CN114036805A - Forward modeling method, device, equipment and medium for three-dimensional steady-state heat conduction geothermal field - Google Patents

Forward modeling method, device, equipment and medium for three-dimensional steady-state heat conduction geothermal field Download PDF

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CN114036805A
CN114036805A CN202111423009.XA CN202111423009A CN114036805A CN 114036805 A CN114036805 A CN 114036805A CN 202111423009 A CN202111423009 A CN 202111423009A CN 114036805 A CN114036805 A CN 114036805A
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贾金荣
戴世坤
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Central South University
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Abstract

The method, the device, the equipment and the medium for the forward modeling of the three-dimensional steady-state heat conduction geothermal field are characterized in that a three-dimensional prism model of a target area containing a three-dimensional abnormal body inside is constructed and is subjected to grid subdivision, the thermophysical parameter of each subdivision node in the three-dimensional prism model is assigned according to the distribution condition of the thermophysical parameters of the target area, boundary conditions are loaded, the background field temperature of a space domain is calculated, and the background field temperature is used as an initial space domain temperature total field; calculating an abnormal temperature field of the spatial wave number mixed domain based on the thermophysical parameters and the current total spatial domain temperature field; carrying out inverse Fourier transform on the spatial wave number mixed domain abnormal temperature field to obtain the spatial domain abnormal field temperature; obtaining a new total spatial domain temperature field based on the spatial domain background field temperature and the spatial domain abnormal field temperature; and continuously iterating until the new space domain temperature total field obtained by iteration meets the iteration convergence condition. The invention realizes the high-efficiency and high-precision numerical simulation of the three-dimensional stable heat conduction ground temperature field.

Description

Forward modeling method, device, equipment and medium for three-dimensional steady-state heat conduction geothermal field
Technical Field
The invention belongs to the technical field of geothermal field numerical simulation, and particularly relates to a forward modeling method, a forward modeling device, forward modeling equipment and a forward modeling medium for a three-dimensional steady-state heat conduction geothermal field.
Background
With the development of social and economic environments, the demand of green energy is increasing day by day. Geothermal energy is gaining increasing attention as a clean renewable energy source. However, due to the complexity of the underground geological conditions, exploration, exploitation and utilization of geothermal resources are challenging, and therefore, the development of the numerical simulation technology of the geothermal field is urgently needed.
The current numerical simulation of the ground temperature field has the following defects: a conventional geothermal field numerical simulation method (such as a finite element method, a finite difference method, a boundary element method and a finite volume method) is used for calculating in a spatial domain, a model needs to be finely divided when a high precision requirement is met in a large-scale complex medium, and the number of dividing units is large, so that the storage capacity is large and the calculation time is long.
Disclosure of Invention
Aiming at the current situations of large calculation amount and high storage requirement when processing large-scale temperature field numerical simulation by the conventional methods such as the current finite element method, the finite difference method, the boundary element method and the like, the invention aims to provide a forward modeling method, a device, equipment and a medium of a three-dimensional steady-state heat conduction ground temperature field so as to meet the requirement of refined forward modeling calculation of undulating terrain.
In order to achieve the technical purpose, the technical scheme provided by the invention is as follows:
in one aspect, the present invention provides a method for forward modeling a three-dimensional steady-state heat conduction geothermal field, comprising:
s1, determining a three-dimensional abnormal body, determining a target area containing the three-dimensional abnormal body, and constructing a three-dimensional prism model of the target area;
s2, carrying out mesh subdivision on the three-dimensional prism model along the directions of x, y and z, and subdividing to obtain a series of subdivision nodes and mesh subdivision parameters of the three-dimensional prism model;
s3, assigning a value to the thermophysical parameter of each subdivision node in the three-dimensional prism model according to the distribution condition of the thermophysical parameters of the target area;
s4, loading boundary conditions, calculating the background field temperature of the spatial domain, and taking the background field temperature as an initial spatial domain temperature total field;
s5, calculating an abnormal temperature field of the spatial wave number mixed domain based on the thermal physical parameters and the current total spatial domain temperature field;
s6, performing inverse Fourier transform on the spatial wave number mixed domain abnormal temperature field to obtain the spatial domain abnormal field temperature;
s7, obtaining a new total spatial domain temperature field based on the spatial domain background field temperature and the spatial domain abnormal field temperature;
and S8, setting an iteration convergence condition, outputting a new space domain temperature total field if the new space domain temperature total field meets the iteration convergence condition, and returning to S5 if the new space domain temperature total field is not used as the current space domain temperature total field in the next iteration.
