CN116151154B - Soil groundwater pollutant migration simulation method and related equipment - Google Patents
Soil groundwater pollutant migration simulation method and related equipment Download PDFInfo
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Abstract
The invention provides a soil groundwater pollutant migration simulation method and related equipment, comprising the following steps: collecting a survey data set of a research area to establish a site three-dimensional geological model; coupling the site three-dimensional geological model with the soil groundwater seepage dynamics model to obtain a soil groundwater pollutant three-dimensional dynamics coupling model; performing grid subdivision on the site three-dimensional geological model, discretizing the soil groundwater pollutant three-dimensional dynamic coupling model, and constructing a soil groundwater pollutant three-dimensional finite difference numerical coupling model; dividing the site three-dimensional geological model subjected to mesh dissection to obtain a plurality of subareas and a plurality of boundary areas; solving a three-dimensional finite difference numerical coupling model of the soil groundwater pollutants to obtain numerical changes of groundwater heads and pollutant concentrations in each sub-area and each boundary area, and obtaining migration results of the groundwater pollutants; the simulation accuracy in time and space is improved.
Description
Technical Field
The invention relates to the technical field of simulation research on soil groundwater pollutants, in particular to a simulation method and related equipment for migration of soil groundwater pollutants.
Background
Groundwater is used as a valuable fresh water resource on the earth, and has high ecological value and economic value. However, with the development of economy and society, problems of excessive exploitation, irregular management, reduced groundwater level and deteriorated water quality of groundwater are increasingly prominent, and dynamic monitoring, treatment and sustainable development of groundwater quality have become the current emphasis on solving the problem of groundwater quality. Through a numerical simulation method, the problems encountered in researching groundwater flow and pollutant treatment can be effectively, rapidly and intuitively solved, the groundwater model plays an important role in the aspects of development and management of groundwater resources and effect of prediction management measures, and the groundwater model is widely applied to hydrogeology research.
With the research and development of groundwater models, simulation demands for large areas with long spans of time are increasing. The field is increased, the simulation time period is increased, the scale of the coefficient matrix related in the model is increased, and the number of matrix solving times in the simulation process is increased. However, the solving cost of the traditional numerical model solving method is greatly influenced by the matrix scale, even the matrix scale of the solving is limited, the accuracy of the simulation result is greatly influenced, and meanwhile, the use efficiency of the hardware is low, and the computing capability of a computer is not fully utilized. Therefore, in the research of groundwater simulation, the problem that the model solution is difficult to meet the research requirement of a large area and long time span is very prominent.
Disclosure of Invention
The invention provides a method and related equipment for simulating soil groundwater pollutant migration, and aims to simulate groundwater in a long period of time and improve simulation accuracy in time and space.
In order to achieve the above object, the present invention provides a soil groundwater pollutant migration simulation method, including:
step 1, collecting a survey data set of a research area, and building a site three-dimensional geological model based on the survey data;
step 2, coupling the site three-dimensional geological model with the soil groundwater seepage dynamics model to obtain a soil groundwater pollutant three-dimensional dynamics coupling model;
step 3, mesh subdivision is carried out on the three-dimensional geological model of the site by a finite difference method, discretization is carried out on the three-dimensional dynamic coupling model of the soil groundwater pollutants, and a three-dimensional finite difference numerical coupling model of the soil groundwater pollutants is constructed;
step 4, dividing the three-dimensional geological model of the site after grid dissection according to the spatial position relation to obtain a plurality of subareas and a plurality of boundary areas;
and 5, transforming the three-dimensional finite difference numerical coupling model of the soil groundwater pollutants by utilizing Schur-supplemented region decomposition to obtain a linear system of Schur-supplemented region decomposition, solving the linear system by using a Gaussian elimination method to obtain solution vectors of a plurality of subareas, and solving numerical changes of groundwater heads and pollutant concentrations in each subarea and each boundary region according to the solution vectors of the subareas to obtain migration results of the groundwater pollutants.
Further, the soil groundwater seepage dynamics model is as follows:
coupling the site three-dimensional geological model with the soil groundwater seepage dynamics model to obtain a soil groundwater pollutant three-dimensional dynamics coupling model which is:
wherein,,is the permeability coefficient of the groundwater in the directions of x, y and z, and is->Is the water head value of groundwater, < >>Is the source/sink item of fluid, +.>Is water storage unit->For porosity->For delay factor, ++>Adsorption concentration for contaminants，/>Is of dispersion coefficient->Representing the true flow of fluid through the aquifer volume in all directions,/and>represents the solute concentration of the source/sink, +.>Is the rate constant of the chemical reaction, +.>For the volume dry density of the soil medium, +.>Is the dissolution concentration.
