CN116341279A - Anisotropic medium three-dimensional transient earth temperature field forward modeling method, equipment and medium - Google Patents
Anisotropic medium three-dimensional transient earth temperature field forward modeling method, equipment and medium Download PDFInfo
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Abstract
The invention discloses a forward modeling method, equipment and medium of an anisotropic medium three-dimensional transient ground temperature field, which are characterized in that a target area is modeled, then the target area is subjected to spatial discretization and time discretization, and the total field temperature of a spatial domain is calculated in an iterative manner by using a spatial-wave number mixed domain iterative method in space; in time, combining with a ground temperature field recursion formula in an explicit differential format, calculating to obtain the initial space domain total field temperature of the next time node, and then calculating the space domain total field temperature of the next time node by using a space-wave number mixed domain iteration method; and so on, the total field temperature of the spatial domain of all time nodes is forward developed. The invention realizes the forward modeling of the three-dimensional transient ground temperature field of the anisotropic medium, can truly reflect the dynamic change of the ground temperature field, combines the space-wave number mixed domain iteration method with the ground temperature field recursion technology, ensures the fine forward modeling of the ground temperature field, reduces the calculation and storage cost and improves the calculation efficiency.
Description
Technical Field
The invention relates to the technical field of ground temperature field numerical simulation, in particular to a three-dimensional transient ground temperature field forward modeling method, equipment and medium for an anisotropic medium.
Background
In geothermal exploration, due to the general distribution of subsurface medium non-uniformities, studying the anisotropy of the medium is of great importance for the processing and interpretation of geothermal data. And the complexity of the geological structure and the diversity of the thermal storage occurrence form lead to the problems of long calculation time and high storage requirement of the existing three-dimensional ground temperature field forward modeling method when simulating large-scale complex geological conditions.
At present, most of forward modeling methods for ground temperature fields are steady forward modeling methods, for example, chinese patent CN202111423009X discloses a forward modeling method, device, equipment and medium for three-dimensional steady-state heat conduction ground temperature fields. However, the geothermal field is dynamically changed, i.e. transient, and the realization of the three-dimensional transient geothermal field forward calculation of the anisotropic medium has important practical significance for geothermal research. At present, although researches on transient ground temperature fields exist, the complexity of geological structures and the diversity of heat storage occurrence forms lead to the problems of long calculation time and high storage requirement of the existing three-dimensional ground temperature field forward modeling method when simulating large-scale complex geological conditions. Aiming at the problem, the invention provides a fine and efficient anisotropic medium three-dimensional transient geothermal field forward modeling technology, which provides important technical support for fine inversion of large-scale geothermal data.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a three-dimensional transient ground temperature field forward modeling method, equipment and medium for an anisotropic medium, which realize the fine and efficient three-dimensional transient ground temperature field forward modeling of the anisotropic medium.
In a first aspect, there is provided a three-dimensional transient earth temperature field forward modeling method for an anisotropic medium, including:
s1: selecting a target area containing an abnormal body, and constructing a target model;
s2: performing spatial discretization and time discretization on the target model to obtain a series of sampling nodes and a series of time nodes;
s3: giving a thermophysical parameter value on each sampling node, wherein the thermophysical parameter comprises heat conductivity, heat generation rate and heat capacity, and the heat conductivity of the sampling node in the abnormal body area has anisotropy;
s4: loading initial conditions and boundary conditions;
s5: calculating the total field temperature of the space domain of the current time node by using a space-wave number mixed domain iteration method;
s6: combining a ground temperature field recursive formula of an explicit differential format, calculating to obtain an initial space domain total field temperature of a next time node, and then calculating the space domain total field temperature of the next time node by using a space-wave number mixed domain iteration method; and so on, the total field temperature of the spatial domain of all time nodes is forward developed.
According to the first aspect, in a possible implementation manner, in the step S2, when the spatial discretization is performed, the target area is spatially subjected to three-dimensional mesh subdivision, and the x direction and the y direction are uniformly subdivided, and the z direction is uniformly or non-uniformly subdivided.