In another aspect, the present invention provides a device for forward modeling a three-dimensional steady-state heat-conductive geothermal field, comprising:
the system comprises a first module, a second module and a third module, wherein the first module is used for determining a three-dimensional abnormal body, determining a target area containing the three-dimensional abnormal body inside and constructing a three-dimensional prism model of the target area;
the second module is used for carrying out mesh subdivision on the three-dimensional prism model along the directions of x, y and z to obtain a series of subdivision nodes and mesh subdivision parameters of the three-dimensional prism model through subdivision;
the third module is used for assigning values to the thermophysical parameters of each subdivision node in the three-dimensional prism model according to the distribution condition of the thermophysical parameters of the target area;
the fourth module is used for loading boundary conditions, calculating the ambient field temperature of the spatial domain and taking the ambient field temperature as the total temperature field of the initial spatial domain;
a fifth module, configured to calculate a spatial wave number mixed domain abnormal temperature field based on the thermophysical parameters and the current spatial domain total temperature field;
the sixth module is used for performing inverse Fourier transform on the spatial wave number mixed domain abnormal temperature field to obtain the spatial domain abnormal field temperature;
the seventh module is used for obtaining a new total temperature field of the space domain based on the background field temperature of the space domain and the abnormal field temperature of the space domain;
an eighth module, configured to set an iterative convergence condition, determine whether the new spatial domain total temperature field meets the iterative convergence condition, and if yes, output the new spatial domain total temperature field; and otherwise, taking the new total spatial domain temperature field as the current total spatial domain temperature field in the next iteration, and inputting the current total spatial domain temperature field into the fifth module.
In another aspect, the present invention provides a computer device comprising a memory and a processor, the memory storing a computer program, the processor implementing the steps in the method for forward modeling of a three-dimensional steady-state heat conduction geothermal field when executing the computer program.
In yet another aspect, the present invention further provides a computer readable storage medium having stored thereon a computer program which, when being executed by a processor, carries out the steps of the method for forward modeling of a three-dimensional steady-state heat-conduction geothermal field.
Compared with the prior art, the invention has the advantages that:
the method determines a model by setting a calculation range of a geothermal field and the shape, size and position of an abnormal body, and provides thermophysical property parameters of the model; the three-dimensional problem is converted into the one-dimensional problem by using two-dimensional Fourier transform, and the high-efficiency and high-precision numerical simulation of the three-dimensional stable heat conduction ground temperature field is realized.
The method solves the problems of large calculated amount and high storage requirement of the conventional method in the large-scale numerical simulation of the three-dimensional geothermal field at present, and provides an effective forward modeling scheme for realizing the fine inversion and interpretation of the measured data of the geothermal exploration in the field complex terrain or underground complex structure.
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FIG. 1 is a flow chart in one embodiment of the present invention;
FIG. 2 is a schematic diagram of a calculation region and a model according to an embodiment of the invention;
FIG. 3 is a comparison graph of the calculation results of the method of the present invention and the conventional COMSOL Multiphysics method according to an embodiment of the present invention;
FIG. 4 is a diagram illustrating relative error of the calculation results of the method of the present invention and the conventional COMSOL Multiphysics method according to an embodiment of the present invention;
fig. 5 is a schematic structural diagram according to an embodiment of the present invention.