Further, step 3 includes:
performing grid subdivision on the site three-dimensional geological model by a finite difference and finite element method to obtain a site three-dimensional geological model subjected to grid subdivision;
discretizing the three-dimensional dynamic coupling model of the soil groundwater pollutants by a Galerkin method by combining initial conditions and boundary conditions of a site permeation field and a pollutant concentration field to obtain a discretized three-dimensional dynamic coupling model of the soil groundwater pollutants;
Constructing a soil groundwater pollutant three-dimensional finite difference numerical coupling model according to the site three-dimensional geological model subjected to mesh dissection and the discretized soil groundwater pollutant three-dimensional dynamic coupling model;
the field penetration field numerical model is:
the contaminant concentration field numerical model is:
wherein,,representing the total number of volume elements divided by finite elements, < >>Index representing volume element->For the water head to be required>Indicating the rate of change of head>Indicates seepage term, ++>Representing fluid source/sink item->For the contaminant concentration to be determined at the present time, < >>Contaminant concentration indicative of the last time step, +.>Indicating the rate of change of concentration>Representing diffuse items->Representing convection item->Representing the adsorption term.
Further, step 5 includes:
performing row-column transformation on a linear system of a field permeation field numerical model and a pollutant concentration numerical model to obtain a small-area Schur complement area decomposition linear system, wherein the linear system comprises the following steps:
wherein,,is a linear system of the nth sub-region,is a relation matrix of sub-area and boundary area for information transfer, < >>Is a linear system of boundary areas, +.>A relation matrix representing the nth sub-area and the border area,/->Representing the solution vector corresponding to the nth sub-region, < - >Representing the corresponding solution vector of the boundary region, +.>Right vector representing n-th sub-region, ">A right vector representing a boundary region correspondence;
writing a linear system of Schur complement region decomposition into an equation set form, and solving the equation set by using a Gaussian elimination method to obtain a solution vector of the subarea, wherein the formula is as follows:
the back-substitution equation can be derived from the system of equations:
will replace equationSubstitution intoThe method can obtain:
wherein,,
wherein,,linear system of the ith sub-zone b +.>Representing the solution vector corresponding to the ith sub-region, < ->Is a relation matrix of sub-region b and boundary region c for information transfer,/for information transfer>Representing a right side vector corresponding to the ith sub-region;
solving for boundary regionsAnd substitute equation->The solution vector of each sub-region can be solved>；
According to the solution vector of each subarea, solving the numerical variation of the groundwater head and the pollutant concentration in each subarea and each boundary area;
the migration result of groundwater contaminants is obtained according to the numerical variation of groundwater head and contaminant concentration in each sub-zone and each boundary zone.
Further, before solving the numerical changes of the groundwater head and the pollutant concentration in each sub-region and each boundary region according to the solution vector of each sub-region, the method further comprises:
Bistable conjugate gradient method pair using pretreatmentAnd solving, namely using the S matrix as a pretreatment matrix, and solving the pretreatment matrix by using a Schur complement region decomposition method.
Further, before solving the preprocessing matrix by using the Schur complement region decomposition method, the method further comprises:
dividing a boundary region corresponding to the S matrix to obtain volume elements adjacent to other sub-regions as boundary surfaces, wherein the volume elements adjacent to the boundary surfaces are used as wire frames, and the volume elements adjacent to the wire frames are used as cross point regions;
and (3) combining with a pretreatment method of the block jacobian, extracting a diagonal block matrix from the S matrix to obtain a pretreatment matrix M:
performing row-column transformation on the boundary linear system to obtain a linear system of a boundary region:
wherein,,is a linear system of the n-th boundary surface,is a relation matrix of boundary surfaces and wire frames for information transfer,>is a linear system of crossing points, < >>Is a linear system of wire frames, < >>A relation matrix representing the q-th boundary surface d and the current state area,a relation matrix representing the intersection area e and the wire frame f, < >>Represents the solution vector corresponding to the q-th boundary surface d,/->Representing the solution vector corresponding to the intersection region e, +. >Representing the solution vector corresponding to the wireframe f, +.>Right vector corresponding to the q-th boundary surface d +.>Indicating the right corresponding to the intersection region eSide vector (s)/(s)>A right vector corresponding to the wire frame f;
using gaussian elimination, we obtained:
wherein the method comprises the steps of
Wherein,,right vector corresponding to i-th boundary surface d +.>A matrix of relationships representing the i-th boundary surface d and the current region, < >>A linear system representing the i-th boundary surface d, < >>Representing a solution vector corresponding to the ith boundary surface d;
bistable conjugate gradient method pair using pretreatmentSolving to obtain a wire frame solution vector +.>；
Solving the wire frame into vectorsSubstituted into->Solving to obtain solution vector of boundary surface>And (5) completing the solution of the preprocessing matrix M.
The invention also provides a soil groundwater pollutant migration simulation device, which comprises:
the collecting module is used for collecting a survey data set of the research area and establishing a site three-dimensional geological model based on the survey data;
the coupling module is used for coupling the site three-dimensional geological model with the soil groundwater seepage dynamics model to obtain a soil groundwater pollutant three-dimensional dynamics coupling model;
the construction module is used for meshing the three-dimensional geological model of the site through a finite difference method, discretizing the three-dimensional dynamic coupling model of the soil groundwater pollutants, and constructing a three-dimensional finite difference numerical coupling model of the soil groundwater pollutants;
The dividing module is used for dividing the three-dimensional geological model of the site after grid division according to the spatial position relation to obtain a plurality of subareas and a plurality of boundary areas;
the solving module is used for transforming the three-dimensional finite difference numerical coupling model of the soil groundwater pollutants by utilizing Schur complement region decomposition to obtain a linear system of Schur complement region decomposition, solving the linear system by using a Gaussian elimination method to obtain solution vectors of a plurality of subareas, and solving numerical changes of groundwater heads and pollutant concentrations in each subarea and each boundary region according to the solution vectors of the subareas to obtain migration results of groundwater pollutants.