In one possible implementation, according to the first aspect, the thermal conductivity at each sampling node comprises a background thermal conductivity and an abnormal thermal conductivity, the heat generation rate at each sampling node comprises a background heat generation rate and an abnormal heat generation rate, and the heat capacity at each sampling node comprises a background heat capacity and an abnormal heat capacity;
wherein the thermal conductivity
As tensors, the expression is as follows:
in the method, in the process of the invention,
9 components of thermal conductivity; the abnormal thermal conductivity has anisotropy.
In one possible implementation manner according to the first aspect, the step S5 includes:
s51: obtaining a space domain background field temperature based on a background field control equation and a thermophysical parameter value of a background field, and taking the space domain background field temperature as an initial space domain total field temperature;
s52: performing horizontal two-dimensional Fourier transform on the abnormal field control equation to obtain a space-wave number domain abnormal field control equation;
s53: according to the total field temperature of the current round space domain and the thermophysical parameter value of the abnormal field, calculating to obtain the abnormal field temperature of the space-wave number domain by combining a space-wave number domain abnormal field control equation;
s54: performing two-dimensional Fourier inverse transformation on the abnormal field temperature in the space-wave number domain to obtain the abnormal field temperature in the space domain;
s55: obtaining a new spatial domain total field temperature based on the spatial domain background field temperature and the spatial domain abnormal field temperature;
s56: judging whether the new space domain total field temperature meets the iteration convergence condition, if so, outputting the new space domain total field temperature as the space domain total field temperature of the current time node; otherwise, the new spatial domain total field temperature is taken as the current round of spatial domain total field temperature in the next round of iteration, and the step S53 is returned.
In one possible implementation form according to the first aspect, the background field control equation is expressed as follows:
in the method, in the process of the invention,
for background field temperature, +.>
For background thermal conductivity, +.>
For background heat generation rate, < >>
Is background heat capacity, t is time;
the space-wavenumber domain abnormal field control equation is expressed as follows:
in the method, in the process of the invention,
for abnormal thermal conductivity +.>
Is abnormal heat capacity->
Abnormal field temperature for the space-wavenumber domain, +.>
Abnormal heat generation rate for space-wave number domain, < >>
Respectively->
Wave number in direction, +.>
For the two-dimensional Fourier transform symbol, i is the imaginary unit, T is the total field temperature, +.>
Is the heat capacity of the fluid, v x 、v y 、v z The flow rates of the fluid in the x, y, and z directions, respectively.
In one possible implementation manner, according to the first aspect, the iterative convergence condition is that an error is smaller than a preset value; the expression of the error is as follows:
wherein e is an error,
the number of sampling nodes in the x, y and z directions is +.>
、/>
The spatial domain total field temperature for the nth and n+1th iterations, respectively.
In one possible implementation manner according to the first aspect, the step S6 includes:
s61: combining a ground temperature field recursion formula in an explicit differential format, and solving the space-wave number domain abnormal field temperature in the last iteration of the current time node by adopting a catch-up method to obtain the space-wave number domain abnormal field temperature of the next time node;
s62: performing two-dimensional Fourier inverse transformation on the abnormal field temperature of the space-wave number domain of the next time node to obtain the abnormal field temperature of the space domain of the next time node;
s63: obtaining an initial spatial domain total field temperature of the next time node based on the spatial domain abnormal field temperature and the spatial domain background field temperature of the next time node;
s64: calculating the total field temperature of the space domain of the next time node by using a space-wave number mixed domain iteration method;
s65: and (6) circularly executing the steps S61-S64 until the total field temperature of the space domain of all the time nodes is obtained by forward modeling.
In one possible implementation form according to the first aspect, the ground temperature field recurrence formula is as follows:
in the method, in the process of the invention,
for the last time node->
Is a spatially-wavenumber domain abnormal field temperature, +.>
For next time node->
Is a spatially-wavenumber domain abnormal field temperature, +.>
For the time interval between adjacent time nodes, K is the coefficient matrix related to the abnormal field in the space-wave number domain, G is the coefficient matrix related to the time derivative term of the abnormal field in the space-wave number domain, and P is the source term.