Detailed Description
For the purpose of promoting a clear understanding of the objects, aspects and advantages of the embodiments of the invention, reference will now be made to the drawings and detailed description, wherein there are shown in the drawings and described below specific embodiments of the invention, in which modifications and variations can be made by one skilled in the art without departing from the spirit and scope of the invention. The exemplary embodiments of the present invention and the description thereof are provided to explain the present invention and not to limit the present invention.
Referring to fig. 1, in an embodiment of the present invention, a method for forward modeling a three-dimensional steady-state heat conduction geothermal field is provided, including:
s1, determining a three-dimensional abnormal body, determining a target area containing the three-dimensional abnormal body, and constructing a three-dimensional prism model of the target area;
s2, carrying out mesh subdivision on the three-dimensional prism model along the directions of x, y and z, and subdividing to obtain a series of subdivision nodes and mesh subdivision parameters of the three-dimensional prism model;
s3, assigning a value to the thermophysical parameter of each subdivision node in the three-dimensional prism model according to the distribution condition of the thermophysical parameters of the target area;
s4, loading boundary conditions, calculating the background field temperature of the spatial domain, and taking the background field temperature as an initial spatial domain temperature total field;
s5, calculating an abnormal temperature field of the spatial wave number mixed domain based on the thermal physical parameters and the current total spatial domain temperature field;
s6, performing inverse Fourier transform on the spatial wave number mixed domain abnormal temperature field to obtain the spatial domain abnormal field temperature;
s7, obtaining a new total spatial domain temperature field based on the spatial domain background field temperature and the spatial domain abnormal field temperature;
and S8, setting an iteration convergence condition, outputting a new space domain temperature total field if the new space domain temperature total field meets the iteration convergence condition, and returning to S5 if the new space domain temperature total field is not used as the current space domain temperature total field in the next iteration.
The thermophysical parameters comprise background thermal conductivity, background heat generation rate, abnormal thermal conductivity and abnormal heat generation rate, and the background thermal conductivity, the background heat generation rate, the abnormal thermal conductivity and the abnormal heat generation rate of each subdivision node are assigned in step S3.
The boundary conditions of the present invention are boundary conditions of a ground temperature field, and generally include three types, namely, boundary conditions of a given temperature, boundary conditions of a given heat flow, and boundary conditions of a given heat exchange coefficient. In the present invention S4, any of the above boundary conditions of the earth temperature field may be loaded. The boundary condition of the given temperature means that the temperature of the subdivision nodes distributed on the boundary of the target area is known, the boundary condition of the given heat flow means that the heat flow density of the subdivision nodes distributed on the boundary of the target area is known, and the boundary condition of the given heat exchange coefficient means that the temperature of a heat source and the heat exchange coefficient on the boundary of the target area are known.
In the invention S4, a one-dimensional finite element method based on quadratic function interpolation is adopted to calculate the ambient field temperature in the spatial domain, and the calculation formula is as follows:
Figure BDA0003377192380000051
in the formula of0(xi,yj,zk) Is set as (x) at the coordinate positioni,yj,zk) Background thermal conductivity, T, of the subdivision node0(xi,yj,zk) Is set as (x) at the coordinate positioni,yj,zk) The spatial domain background field temperature, Q, of the subdivision node0(xi,yj,zk) Is set as (x) at the coordinate positioni,yj,zk) The background heat generation rate of the subdivision nodes. Within each cell, the function is assumed to be a quadratic function.
