficient->For the source sink item->For adsorbate density, ++>For various chemical reactions, ++>For adsorption term rate constant, +.>Is dynamic adsorption rate coefficient, +.>The mass of the compound adsorbed per unit mass of adsorbate, C being the solute concentration.
The seepage coupling equation and the convection-dispersion coupling equation of the pumping well model are as follows:
wherein ,for pumping rate->Respectively indicate->The permeability coefficient in the direction of the flow,respectively represent the unit voxels at +.>Side length in direction, ++>Is of dispersion coefficient->The mass of the compound adsorbed per unit mass of adsorbate, C being the solute concentration.
Further, in the two variable parameter models described above:
further, in this example, state machine management is set for the simulation solver, and the next step can be entered only if the current step is successfully completed, otherwise, the simulation solver is ended.
And 7, carrying out simulation iteration according to the simulation numerical model and the variable parameter model, and generating an analysis result and a data report.
In the specific implementation, numerical simulation is carried out after the model construction is completed and the parameter setting is completed, and simulation process and results are displayed in a graphical mode through a modeling technology, wherein the simulation process and results comprise static and dynamic demonstration of pollution diffusion distribution, underground water level and three-dimensional topography. Aiming at the pollutant characteristics and the underground water flow characteristics, the simulation of pollution diffusion is realized, the pollutant migration path and the risk are analyzed, and the visualization and analysis of the simulation process and the result comprise the effects of scene interaction, three-view plan view, longitudinal and transverse sectioning of the model, stratum screening sectioning, contour lines, attribute grading display, dynamic change and the like of a three-dimensional model.
Meanwhile, quantitative analysis and evaluation, namely precision test, are carried out on the simulation result, and the simulation result is aimed at a sparse linear equation setThe solving precision inspection scheme is that a sparse matrix is +.>And solving the result vector->Is>Performing error check when the vector is relatively error +.>Absolute error of vector->Vector and relative error->And when the threshold limit is met, the solving result is considered to be correct.
When the above conditions are all met,and returning to 0, namely solving correctly under the current time step.
As a further technical scheme of the invention, the model output is a data file in the form of grid organization, and the result output is a normalized or formatted data file for each attribute item parameter or groundwater level and pollutant concentration.
The invention further provides a groundwater pollution visual simulation system applied to the groundwater pollution migration visual numerical simulation method, the structure of the groundwater pollution visual simulation system is shown in (a) of fig. 7, and the simulation system integrates data management, model management, modeling process graphics, scene visualization and parameter setting linear flow, so that site pollution assessment and prediction capability is intuitively and efficiently improved. As shown in fig. 7 (b) and 7 (c), the simulation results of the groundwater level and the concentration distribution of the contaminants in the simulation system are visualized, and in this embodiment, the distribution and diffusion trend of the contaminants are clearly seen and have a strong correlation with the groundwater level.
According to the visual numerical simulation method for the groundwater pollution migration, data in different periods are checked and analyzed through setting and management of the data in the modeling process, the model is checked and modified, different simulation parameters and solvers are adopted for the pollution migration under different conditions, a parameter feedback module is established, a parameter list is updated in real time, and the efficiency and the accuracy of the groundwater pollution numerical simulation are improved; the underground water pollution monitoring, collecting and simulating data and parameters are integrated and visualized, so that the simulation flow links can be intuitively known, and the comprehensive management, evaluation and prediction capabilities of site pollution are improved.
In particular, according to embodiments of the present invention, the processes described above with reference to flowcharts may be implemented as computer software programs. For example, embodiments of the present invention include a computer program product comprising a computer program embodied on a computer readable medium, the computer program comprising program code for performing the method shown in the flowcharts. In such an embodiment, the computer program may be downloaded and installed from a network via a communication device, or installed from a storage device, or installed from ROM. The above-described functions defined in the method of the embodiment of the present invention are performed when the computer program is executed by the processing device.
The computer readable medium of the present invention may be a computer readable signal medium or a computer readable storage medium, or any combination of the two. The computer readable storage medium can be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or a combination of any of the foregoing. More specific examples of the computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. In the present invention, however, the computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, with the computer-readable program code embodied therein. Such a propagated data signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination of the foregoing. A computer readable signal medium may also be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to: electrical wires, fiber optic cables, RF (radio frequency), and the like, or any suitable combination of the foregoing.
The computer readable medium may be contained in the electronic device; or may exist alone without being incorporated into the electronic device.
The computer readable medium carries one or more programs which, when executed by the electronic device, cause the electronic device to perform the relevant steps of the method embodiments described above.
Alternatively, the computer readable medium carries one or more programs which, when executed by the electronic device, cause the electronic device to perform the relevant steps of the method embodiments described above.
Computer program code for carrying out operations of the present invention may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, smalltalk, C ++ and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any kind of network, including a Local Area Network (LAN) or a Wide Area Network (WAN), or may be connected to an external computer (for example, through the Internet using an Internet service provider).
The flowcharts and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
The units involved in the embodiments of the present invention may be implemented in software or in hardware.
It is to be understood that portions of the present invention may be implemented in hardware, software, firmware, or a combination thereof.
The foregoing is merely illustrative of the present invention, and the present invention is not limited thereto, and any changes or substitutions easily contemplated by those skilled in the art within the scope of the present invention should be included in the present invention. Therefore, the protection scope of the invention is subject to the protection scope of the claims.