In a possible implementation manner according to the first aspect, the total field temperature for the spatial domain between adjacent time nodes is obtained by the following method:
acquiring adjacent time nodes
And time node->
Is>
And->
And acquisition time node->
And time node->
Is +.f. in the space-wavenumber domain>
And->
；
Calculating adjacent time nodes using interpolation algorithm
And time node->
A spatial domain background field temperature at a time t' in between +.>
And space-wavenumber domain abnormal field temperature +.>
；
Where a is a coefficient constant,
；
performing two-dimensional Fourier inverse transformation on the abnormal field temperature of the space-wave number domain at the time t 'to obtain the abnormal field temperature of the space domain at the time t';
and adding the space domain background field temperature at the time t 'and the space domain abnormal field temperature to obtain the space domain total field temperature at the time t'.
In a possible implementation manner according to the first aspect, the time intervals between adjacent time nodes in the series of time nodes are equal, or are not equal, or are partially equal.
In a second aspect, there is provided an electronic device comprising:
a memory storing a computer program;
and a processor for loading and executing the computer program to implement the steps of the anisotropic medium three-dimensional transient earth temperature field forward modeling method as described above.
In a third aspect, a computer readable storage medium is provided, storing a computer program which when executed by a processor implements the steps of the anisotropic medium three-dimensional transient earth temperature field forward method as described above.
The invention provides a forward modeling method, equipment and medium of an anisotropic medium three-dimensional transient ground temperature field, which are used for carrying out space discretization and time discretization on a target area, and iteratively calculating the total field temperature of a space domain by using a space-wave number mixed domain iteration method in space; in time, combining with a ground temperature field recursion formula in an explicit differential format, calculating to obtain the initial space domain total field temperature of the next time node, and then calculating the space domain total field temperature of the next time node by using a space-wave number mixed domain iteration method; and so on, the total field temperature of the spatial domain of all time nodes is forward developed. The invention realizes the forward modeling of the three-dimensional transient ground temperature field of the anisotropic medium, can truly reflect the dynamic change of the ground temperature field, combines the space-wave number mixed domain iteration method with the ground temperature field recursion technology, ensures the fine forward modeling of the ground temperature field, reduces the calculation and storage cost and improves the calculation efficiency.
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In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for simulating dynamic numerical values of a three-dimensional ground temperature field provided by an embodiment of the invention;
FIG. 2 is a flowchart of calculating a total field temperature of a spatial domain of a current time node by using a spatial-wavenumber mixed domain iterative method according to an embodiment of the present invention;
FIG. 3 is a flow chart of the total field temperature of the spatial domain of forward all time nodes provided by an embodiment of the present invention;
FIG. 4 is a cross-sectional view of a target model provided by an embodiment of the present invention, wherein (a) is a cross-sectional view of the target model XOY and (b) is a cross-sectional view of the target model XOZ;
FIG. 5 is a schematic diagram of the calculation results of the method and COMSOL Multiphysics software at a sampling node according to the present invention;
FIG. 6 is a graph showing the relative error between the method of the present invention and the COMSOL Multiphysics software calculation at a sampling node according to an embodiment of the present invention;
FIG. 7 is a schematic diagram of the calculation results of the method and COMSOL Multiphysics software at another sampling node according to the present invention;
fig. 8 is a schematic diagram of the relative error between the calculation result of the method and COMSOL Multiphysics software at another sampling node according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be described in detail below. It will be apparent that the described embodiments are only some, but not all, embodiments of the invention. All other embodiments, based on the examples herein, which are within the scope of the invention as defined by the claims, will be within the scope of the invention as defined by the claims.
The embodiment of the invention provides a three-dimensional ground temperature field dynamic numerical simulation method, which is shown in fig. 1 and comprises the following steps:
s1: and selecting a target area containing an abnormal body, and constructing a target model.
S2: and performing spatial discretization and time discretization on the target model to obtain a series of sampling nodes and a series of time nodes.