In the invention S5, the spatial domain abnormal field temperature, the spatial domain abnormal heat flow density and the spatial domain abnormal heat generation rate are subjected to two-dimensional Fourier transform to obtain the spatial wave number mixed domain abnormal field temperature
Figure BDA0003377192380000052
Spatial wavenumber mixed domain abnormal heat flux density
Figure BDA0003377192380000053
Abnormal heat generation rate of space wave number mixed domain
Figure BDA0003377192380000054
Figure BDA0003377192380000055
Figure BDA0003377192380000056
Figure BDA0003377192380000057
Wherein: n ═ 1,2x，j＝1,2,...Ny，k＝1,2,...Nk，Nx、Ny、NkRespectively obtaining the number of subdivision nodes after the three-dimensional prism model carries out mesh subdivision along the directions of x, y and z; t isa(xi,yj,zk) Is set as (x) at the coordinate positioni,yj,zk) The temperature of the spatial domain abnormal field of the subdivision node of (q)a(xi,yj,zk) Is set as (x) at the coordinate positioni,yj,zk) The spatial domain abnormal heat flux, Q, of the subdivision nodea(xi,yj,zk) Is set as (x) at the coordinate positioni,yj,zk) The abnormal heat generation rate k of the space domain of the subdivision nodex，kyThe discrete offset wave number in the x direction and the y direction, Deltax and Delay are sampling interval intervals when the three-dimensional prism model carries out grid splitting along the x direction and the y direction respectively, e represents a natural constant,
Figure BDA0003377192380000061
denotes the unit of imaginary number, (k)x,ky,zk) Is set as (x) at the coordinate positioni,yj,zk) The corresponding coordinate position of the subdivision node in the space wave number mixed domain;
calculating the abnormal field temperature of the spatial wave number mixed domain
Figure BDA0003377192380000062
And then, solving by adopting a finite element method based on quadratic function interpolation, wherein the calculation formula is as follows:
Figure BDA0003377192380000063
Figure BDA0003377192380000064
Figure BDA0003377192380000065
Figure BDA0003377192380000066
in the formula, T(n-1)Is a total field of the temperature of the current space domain corresponding to the nth iteration, and the background field temperature T of the space domain during the first iteration0The total field of temperature T of the current space domain corresponding to the first iteration(0)，
Figure BDA0003377192380000067
i is a unit of an imaginary number,
Figure BDA0003377192380000068
respectively abnormal heat flux density of space wave number mixed domain
Figure BDA0003377192380000069
Three components in the x, y, z directions, λa(xi,yj,zk) Is set as (x) at the coordinate positioni,yj,zk) Of the subdivision nodeSpatial domain anomalous thermal conductivity.
Then, for the abnormal field temperature of the spatial-wavenumber mixed domain
Figure BDA0003377192380000071
Performing two-dimensional inverse Fourier transform to obtain an abnormal temperature field T of a spatial domaina(xi,yj,zk)。
In the nth iteration, the sum of the spatial domain background field temperature and the spatial domain abnormal field temperature calculated in the nth iteration is a new spatial domain temperature total field:
T(n)(xi,yj,zk)＝T0(xi,yj,zk)+Ta(xi,yj,zk)
in another embodiment of the present invention, kx，kyThe calculation method of (2) is as follows:
the number of the selected Gaussian points is 4, and the node coordinate t is as follows:
Figure BDA0003377192380000072
discrete offset wavenumber k in x, y directionx，kyComprises the following steps:
Figure BDA0003377192380000073
Figure BDA0003377192380000074
in the formula,. DELTA.kx,ΔkyThe number of fundamental waves in the x and y directions,
Figure BDA0003377192380000075
when N is presentx、NyIn the case of an even number, the number of the first,
Figure BDA0003377192380000076
Figure BDA0003377192380000077
when N is presentx、NyIn the case of an odd number of the groups,
Figure BDA0003377192380000078
Figure BDA0003377192380000079
it is understood that the preset iteration termination condition refers to a preset model calculation constraint condition for constraining the whole model to converge in the performance calculation process, so that the model can output a result meeting the condition. In the present invention, the iteration termination condition in (S8) may be set to:
Figure BDA0003377192380000081
wherein: t is(n-1)Represents the current total field of space domain temperature, T, corresponding to the nth iteration(n)Represents the new total temperature field of the space domain, epsilon, obtained by the nth iteration calculation0Is the set numerical precision.