The invention also provides a computer readable storage medium, wherein the computer readable storage medium stores a computer program, and the computer program realizes the soil groundwater pollutant migration simulation method when being executed by a processor.
The invention also provides a terminal device which comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the processor realizes the soil groundwater pollutant migration simulation method when executing the computer program.
The scheme of the invention has the following beneficial effects:
The method comprises the steps of collecting a survey data set of a research area, and establishing a site three-dimensional geological model based on the survey data; coupling the site three-dimensional geological model with the soil groundwater seepage dynamics model to obtain a soil groundwater pollutant three-dimensional dynamics coupling model; performing grid subdivision on the site three-dimensional geological model by a finite difference method, discretizing the soil groundwater pollutant three-dimensional dynamic coupling model, and constructing a soil groundwater pollutant three-dimensional finite difference numerical coupling model; dividing the site three-dimensional geological model subjected to mesh division according to the spatial position relationship to obtain a plurality of subareas and a plurality of boundary areas; transforming the three-dimensional finite difference numerical coupling model of the soil groundwater pollutants by utilizing Schur complement region decomposition to obtain a linear system of Schur complement region decomposition, solving the linear system by utilizing a Gaussian elimination method to obtain solution vectors of a plurality of subareas, and solving numerical changes of groundwater heads and pollutant concentrations in each subarea and each boundary region according to the solution vectors of the subareas to obtain migration results of the groundwater pollutants; the problem of matrix size limitation of solving a sparse matrix in a traditional algorithm library is solved, and the simulation method is more suitable for the simulation problem of fine resolution of a large field; the method of regional decomposition is used, and the method is divided into a plurality of subareas and boundary areas, so that the size of a matrix to be solved in a model is reduced, global communication of information is promoted, and convergence speed is increased; the method improves the solving efficiency, reduces the time for solving, is suitable for long-time simulation of groundwater, is beneficial to improving the simulation precision in time and space, and simultaneously provides a foundation for subsequent groundwater pollution treatment.
Other advantageous effects of the present invention will be described in detail in the detailed description section which follows.
Drawings
FIG. 1 is a schematic flow chart of an embodiment of the present invention;
FIG. 2 is a schematic diagram of region division in an embodiment of the present invention.
Detailed Description
In order to make the technical problems, technical solutions and advantages to be solved more apparent, the following detailed description will be given with reference to the accompanying drawings and specific embodiments. It will be apparent that the described embodiments are some, but not all, embodiments of the invention. 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.
In the description of the present invention, it should be noted that the directions or positional relationships indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. are based on the directions or positional relationships shown in the drawings, are merely for convenience of describing the present invention and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a specific orientation, be configured and operated in a specific orientation, and thus should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it should be noted that, unless explicitly stated and limited otherwise, the terms "mounted," "connected," and "connected" are to be construed broadly, and may be, for example, a locked connection, a removable connection, or an integral connection; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in the present invention will be understood in specific cases by those of ordinary skill in the art.
In addition, the technical features of the different embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
Aiming at the existing problems, the invention provides a soil groundwater pollutant migration simulation method and related equipment.
As shown in fig. 1, an embodiment of the present invention provides a soil groundwater pollutant migration simulation method, including:
step 1, collecting a survey data set of a research area, and building a site three-dimensional geological model based on the survey data;
step 2, coupling the site three-dimensional geological model with the soil groundwater seepage dynamics model to obtain a soil groundwater pollutant three-dimensional dynamics coupling model;
Step 3, mesh subdivision is carried out on the three-dimensional geological model of the site by a finite difference method, discretization is carried out on the three-dimensional dynamic coupling model of the soil groundwater pollutants, and a three-dimensional finite difference numerical coupling model of the soil groundwater pollutants is constructed;
step 4, dividing the three-dimensional geological model of the site after grid dissection according to the spatial position relation to obtain a plurality of subareas and a plurality of boundary areas;
and 5, transforming the three-dimensional finite difference numerical coupling model of the soil groundwater pollutants by utilizing Schur-supplemented region decomposition to obtain a linear system of Schur-supplemented region decomposition, solving the linear system by using a Gaussian elimination method to obtain solution vectors of a plurality of subareas, and solving numerical changes of groundwater heads and pollutant concentrations in each subarea and each boundary region according to the solution vectors of the subareas to obtain migration results of the groundwater pollutants.