In the embodiment, when the space discretization is performed, the target area is spatially subjected to three-dimensional grid subdivision, the x and y directions are uniform subdivision, and the z direction is uniform or non-uniform subdivision; the number of sampling nodes in the x direction is
The number of sampling nodes in the y direction is +.>
The number of sampling nodes in the z direction is +.>
. When time discretization is carried out, a series of time nodes are selected in time, and the number of the time nodes is +.>
。
S3: given the values of the thermophysical parameters on each sampling node, the thermophysical parameters include thermal conductivity, heat generation rate, and heat capacity, wherein the thermal conductivity of the sampling nodes within the abnormal body region has anisotropy.
Specifically, the thermal conductivity at each sampling node includes a background thermal conductivity and an abnormal thermal conductivity, the heat generation rate at each sampling node includes a background heat generation rate and an abnormal heat generation rate, and the heat capacity at each sampling node includes a background heat capacity and an abnormal heat capacity; for the abnormal heat conductivity, abnormal heat generation rate and abnormal heat capacity of the non-abnormal body sampling node are all 0; setting the background heat conductivity, the heat generation rate and the heat capacity at the abnormal body sampling node as uniform lamellar model parameters;
wherein the thermal conductivity
As tensors, the expression is as follows:
in the method, in the process of the invention,
9 components of thermal conductivity; the abnormal thermal conductivity has anisotropy.
S4: the initial conditions and boundary conditions are loaded.
In particular, the boundary condition refers to a known temperature value or a known heat flux density value or a known heat exchange coefficient at the boundary. The initial condition is given initial time
The initial temperature of each sampling node in the target area can be given as original data, and can be calculated based on boundary conditions and model parameters.
S5: and calculating the total field temperature of the space domain of the current time node by using a space-wave number mixed domain iteration method. Specifically, as shown in fig. 2, the step S5 includes:
s51: the spatial domain background field temperature is derived based on the background field control equation and the thermophysical parameter values of the background field (i.e., values of background thermal conductivity, background heat generation rate, and background heat capacity) and is taken as the initial spatial domain total field temperature.
Wherein the background field control equation is expressed as follows:
in the method, in the process of the invention,
for background field temperature, +.>
For background thermal conductivity, +.>
For background heat generation rate, < >>
Is background heat capacity, t is time.
S52: and carrying out horizontal two-dimensional Fourier transform on the abnormal field control equation to obtain a space-wave number domain abnormal field control equation.
Specifically, the abnormal field control equation is expressed as follows:
in the method, in the process of the invention,
for abnormal field temperature, +.>
For background thermal conductivity, +.>
For background heat capacity, +.>
For abnormal thermal conductivity +.>
For abnormal heat generation rate, < >>
Is the abnormal heat capacity, T is the total field temperature, < >>
Is the heat capacity of the fluid, v is the flow rate of the fluid;
performing horizontal two-dimensional Fourier transform on the abnormal field control equation to obtain a space-wave number domain abnormal field control equation (namely a one-dimensional space domain abnormal field control equation under a two-dimensional wave number domain), wherein the method comprises the following steps of:
in the method, in the process of the invention,
abnormal field temperature for the space-wavenumber domain, +.>
Abnormal heat generation rate for space-wave number domain, < >>
Respectively->
Wave number in direction, +.>
Is a two-dimensional Fourier transform symbol, i is an imaginary unit, v x 、v y 、v z The flow rates of the fluid in the x, y, and z directions, respectively.
S53: according to the total field temperature of the current round space domain and the thermophysical parameter values (namely values of abnormal heat conductivity, abnormal heat generation rate and abnormal heat capacity) of the abnormal field, combining a space-wave number domain abnormal field control equation, and solving and calculating by adopting a one-dimensional finite element method based on quadratic interpolation to obtain the space-wave number domain abnormal field temperature.
S54: performing two-dimensional Fourier inverse transformation on the abnormal field temperature in the space-wave number domain to obtain the abnormal field temperature in the space domain;
s55: obtaining a new spatial domain total field temperature based on the spatial domain background field temperature and the spatial domain abnormal field temperature;
s56: judging whether the new space domain total field temperature meets the iteration convergence condition, if so, outputting the new space domain total field temperature as the space domain total field temperature of the current time node; otherwise, the new spatial domain total field temperature is taken as the current round of spatial domain total field temperature in the next round of iteration, and the step S53 is returned.