When the above iteration convergence condition is satisfied, the iteration is stopped. Of course, in practical applications, a person skilled in the art may set other iteration termination conditions based on the prior art, the conventional technical means in the field, or the common general knowledge, and is not limited to the iteration termination conditions set in the above preferred embodiments of the present application.
The accuracy and efficiency of the forward modeling method of the three-dimensional steady-state heat conduction geothermal field provided by the invention are tested.
The method of the embodiment is realized by Fortran language programming, and the configuration of a test computer is i5-4590, the main frequency is 3.30GHz and the memory is 16 GB.
A three-dimensional thermal conductivity model is designed, the size of the model is 10km multiplied by 10km, the thermal conductivity is 2W/(m.DEG C), an abnormal body is arranged in the center of the model, the size of the abnormal body is 2km multiplied by 2km, the thermal conductivity is 6W/(m.DEG C), the projection of the center position of the abnormal body on the ground is taken as a coordinate origin, and the model schematic diagram is shown in figure 2. The grid node is 51 multiplied by 51, the upper boundary adopts the first type of boundary conditions, the temperature value is 10 ℃, the lower boundary adopts the second type of boundary conditions, and the heat flow density value is 41.86mW/m2. In the case of a single thread, a fourier transform of four gaussian points is taken, and the numerical precision expected by the iteration is 10-4. The calculation is performed by using the algorithm of the present invention and COMSOL Multiphysics software respectively, fig. 3 is a comparison graph of the calculation results of the algorithm and COMSOL Multiphysics on a measuring line where x is 0 and y is 0, and fig. 4 is a relative error graph between the two algorithms, and it can be seen that the relative error of the calculation results of the two algorithms is below 0.2%, which illustrates the correctness of the method of the present embodiment. Under the same grid condition, the algorithm consumes 0.5s, occupies 0.05GB of memory, and COMSOL multiprophy consumes 31s and 4.2GB of memory, thus fully illustrating the high efficiency of the method of the embodiment.
In an embodiment of the present invention, a three-dimensional steady-state heat conduction geothermal field forward modeling apparatus is provided, including:
the system comprises a first module, a second module and a third module, wherein the first module is used for determining a three-dimensional abnormal body, determining a target area containing the three-dimensional abnormal body inside and constructing a three-dimensional prism model of the target area;
the second module is used for carrying out mesh subdivision on the three-dimensional prism model along the directions of x, y and z to obtain a series of subdivision nodes and mesh subdivision parameters of the three-dimensional prism model through subdivision;
the third module is used for assigning values to the thermophysical parameters of each subdivision node in the three-dimensional prism model according to the distribution condition of the thermophysical parameters of the target area;
the fourth module is used for loading boundary conditions, calculating the ambient field temperature of the spatial domain and taking the ambient field temperature as the total temperature field of the initial spatial domain;
a fifth module, configured to calculate a spatial wave number mixed domain abnormal temperature field based on the thermophysical parameters and the current spatial domain total temperature field;
the sixth module is used for performing inverse Fourier transform on the spatial wave number mixed domain abnormal temperature field to obtain the spatial domain abnormal field temperature;
the seventh module is used for obtaining a new total temperature field of the space domain based on the background field temperature of the space domain and the abnormal field temperature of the space domain;
an eighth module, configured to set an iterative convergence condition, determine whether the new spatial domain total temperature field meets the iterative convergence condition, and if yes, output the new spatial domain total temperature field; and otherwise, taking the new total spatial domain temperature field as the current total spatial domain temperature field in the next iteration, and inputting the current total spatial domain temperature field into the fifth module.
The implementation method of the functions of the modules can be implemented by the same method in the foregoing embodiments, and details are not repeated here.