Specifically, the embodiment of the invention collects elevation data or drilling, combined section and other data of the Hunan iron alloy site, and establishes a site three-dimensional geological model; and then, the relevant parameters of local soil such as porosity, permeability coefficient, diffusion coefficient, water storage rate and the like are not considered, and the model of the processes such as equilibrium adsorption, non-equilibrium adsorption and the like used in the process of treating the groundwater pollutants is considered in the processes of convection, diffusion and release of the pollutants and is coupled with the soil groundwater seepage dynamics model, so that the soil groundwater pollutant three-dimensional dynamics coupling model in the process of transferring and repairing the pollutants can be obtained. According to the different methods of the actual pollution treatment, different repair item models can be used for coupling, and the soil groundwater seepage dynamics model is as follows:
Coupling the site three-dimensional geological model with the soil groundwater seepage dynamics model to obtain a soil groundwater pollutant three-dimensional dynamics coupling model which is:
wherein,,is the permeability coefficient of the groundwater in the directions of x, y and z, and is->Is the water head value of groundwater, < >>Is the source/sink item of fluid, +.>Is water storage unit->For porosity->For delay factor, ++>For contaminant adsorption concentration, ++>Is of dispersion coefficient->Representing the true flow of fluid through the aquifer volume in all directions,/and>represents the solute concentration of the source/sink, +.>Is the rate constant of the chemical reaction, +.>For the volume dry density of the soil medium, +.>Is the dissolution concentration; wherein->These two terms represent equilibrium and non-equilibrium adsorption processes for contaminants.
Specifically, step 3 includes:
performing grid subdivision on the site three-dimensional geological model by a finite difference and finite element method to obtain a site three-dimensional geological model subjected to grid subdivision;
discretizing the three-dimensional dynamic coupling model of the soil groundwater pollutants by a Galerkin method by combining initial conditions and boundary conditions of a site permeation field and a pollutant concentration field to obtain a discretized three-dimensional dynamic coupling model of the soil groundwater pollutants;
Constructing a soil groundwater pollutant three-dimensional finite difference numerical coupling model according to the site three-dimensional geological model subjected to mesh dissection and the discretized soil groundwater pollutant three-dimensional dynamic coupling model;
the field penetration field numerical model is:
the contaminant concentration field numerical model is:
wherein,,representing the total number of volume elements divided by finite elements, < >>Index representing volume element->For the water head to be required>Indicating the rate of change of head>Indicates seepage term, ++>Representing fluid source/sink item->For the contaminant concentration to be determined at the present time, < >>Contaminant concentration indicative of the last time step, +.>Indicating the rate of change of concentration>Representing diffuse items->Representing convection item->Representing the adsorption term.
Specifically, step 5 includes:
performing row-column transformation on a linear system of a field permeation field numerical model and a pollutant concentration numerical model to obtain a linear system of Schur complement region decomposition of a small region a, wherein the linear system comprises the following steps:
wherein,,is a linear system of the nth sub-region b,is a relation matrix of sub-region b and boundary region c for information transfer,/for information transfer>Is a linear system of boundary areas c, +.>A relation matrix representing the nth sub-area and the border area,/->Representing the solution vector corresponding to the nth sub-region, < - >Representing the corresponding solution vector of the boundary region, +.>Right vector representing n-th sub-region, ">A right vector representing a boundary region correspondence;
writing a linear system of Schur complement region decomposition into an equation set form, and solving the equation set by using a Gaussian elimination method to obtain a solution vector of the subarea b, wherein the formula is as follows:
the back-substitution equation can be derived from the system of equations:
will replace equationSubstitution intoThe method can obtain:
wherein,,
wherein,,linear system of the ith sub-zone b +.>Representing the solution vector corresponding to the ith sub-region, < ->Is a relation matrix of sub-region b and boundary region c for information transfer,/for information transfer>Representing a right side vector corresponding to the ith sub-region;
the S matrix has better condition number than the original matrix A, and the solution methods such as pre-processed bistable conjugate gradient and the like are used for solvingThe solving method does not need the display expression of the S matrix, and only the multiplication result between the S matrix and different vectors is calculated. For example, a vector +.>Calculation of +.>The +.Can be calculated from the formula>：
Then calculate according to the following formula：
Obtaining solution of boundary region cAnd substitute equation->The solution vector +. >；
According to the solution vector of each subarea b, solving the numerical variation of the groundwater head and the pollutant concentration in each subarea b and each boundary area d;
the migration result of groundwater pollutants is obtained according to the numerical variation of groundwater head and pollutant concentration in each sub-zone b and each boundary zone c.
Specifically, before solving for the numerical changes in the groundwater head and contaminant concentration in each sub-region b and each boundary region s based on the solution vectors of the respective sub-regions, the method further includes:
bistable conjugate gradient method pair using pretreatmentAnd solving, namely using the S matrix as a pretreatment matrix, and solving the pretreatment matrix by using a Schur complement region decomposition method.