Claims (5)
1. The visual numerical simulation method for groundwater pollution migration is characterized by comprising the following steps of:
step 1, obtaining groundwater pollution data of a target area;
step 2, constructing a conceptual model according to groundwater pollution data;
the step 2 specifically includes:
according to the hydrogeological plan and the section in the groundwater pollution data, the frame modeling range on the basis of the subsequent construction of the site three-dimensional model is deduced, and a conceptual model is established;
step 3, constructing a geologic body structure model according to the conceptual model;
the step 3 specifically includes:
based on the conceptual model, establishing a geologic body structure model by combining an observation well distribution table, borehole lithology data and a geological profile;
step 4, constructing a three-dimensional grid model according to the space data, the conceptual model and the structural model;
the step 4 specifically includes:
based on the space data, the conceptual model and the structural model, dividing the three-dimensional space into unit bodies by utilizing a three-dimensional mesh subdivision algorithm, and forming a three-dimensional mesh model by all unit body sets;
step 5, establishing an attribute field model according to the three-dimensional grid model;
the step 5 specifically includes:
an interpolation method is adopted to distribute initial attributes to each grid cut by the three-dimensional grid model to form an attribute field model, wherein the initial attributes comprise an initial water level, an initial pollutant concentration, a water storage rate, a delay factor, effective porosity, a diffusion coefficient, a permeability coefficient and boundary conditions;
step 6, establishing a simulation numerical model of multiple solver types according to the three-dimensional grid model and the attribute field model, performing flow field simulation and pollutant diffusion simulation by using the simulation numerical model, and performing parameter correction by using a parameter correction module in the simulation process to construct a variable parameter model;
the step 6 specifically includes:
according to a three-dimensional grid model and an attribute field model, combining the influence factors of underground water flow and solute migration, adopting a finite difference method to establish a mass conservation equation and a motion equation on nodes and units, establishing a simulation numerical model using a multi-solver type, performing flow field simulation and pollutant diffusion simulation, and performing parameter correction by using a parameter correction model in the simulation process to construct a variable parameter model, wherein the expression of the parameter correction model is as follows
，
，
，
in the formula ,for parameter correction status, ++>Indicating that no parameter correction is performed->Representing the implementation;For model variable parameter dataset, +.>Unique identifier set for model variable parameter, < ->For the total number of variable parameters of the model, +.>For a model variable parameter matrix +.>Unique identifiers for model variable parameters;
the variable parameter model comprises a permeation reaction wall model and a pumping well model;
and 7, carrying out simulation iteration according to the simulation numerical model and the variable parameter model, and generating an analysis result and a data report.
2. The method of claim 1, wherein the step of dividing the three-dimensional space into unit cells using a three-dimensional mesh subdivision algorithm comprises:
establishing a bounding box, dividing cube elements in the range of the bounding box, and determining the function values of eight vertexes of each small cube, wherein the function values of the vertexesTernary function scalar value +.>The spatial position relation between the identification point and the implicit curved surface defined by the ternary function is that
；
And selecting a corresponding implicit function expression, and extracting an implicit function value of a cube element between every two stratum surfaces according to the equivalent surface function in the subdivision process to serve as a stratum identifier of the cube element to form a unit body.
3. The method of claim 2, wherein the expression of the initial attribute is
；
wherein ,representing grid cell->Interpolation function at the center point +.>Representing the attribute value at the cell center point, the interpolation function is conditioned on the maximum search radius and the maximum search point number by using an inverse distance weighting method.
4. The method of claim 3, wherein the solver types include a conjugate gradient solver, a bistable conjugate gradient solver, and a multiple grid solver.
5. The method of claim 4, wherein the simulated numerical model has an expression of
wherein ,representing the number of finite element nodes, +.>Index subscript of representing voxel->Representation->Time->A head value of each node;
coefficients ofFor water head->Is expressed as:
wherein ,is->Permeability coefficient of direction, < >>Is a set of three-dimensional directions->For the current->The head estimate of a node is solved by this method>The change rate in the direction obtains the total water head change rate of the node;
coefficients ofFor water head->Is expressed as:
wherein the subscriptRepresenting the two-dimensional index of the node in the equation, +.>For water storage capacity, add>For time order->Is at presentA head estimate of the node;
coefficients ofAs a source sink item, expressed as:
wherein ,is a fluid source sink item;
the percolation coupling equation and the convection-diffusion coupling equation of the osmotic reaction wall model are expressed as:
wherein ,for osmotic coefficient->For the source sink item->Is water head (or)>For effective porosity, ++>For blocking factor, ->Is of dispersion coefficient->For the source sink item->For adsorbate density, ++>For various chemical reactions, ++>For adsorption term rate constant, +.>Is dynamic adsorption rate coefficient, +.>Is the mass of the compound adsorbed per unit mass of adsorbate, < >>Is the solute concentration;
the pumping well model seepage coupling equation and convection-dispersion coupling equation are expressed as:
，
，
wherein ,for pumping rate->、、Respectively indicate->，，Permeability coefficient in direction, +.>，，Respectively represent the unit voxels at +.>，，Side length in direction, ++>Is of dispersion coefficient->Is the mass of the compound adsorbed per unit mass of adsorbate, < >>Is the solute concentration.
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