In this embodiment, a computer device is provided, and the computer device may be a server, and its internal structure diagram may be as shown in fig. 5. The computer device includes a processor, a memory, a network interface, and a database connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device comprises a nonvolatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of an operating system and computer programs in the non-volatile storage medium. The database of the computer device is used to store sample data. The network interface of the computer device is used for communicating with an external terminal through a network connection. The computer program is executed by a processor to implement the forward method of the three-dimensional steady-state heat conduction geothermal field.
Those skilled in the art will appreciate that the architecture shown in fig. 5 is merely a block diagram of some of the structures associated with the disclosed aspects and is not intended to limit the computing devices to which the disclosed aspects apply, as particular computing devices may include more or less components than those shown, or may combine certain components, or have a different arrangement of components.
In one embodiment, a computer device is provided, comprising a memory storing a computer program and a processor implementing the steps of the method of the preceding embodiments for the forward modeling of a three-dimensional steady-state heat-conducting geothermal field when the computer program is executed.
In one embodiment, a computer readable storage medium is provided, on which a computer program is stored, which computer program, when being executed by a processor, is adapted to carry out the steps of the method for forward modeling of a three-dimensional steady-state heat-conduction geothermal field according to the preceding embodiment.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by hardware instructions of a computer program, which can be stored in a non-volatile computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in the embodiments provided herein may include non-volatile and/or volatile memory, among others. Non-volatile memory can include read-only memory (ROM), Programmable ROM (PROM), Electrically Programmable ROM (EPROM), Electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), Dynamic RAM (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced SDRAM (ESDRAM), Synchronous Link DRAM (SLDRAM), Rambus Direct RAM (RDRAM), direct bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (10)

1. The forward modeling method of the three-dimensional steady-state heat conduction geothermal field is characterized by comprising the following steps:
s1, determining a three-dimensional abnormal body, determining a target area containing the three-dimensional abnormal body, and constructing a three-dimensional prism model of the target area;
s2, carrying out mesh subdivision on the three-dimensional prism model along the directions of x, y and z, and subdividing to obtain a series of subdivision nodes and mesh subdivision parameters of the three-dimensional prism model;
s3, assigning a value to the thermophysical parameter of each subdivision node in the three-dimensional prism model according to the distribution condition of the thermophysical parameters of the target area;
s4, loading boundary conditions, calculating the background field temperature of the spatial domain, and taking the background field temperature as an initial spatial domain temperature total field;
s5, calculating an abnormal temperature field of the spatial wave number mixed domain based on the thermal physical parameters and the current total spatial domain temperature field;
s6, performing inverse Fourier transform on the spatial wave number mixed domain abnormal temperature field to obtain the spatial domain abnormal field temperature;
s7, obtaining a new total spatial domain temperature field based on the spatial domain background field temperature and the spatial domain abnormal field temperature;
and S8, setting an iteration convergence condition, outputting a new space domain temperature total field if the new space domain temperature total field meets the iteration convergence condition, and returning to S5 if the new space domain temperature total field is not used as the current space domain temperature total field in the next iteration.
2. The forward modeling method for the three-dimensional steady-state heat-conduction geothermal field according to claim 2, wherein the thermophysical parameters include background thermal conductivity, background heat generation rate, abnormal thermal conductivity and abnormal heat generation rate, and the background thermal conductivity, the background heat generation rate, the abnormal thermal conductivity and the abnormal heat generation rate of each subdivision node are assigned.
3. The forward modeling method for the three-dimensional steady-state heat-conduction geothermal field according to claim 1 or 2, wherein the boundary condition is any one of a boundary condition of a given temperature, a boundary condition of a given heat flow and a boundary condition of a given heat exchange coefficient, wherein the boundary condition of a given temperature means that the temperature of the subdivision nodes distributed on the boundary of the target area is known, the boundary condition of a given heat flow means that the heat flow density of the subdivision nodes distributed on the boundary of the target area is known, and the boundary condition of a given heat exchange coefficient means that the temperature of the heat source and the heat exchange coefficient on the boundary of the target area are known.