In this embodiment, the iteration convergence condition is that an error is smaller than a preset value; the expression of the error is as follows:
wherein e is an error,
the number of sampling nodes in the x, y and z directions is +.>
、/>
The spatial domain total field temperature for the nth and n+1th iterations, respectively. If the error e between the space domain total field temperature obtained by the current iteration round and the space domain total field temperature obtained by the previous iteration round is smaller than a set value, meeting a convergence condition, ending the iteration and outputting the space domain total field temperature; otherwise, if the convergence condition is not satisfied, repeating the steps S6-S9 to continue the iterative computation until convergence.
S6: combining a ground temperature field recursive formula of an explicit differential format, calculating to obtain an initial space domain total field temperature of a next time node, and then calculating the space domain total field temperature of the next time node by using a space-wave number mixed domain iteration method; and so on, the total field temperature of the spatial domain of all time nodes is forward developed.
Specifically, as shown in fig. 3, the step S6 includes:
s61: combining with a ground temperature field recursion formula in an explicit differential format, and solving the space-wave number domain abnormal field temperature in the last iteration of the current time node by adopting a catch-up method to obtain the space-wave number domain abnormal field temperature of the next time node.
Wherein, the ground temperature field recurrence formula is expressed as follows:
in the method, in the process of the invention,
for the last time node->
Is a spatially-wavenumber domain abnormal field temperature, +.>
For the next time node
K is a coefficient matrix related to the abnormal field of the space-wave number domain,/I->
G is a coefficient matrix related to a space-wave number domain abnormal field time derivative term for the time interval between adjacent time nodes, and P is a source term; in the process of solving the abnormal field control equation of the space-wave number domain by adopting the finite element method to obtain the abnormal field temperature of the space-wave number domain, the value of K, G, P can be obtained by carrying out unit analysis and overall synthesis. The above can be simplified into a diagonal system of equations +.>
Wherein Q is a five-diagonal matrix, X is the unknown quantity to be solved, and B is the right-hand term. The diagonal equation set adopts a catch-up method to realize quick solution and adopts the catch-up method to solve the ordinary differential squareThe process has high parallelism, and the calculation time and the memory occupation are greatly reduced.
S62: and performing two-dimensional Fourier inverse transformation on the abnormal field temperature of the space-wave number domain of the next time node to obtain the abnormal field temperature of the space domain of the next time node.
S63: and adding the space domain abnormal field temperature of the next time node and the space domain background field temperature to obtain the initial space domain total field temperature of the next time node.
S64: calculating the total field temperature of the space domain of the next time node by using a space-wave number mixed domain iteration method (corresponding to the steps S53-S56);
s65: and (6) circularly executing the steps S61-S64 until the total field temperature of the space domain of all the time nodes is obtained by forward modeling.
In a preferred embodiment of the present invention, further comprising:
s7: and obtaining the total field temperature of the space domain between every two adjacent time nodes by using an interpolation algorithm.
The step S7 specifically includes:
s71: acquiring adjacent time nodes
And time node->
Is>
And->
And acquisition time node->
And time node->
Is +.f. in the space-wavenumber domain>
And->
；
S72: calculating adjacent time nodes using interpolation algorithm
And time node->
A spatial domain background field temperature at a time t' in between +.>
And space-wavenumber domain abnormal field temperature +.>
；
Where a is a coefficient constant,
；
s73: performing two-dimensional Fourier inverse transformation on the abnormal field temperature of the space-wave number domain at the time t 'to obtain the abnormal field temperature of the space domain at the time t';
s74: and adding the space domain background field temperature at the time t 'and the space domain abnormal field temperature to obtain the space domain total field temperature at the time t'.
It should be noted that, the time intervals between adjacent time nodes in the series of time nodes may be equal, or may be unequal, or some of them may be equal.
The embodiment of the invention also provides electronic equipment, which comprises:
a memory storing a computer program;
and the processor is used for loading and executing the computer program to realize the steps of the anisotropic medium three-dimensional transient earth temperature field forward modeling method according to the embodiment.
The embodiment of the invention also provides a computer readable storage medium storing a computer program which when executed by a processor implements the steps of the anisotropic medium three-dimensional transient earth temperature field forward modeling method as described in the above embodiment.