Specifically, before solving the preprocessing matrix by using the Schur complement region decomposition method, the method further comprises:
dividing a boundary region c corresponding to the S matrix to obtain a voxel adjacent to other sub-regions b as a boundary surface d, wherein the voxel adjacent to the boundary surface d is used as a wire frame f, and the voxel adjacent to the wire frame f is used as a crossing point region e, as shown in fig. 2;
and (3) combining with a pretreatment method of the block jacobian, extracting a diagonal block matrix from the S matrix to obtain a pretreatment matrix M:
Performing row-column transformation on the boundary linear system to obtain a linear system of a boundary region:
wherein,,is a linear system of the n-th boundary surface d, is->Is a relation matrix of boundary surface d and wire frame f for information transmission, ">Is a linear system of crossing points e, +.>Is a linear system of wire frames f, +.>A relation matrix representing the q-th boundary surface d and the current state area,a relation matrix representing the intersection area e and the wire frame f, < >>Represents the solution vector corresponding to the q-th boundary surface d,/->Representing the solution vector corresponding to the intersection region e, +.>Representing the solution vector corresponding to the wireframe f, +.>Right vector corresponding to the q-th boundary surface d +.>Right vector representing intersection region e, +.>A right vector corresponding to the wire frame f;
using gaussian elimination, we obtained:
wherein the method comprises the steps of
Wherein,,right vector corresponding to i-th boundary surface d +.>A matrix of relationships representing the i-th boundary surface d and the current region, < >>A linear system representing the i-th boundary surface d, < >>The solution vector corresponding to the i-th boundary surface d is represented.
Bistable conjugate gradient method pair using pretreatmentSolving to obtain the solution vector of the wire frame f；
Solution vector of wire frame fSubstituted into->Solving to obtain solution vector of boundary surface d >。
Specifically, in the step 3 and the step 4, the embodiment of the invention carries out regional decomposition on the three-dimensional geological model of the field to obtain a plurality of mutually independent small regions, and the coefficient matrix to be solved in the integral field permeation field numerical model and the pollutant concentration numerical model is also transformed into a plurality of mutually independent small-scale coefficient matrices according to the divided regions. As can be seen from the above formula, the linear system of sub-regions and boundary regions is required during the solving processThe method and the device for solving and calculating the coefficient matrix of the sub-region and the boundary region are divided into a plurality of parts by utilizing the characteristic that the coefficient matrices are mutually independent, the related calculation of the coefficient matrices of different regions contained in each part is put into one thread, and the plurality of threads are put into the GPU for operation, namely, in the solving process, the calculation is neededIs calculated according to the formula +.>And formula->Transform is performed, vector +.>Is the bridge for information exchange between GPU and CPU, and CPU will vector +.>On to each computational thread in the GPU, vector +.>And matrix->Multiplication of->Solving and AND- >After multiplication calculation, relaying the calculated result from the GPU to the CPU from each thread in the opposite direction, and processing the sum of sub-area vectors and subsequent calculation on the CPU completely; similarly, the calculation of the boundary surface, and the back-substitution process of the boundary surface solution vector and the sub-region solution vector are also the same.
The embodiment of the invention collects a survey data set of a research area and builds a site three-dimensional geological model based on the survey data; coupling the site three-dimensional geological model with the soil groundwater seepage dynamics model to obtain a soil groundwater pollutant three-dimensional dynamics coupling model; performing grid subdivision on the site three-dimensional geological model by a finite difference method, discretizing the soil groundwater pollutant three-dimensional dynamic coupling model, and constructing a soil groundwater pollutant three-dimensional finite difference numerical coupling model; dividing the site three-dimensional geological model subjected to mesh division according to the spatial position relationship to obtain a plurality of subareas and a plurality of boundary areas; transforming the three-dimensional finite difference numerical coupling model of the soil groundwater pollutants by utilizing Schur complement region decomposition to obtain a linear system of Schur complement region decomposition, solving the linear system by utilizing a Gaussian elimination method to obtain solution vectors of a plurality of subareas, and solving numerical changes of groundwater heads and pollutant concentrations in each subarea and each boundary region according to the solution vectors of the subareas to obtain migration results of the groundwater pollutants; the problem of matrix size limitation of solving a sparse matrix in a traditional algorithm library is solved, and the simulation method is more suitable for the simulation problem of fine resolution of a large field; the method of regional decomposition is used, and the method is divided into a plurality of subareas and boundary areas, so that the size of a matrix to be solved in a model is reduced, global communication of information is promoted, and convergence speed is increased; the method improves the solving efficiency, reduces the time for solving, is suitable for long-time simulation of groundwater, and is beneficial to improving the simulation precision in time and space.
The embodiment of the invention also provides a device for simulating the migration of soil and groundwater pollutants, which comprises:
the collecting module is used for collecting a survey data set of the research area and establishing a site three-dimensional geological model based on the survey data;
the coupling module is used for coupling the site three-dimensional geological model with the soil groundwater seepage dynamics model to obtain a soil groundwater pollutant three-dimensional dynamics coupling model;
the construction module is used for meshing the three-dimensional geological model of the site through a finite difference method, discretizing the three-dimensional dynamic coupling model of the soil groundwater pollutants, and constructing a three-dimensional finite difference numerical coupling model of the soil groundwater pollutants;
the dividing module is used for dividing the three-dimensional geological model of the site after grid division according to the spatial position relation to obtain a plurality of subareas and a plurality of boundary areas;
the solving module is used for transforming the three-dimensional finite difference numerical coupling model of the soil groundwater pollutants by utilizing Schur complement region decomposition to obtain a linear system of Schur complement region decomposition, solving the linear system by using a Gaussian elimination method to obtain solution vectors of a plurality of subareas, and solving numerical changes of groundwater heads and pollutant concentrations in each subarea and each boundary region according to the solution vectors of the subareas to obtain migration results of groundwater pollutants.