4. The forward modeling method for the three-dimensional steady-state heat-conduction geothermal field according to claim 3, characterized in that the one-dimensional finite element method based on quadratic function interpolation is used to calculate the ambient field temperature in the spatial domain, and the calculation formula is:
Figure FDA0003377192370000021
in the formula of0(xi,yj,zk) Is set as (x) at the coordinate positioni,yj,zk) Background thermal conductivity, T, of the subdivision node0(xi,yj,zk) Is set as (x) at the coordinate positioni,yj,zk) The spatial domain background field temperature, Q, of the subdivision node0(xi,yj,zk) Is set as (x) at the coordinate positioni,yj,zk) The background heat generation rate of the subdivision nodes.
5. The method for forward modeling of a three-dimensional steady-state heat-conducting geothermal field according to claim 3, wherein S5 comprises:
performing two-dimensional Fourier transform on the spatial domain abnormal field temperature, the spatial domain abnormal heat flow density and the spatial domain abnormal heat generation rate to obtain the spatial wave number mixed domain abnormal field temperature
Figure FDA0003377192370000022
Spatial wavenumber mixed domain abnormal heat flux density
Figure FDA0003377192370000023
Abnormal heat generation rate of space wave number mixed domain
Figure FDA0003377192370000024
Figure FDA0003377192370000025
Figure FDA0003377192370000026
Figure FDA0003377192370000027
Wherein: n ═ 1,2x，j＝1,2,...Ny，k＝1,2,...Nk，Nx、Ny、NkRespectively obtaining the number of subdivision nodes after the three-dimensional prism model carries out mesh subdivision along the directions of x, y and z; t isa(xi,yj,zk) Is set as (x) at the coordinate positioni,yj,zk) The temperature of the spatial domain abnormal field of the subdivision node of (q)a(xi,yj,zk) Is set as (x) at the coordinate positioni,yj,zk) The spatial domain abnormal heat flux, Q, of the subdivision nodea(xi,yj,zk) As a coordinateThe position is (x)i,yj,zk) The abnormal heat generation rate k of the space domain of the subdivision nodex，kyThe discrete offset wave number in the x direction and the y direction, Deltax and Delay are sampling interval intervals when the three-dimensional prism model carries out grid splitting along the x direction and the y direction respectively, e represents a natural constant,
Figure FDA0003377192370000031
denotes the unit of imaginary number, (k)x,ky,zk) Is set as (x) at the coordinate positioni,yj,zk) The corresponding coordinate position of the subdivision node in the space wave number mixed domain;
calculating the abnormal field temperature of the spatial wave number mixed domain
Figure FDA0003377192370000032
And then, solving by adopting a finite element method based on quadratic function interpolation, wherein the calculation formula is as follows:
Figure FDA0003377192370000033
Figure FDA0003377192370000034
Figure FDA0003377192370000035
Figure FDA0003377192370000036
in the formula, T(n-1)Is a total field of the temperature of the current space domain corresponding to the nth iteration, and the background field temperature T of the space domain during the first iteration0The total field of temperature T of the current space domain corresponding to the first iteration(0)，
Figure FDA0003377192370000037
i is a unit of an imaginary number,
Figure FDA0003377192370000038
respectively abnormal heat flux density of space wave number mixed domain
Figure FDA0003377192370000039
Three components in the x, y, z directions, λa(xi,yj,zk) Is set as (x) at the coordinate positioni,yj,zk) The space domain of the subdivision node is abnormal in thermal conductivity.