It should be noted that, because the content of information interaction and execution process between the above devices/units is based on the same concept as the method embodiment of the present invention, specific functions and technical effects thereof may be found in the method embodiment section, and will not be described herein.
It will be apparent to those skilled in the art that, for convenience and brevity of description, only the above-described division of the functional units and modules is illustrated, and in practical application, the above-described functional distribution may be performed by different functional units and modules according to needs, i.e. the internal structure of the apparatus is divided into different functional units or modules to perform all or part of the above-described functions. The functional units and modules in the embodiment may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit, where the integrated units may be implemented in a form of hardware or a form of a software functional unit. In addition, specific names of the functional units and modules are only for convenience of distinguishing from each other, and are not used for limiting the protection scope of the embodiments of the present invention. The specific working process of the units and modules in the above system may refer to the corresponding process in the foregoing method embodiment, which is not described herein again.
The embodiment of the invention also provides a computer readable storage medium, wherein the computer readable storage medium stores a computer program, and the computer program realizes the soil groundwater pollutant migration simulation method when being executed by a processor.
The integrated units, if implemented in the form of software functional units and sold or used as stand-alone products, may be stored in a computer readable storage medium. Based on such understanding, the implementation of all or part of the flow of the method of the foregoing embodiments of the present invention may be accomplished by a computer program to instruct related hardware, where the computer program may be stored in a computer readable storage medium, and the computer program may implement the steps of each of the foregoing method embodiments when executed by a processor. Wherein the computer program comprises computer program code which may be in source code form, object code form, executable file or some intermediate form etc. The computer readable medium may include at least: any entity or device capable of carrying computer program code to construct an apparatus/terminal equipment, recording medium, computer Memory, read-Only Memory (ROM), random access Memory (RAM, random Access Memory), electrical carrier signals, telecommunications signals, and software distribution media. Such as a U-disk, removable hard disk, magnetic or optical disk, etc. In some jurisdictions, computer readable media may not be electrical carrier signals and telecommunications signals in accordance with legislation and patent practice.
The embodiment of the invention also provides a terminal device which comprises a memory, a processor and a computer program which is stored in the memory and can run on the processor, wherein the processor realizes the soil groundwater pollutant migration simulation method when executing the computer program.
It should be noted that the terminal device may be a mobile phone, a tablet computer, a notebook computer, an Ultra mobile personal computer (UMPC, ultra-mobile Personal Computer), a netbook, a personal digital assistant (PDA, personal Digital Assistant), or the like, and the terminal device may be a station (ST, stand) in a WLAN, for example, a cellular phone, a cordless phone, a session initiation protocol (SIP, session Initiation Protocol) phone, a wireless local loop (WLL, wireless Local Loop) station, a personal digital processing (PDA, personal Digital Assistant) device, a handheld device having a wireless communication function, a computing device, or other processing device connected to a wireless modem, a computer, a laptop computer, a handheld communication device, a handheld computing device, a satellite wireless device, or the like. The embodiment of the invention does not limit the specific type of the terminal equipment.
The processor may be a central processing unit (CPU, central Processing Unit), but may also be other general purpose processors, digital signal processors (DSP, digital Signal Processor), application specific integrated circuits (ASIC, application Specific Integrated Circuit), off-the-shelf programmable gate arrays (FPGA, field-Programmable Gate Array) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory may in some embodiments be an internal storage unit of the terminal device, such as a hard disk or a memory of the terminal device. The memory may in other embodiments also be an external storage device of the terminal device, such as a plug-in hard disk provided on the terminal device, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), etc. Further, the memory may also include both an internal storage unit and an external storage device of the terminal device. The memory is used to store an operating system, application programs, boot loader (BootLoader), data, and other programs, etc., such as program code for the computer program, etc. The memory may also be used to temporarily store data that has been output or is to be output.
It should be noted that, because the content of information interaction and execution process between the above devices/units is based on the same concept as the method embodiment of the present invention, specific functions and technical effects thereof may be found in the method embodiment section, and will not be described herein.
While the foregoing is directed to the preferred embodiments of the present invention, it will be appreciated by those skilled in the art that various modifications and adaptations can be made without departing from the principles of the present invention, and such modifications and adaptations are intended to be comprehended within the scope of the present invention.
Claims (7)
1. A method for simulating migration of soil groundwater pollutants, comprising:
step 1, collecting a survey data set of a research area, and building a site three-dimensional geological model based on the survey data;
step 2, coupling the site three-dimensional geological model with a soil groundwater seepage dynamics model to obtain a soil groundwater pollutant three-dimensional dynamics coupling model;
step 3, meshing the site three-dimensional geological model by a finite difference method, discretizing the soil groundwater pollutant three-dimensional dynamic coupling model, and constructing a soil groundwater pollutant three-dimensional finite difference numerical coupling model;
Performing grid subdivision on the site three-dimensional geological model by a finite difference and finite element method to obtain a site three-dimensional geological model subjected to grid subdivision;
discretizing the three-dimensional dynamic coupling model of the soil groundwater pollutants by a Galerkin method by combining initial conditions and boundary conditions of a site permeation field and a pollutant concentration field to obtain a discretized three-dimensional dynamic coupling model of the soil groundwater pollutants;
constructing a soil groundwater pollutant three-dimensional finite difference numerical coupling model according to the site three-dimensional geological model subjected to mesh dissection and the discretized soil groundwater pollutant three-dimensional dynamic coupling model;
the field penetration field numerical model is as follows:
the pollutant concentration field numerical model is as follows:
wherein,,representing the total number of volume elements divided by finite elements, < >>Index representing volume element->For the water head to be required>Indicating the rate of change of head>Indicates seepage term, ++>Representing fluid source/sink item->For the contaminant concentration to be determined at the present time, < >>Contaminant concentration indicative of the last time step, +.>Indicating the rate of change of concentration>Representing the dispersion term(s),/>representing convection item->Represents an adsorption term;
Step 4, dividing the three-dimensional geological model of the field after grid dissection according to the spatial position relation to obtain a plurality of subareas and a plurality of boundary areas;
step 5, transforming the three-dimensional finite difference numerical coupling model of the soil groundwater pollutants by utilizing Schur complement region decomposition to obtain a linear system of Schur complement region decomposition, solving the linear system by utilizing a Gaussian elimination method to obtain solution vectors of a plurality of subareas, and solving numerical changes of groundwater heads and pollutant concentrations in each subarea and each boundary region according to the solution vectors of each subarea to obtain migration results of groundwater pollutants;
performing row-column transformation on the linear system of the field permeation field numerical model and the pollutant concentration numerical model to obtain a small-area Schur complement area decomposition linear system, wherein the linear system comprises the following steps:
wherein,,is the linear system of the nth sub-region, +.>Is a relation matrix of sub-area and boundary area for information transfer, < >>Is a linear system of boundary areas, +.>A relation matrix representing the nth sub-area and the border area,/->Representing the solution vector corresponding to the nth sub-region, < - >Representing the corresponding solution vector of the boundary region, +.>Right vector representing n-th sub-region, ">A right vector representing a boundary region correspondence;
writing a linear system of Schur complement region decomposition into an equation set form, and solving the equation set by using a Gaussian elimination method to obtain a solution vector of the subarea, wherein the formula is as follows:
the back-substitution equation can be derived from the system of equations:
will replace equationSubstituted into->The method can obtain:
wherein,,
wherein,,linear system of the ith sub-zone b +.>Representing the solution vector corresponding to the ith sub-region, < ->Is a relation matrix of sub-region b and boundary region c for information transfer,/for information transfer>Representing a right side vector corresponding to the ith sub-region;
solving for boundary regionsAnd substitute equation->The solution vector of each subarea can be solved；
According to the solution vector of each subarea, solving the numerical variation of the groundwater head and the pollutant concentration in each subarea and each boundary area;
and obtaining migration results of groundwater pollutants according to the numerical changes of the groundwater head and the pollutant concentration in each subarea and each boundary area.
2. The method for simulating migration of soil groundwater pollutants according to claim 1,
The soil groundwater seepage dynamics model is as follows:
coupling the site three-dimensional geological model with the soil groundwater seepage dynamics model to obtain a soil groundwater pollutant three-dimensional dynamics coupling model which is:
wherein,,is the permeability coefficient of the groundwater in the directions of x, y and z, and is->Is the water head value of the underground water,is the source/sink item of fluid, +.>Is water storage unit->For porosity->For delay factor, ++>For contaminant adsorption concentration, ++>Is of dispersion coefficient->Representing the true flow of fluid through the aquifer volume in all directions,/and>representing the solute concentration of the source/sink,is the rate constant of the chemical reaction, +.>For the volume dry density of the soil medium, +.>Is the dissolution concentration.
3. The method of simulating migration of soil groundwater contaminants according to claim 1, further comprising, before solving for a numerical change in groundwater head and contaminant concentration in each of said subregions and each of said boundary regions based on solution vectors of the respective subregions:
bistable conjugate gradient method pair using pretreatmentAnd solving, namely using an S matrix as a pretreatment matrix, and solving the pretreatment matrix by using a Schur complement region decomposition method.