6. The method of claim 5, wherein k is kx，kyThe calculation method of (2) is as follows:
the number of the selected Gaussian points is 4, and the node coordinate t is as follows:
Figure FDA0003377192370000041
discrete offset wavenumber k in x, y directionx，kyComprises the following steps:
Figure FDA0003377192370000042
Figure FDA0003377192370000043
in the formula,. DELTA.kx,ΔkyThe number of fundamental waves in the x and y directions,
Figure FDA0003377192370000044
when N is presentx、NyIn the case of an even number, the number of the first,
Figure FDA0003377192370000045
Figure FDA0003377192370000046
when N is presentx、NyIn the case of an odd number of the groups,
Figure FDA0003377192370000047
Figure FDA0003377192370000048
7. the method for forward modeling of a three-dimensional steady-state heat-conducting geothermal field according to claim 1,2, 4, 5 or 6, wherein the iterative convergence condition is set as:
Figure FDA0003377192370000049
wherein: t is(n-1)Represents the current total field of space domain temperature, T, corresponding to the nth iteration(n)Represents the new total temperature field of the space domain, epsilon, obtained by the nth iteration calculation0Is the set numerical precision.
8. The device that just plays of three-dimensional steady state heat conduction ground temperature field characterized in that includes:
the system comprises a first module, a second module and a third module, wherein the first module is used for determining a three-dimensional abnormal body, determining a target area containing the three-dimensional abnormal body inside and constructing a three-dimensional prism model of the target area;
the second module is used for carrying out mesh subdivision on the three-dimensional prism model along the directions of x, y and z to obtain a series of subdivision nodes and mesh subdivision parameters of the three-dimensional prism model through subdivision;
the third module is used for assigning values to the thermophysical parameters of each subdivision node in the three-dimensional prism model according to the distribution condition of the thermophysical parameters of the target area;
the fourth module is used for loading boundary conditions, calculating the ambient field temperature of the spatial domain and taking the ambient field temperature as the total temperature field of the initial spatial domain;
a fifth module, configured to calculate a spatial wave number mixed domain abnormal temperature field based on the thermophysical parameters and the current spatial domain total temperature field;
the sixth module is used for performing inverse Fourier transform on the spatial wave number mixed domain abnormal temperature field to obtain the spatial domain abnormal field temperature;
the seventh module is used for obtaining a new total temperature field of the space domain based on the background field temperature of the space domain and the abnormal field temperature of the space domain;
an eighth module, configured to set an iterative convergence condition, determine whether the new spatial domain total temperature field meets the iterative convergence condition, and if yes, output the new spatial domain total temperature field; and otherwise, taking the new total spatial domain temperature field as the current total spatial domain temperature field in the next iteration, and inputting the current total spatial domain temperature field into the fifth module.
9. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that: a processor implementing the steps in the method of forward modeling of a three-dimensional steady-state heat-conductive geothermal field of claim 1 when executing a computer program.
10. A computer-readable storage medium having stored thereon a computer program, characterized in that: the computer program when executed by a processor implements the steps in the method of forward modeling of a three-dimensional steady-state heat-conductive geothermal field of claim 1.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116187107A (en) * 2023-04-27 2023-05-30 中南大学 Three-dimensional ground temperature field dynamic numerical simulation method, equipment and medium
CN117148457A (en) * 2023-08-29 2023-12-01 长安大学 Magnetic layer magnetization modulus calculation method and system
CN118581565A (en) * 2024-08-07 2024-09-03 西安交通大学 Method and device for determining crystallization interface of grown crystal by guided mode method

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116187107A (en) * 2023-04-27 2023-05-30 中南大学 Three-dimensional ground temperature field dynamic numerical simulation method, equipment and medium
CN116187107B (en) * 2023-04-27 2023-08-11 中南大学 Three-dimensional ground temperature field dynamic numerical simulation method, equipment and medium
CN117148457A (en) * 2023-08-29 2023-12-01 长安大学 Magnetic layer magnetization modulus calculation method and system
CN118581565A (en) * 2024-08-07 2024-09-03 西安交通大学 Method and device for determining crystallization interface of grown crystal by guided mode method

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