4. A method of modeling soil groundwater contaminant migration according to claim 3, further comprising, prior to solving said pretreatment matrix using Schur patch decomposition method:
dividing a boundary region corresponding to the S matrix to obtain volume elements adjacent to other sub-regions as boundary surfaces, wherein the volume elements adjacent to the boundary surfaces are used as wire frames, and the volume elements adjacent to the wire frames are used as intersection regions;
and (3) combining with a pretreatment method of the block jacobian, extracting a diagonal block matrix from the S matrix to obtain a pretreatment matrix M:
performing row-column transformation on the boundary linear system to obtain a linear system of a boundary region:
wherein,,is a linear system of the n-th boundary surface, < >>Is a relation matrix of boundary surfaces and wire frames for information transfer,>is a linear system of crossing points, < >>Is a linear system of wire frames, < >>A matrix of relationships representing the q-th boundary surface d and the current region, < >>A relation matrix representing the intersection area e and the wire frame f, < >>Represents the solution vector corresponding to the q-th boundary surface d,/->Representing the solution vector corresponding to the intersection region e, +.>The solution vector corresponding to the wire frame f is represented,right vector corresponding to the q-th boundary surface d +. >Right vector representing intersection region e, +.>A right vector corresponding to the wire frame f;
using gaussian elimination, we obtained:
wherein the method comprises the steps of
Wherein,,right vector corresponding to i-th boundary surface d +.>A matrix of relationships representing the i-th boundary surface d and the current region, < >>A linear system representing the i-th boundary surface d, < >>Representing a solution vector corresponding to the ith boundary surface d;
bistable conjugate gradient method pair using pretreatmentSolving to obtain a wire frame solution vector +.>；
Solving the wire frame into vectorsSubstituted into->Solving to obtain solution vector of boundary surface。
5. A soil groundwater contaminant migration simulation device, comprising:
the collecting module is used for collecting a survey data set of a research area and establishing a site three-dimensional geological model based on the survey data;
the coupling module is used for coupling the site three-dimensional geological model with the soil groundwater seepage dynamics model to obtain a soil groundwater pollutant three-dimensional dynamics coupling model;
performing grid subdivision on the site three-dimensional geological model by a finite difference and finite element method to obtain a site three-dimensional geological model subjected to grid subdivision;
discretizing the three-dimensional dynamic coupling model of the soil groundwater pollutants by a Galerkin method by combining initial conditions and boundary conditions of a site permeation field and a pollutant concentration field to obtain a discretized three-dimensional dynamic coupling model of the soil groundwater pollutants;
Constructing a soil groundwater pollutant three-dimensional finite difference numerical coupling model according to the site three-dimensional geological model subjected to mesh dissection and the discretized soil groundwater pollutant three-dimensional dynamic coupling model;
the field penetration field numerical model is as follows:
the pollutant concentration field numerical model is as follows:
wherein,,representing the total number of volume elements divided by finite elements, < >>Index representing volume element->For the water head to be required>Indicating the rate of change of head>Indicates seepage term, ++>Representing fluid source/sink item->For the contaminant concentration to be determined at the present time, < >>Contaminant concentration indicative of the last time step, +.>Indicating the rate of change of concentration>Representing diffuse items->Representing convection item->Represents an adsorption term;
the construction module is used for meshing the site three-dimensional geological model through a finite difference method, discretizing the soil groundwater pollutant three-dimensional dynamic coupling model and constructing a soil groundwater pollutant three-dimensional finite difference numerical coupling model;
the dividing module is used for dividing the three-dimensional geological model of the field after grid division according to the spatial position relation to obtain a plurality of subareas and a plurality of boundary areas;
The solving module is used for transforming the three-dimensional finite difference numerical coupling model of the soil groundwater pollutants by utilizing Schur-supplemented region decomposition to obtain a linear system of Schur-supplemented region decomposition, solving the linear system by using a Gaussian elimination method to obtain solution vectors of a plurality of subareas, and solving numerical changes of groundwater heads and pollutant concentrations in each subarea and each boundary region according to the solution vectors of each subarea to obtain migration results of the groundwater pollutants;
performing row-column transformation on the linear system of the field permeation field numerical model and the pollutant concentration numerical model to obtain a small-area Schur complement area decomposition linear system, wherein the linear system comprises the following steps:
wherein,,is the linear system of the nth sub-region, +.>Is a relation matrix of sub-area and boundary area for information transfer, < >>Is a linear system of boundary areas, +.>A relation matrix representing the nth sub-area and the border area,/->Representing the solution vector corresponding to the nth sub-region, < ->Representing the corresponding solution vector of the boundary region, +.>Right vector representing n-th sub-region, ">A right vector representing a boundary region correspondence;
Writing a linear system of Schur complement region decomposition into an equation set form, and solving the equation set by using a Gaussian elimination method to obtain a solution vector of the subarea, wherein the formula is as follows:
the back-substitution equation can be derived from the system of equations:
will replace equationSubstituted into->The method can obtain:
wherein,,
wherein,,linear system of the ith sub-zone b +.>Representing the solution vector corresponding to the ith sub-region, < ->Is a relation matrix of sub-region b and boundary region c for information transfer,/for information transfer>Representing a right side vector corresponding to the ith sub-region;
solving for boundary regionsAnd substitute equation->The solution vector of each subarea can be solved；
According to the solution vector of each subarea, solving the numerical variation of the groundwater head and the pollutant concentration in each subarea and each boundary area;
and obtaining migration results of groundwater pollutants according to the numerical changes of the groundwater head and the pollutant concentration in each subarea and each boundary area.
6. A computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the soil groundwater contaminant migration simulation method according to any one of claims 1 to 4.
7. A terminal device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that the processor implements the soil groundwater contaminant migration simulation method according to any one of claims 1 to 4 when executing the computer program.
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