The effect of the solution provided by the invention is examined in connection with a specific example.
The computer tested was configured as an Intel (R) Core (TM) i7-11800H, main frequency 2.30GHz, memory 16GB,64 bit win11 system.
The projection of the target model XOY plane and XOZ cross section is shown in (a) and (b) of FIG. 4, and the calculation range x-5000 m, y-5000 m, and z-0-10000 m.
The background is a full space medium, the background thermal conductivity is 2W/(m. DEGC), and the thermal capacity is 5×10 5 J/(m 3 Temperature c), anisotropic abnormal thermal conductivity component
3, 1, 3, 1, 3, 2, 3, 2, 4W/(m..degree.C.), the abnormal heat capacity is 1X 10 6 J/(m3..degree.C.) the background has no internal heat generation, and the abnormal heat generation rate is 4X 10 -6 W/m 3 . The upper boundary adopts a first type boundary condition (the temperature value is known), the initial temperature value of the boundary is 10 ℃, the lower boundary adopts a second type boundary condition (the heat flux density value is known), and the heat flux density value is 41.86 mW/m 2 . The spatial grid subdivision is 51 x 51, the time nodes are 21, iterative convergence accuracy (preset value) of 10 -4 . Forward modeling is performed by using the method and COMSOL Multiphysics software respectively, and sampling nodes are selected>
And sampling node->
The temperature was varied with time. FIG. 5 is a sample node->
Calculating results and graphs of two methods6 is a relative error diagram, and FIG. 7 is a sampling node +.>
The results of the two methods are calculated, and FIG. 8 is a relative error chart. It can be seen that the relative error of both calculation results is less than 0.06%. Under the same condition, the method takes 58s, occupies memory 0.17GB,COMSOL Multiphysics to calculate time 287s and occupies 7.79GB of memory, thereby illustrating the advantages of the method of the embodiment.
It is to be understood that the same or similar parts in the above embodiments may be referred to each other, and that in some embodiments, the same or similar parts in other embodiments may be referred to.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the invention, and that variations, modifications, alternatives and variations may be made to the above embodiments by one of ordinary skill in the art within the scope of the invention.
Claims (10)
1. The forward modeling method of the three-dimensional transient earth temperature field of the anisotropic medium is characterized by comprising the following steps of:
s1: selecting a target area containing an abnormal body, and constructing a target model;
s2: performing spatial discretization and time discretization on the target model to obtain a series of sampling nodes and a series of time nodes;
s3: giving a thermophysical parameter value on each sampling node, wherein the thermophysical parameter comprises heat conductivity, heat generation rate and heat capacity, and the heat conductivity of the sampling node in the abnormal body area has anisotropy;
s4: loading initial conditions and boundary conditions;
s5: calculating the total field temperature of the space domain of the current time node by using a space-wave number mixed domain iteration method;
s6: combining a ground temperature field recursive formula of an explicit differential format, calculating to obtain an initial space domain total field temperature of a next time node, and then calculating the space domain total field temperature of the next time node by using a space-wave number mixed domain iteration method; and so on, the total field temperature of the spatial domain of all time nodes is forward developed.
2. The anisotropic medium three-dimensional transient earth temperature field forward modeling method of claim 1, wherein the thermal conductivity at each sampling node comprises a background thermal conductivity and an abnormal thermal conductivity, the heat generation rate at each sampling node comprises a background heat generation rate and an abnormal heat generation rate, and the heat capacity at each sampling node comprises a background heat capacity and an abnormal heat capacity;
wherein the thermal conductivity
As tensors, the expression is as follows:
3. The anisotropic medium three-dimensional transient earth temperature field forward modeling method according to claim 1, wherein the step S5 comprises:
s51: obtaining a space domain background field temperature based on a background field control equation and a thermophysical parameter value of a background field, and taking the space domain background field temperature as an initial space domain total field temperature;
s52: performing horizontal two-dimensional Fourier transform on the abnormal field control equation to obtain a space-wave number domain abnormal field control equation;
s53: according to the total field temperature of the current round space domain and the thermophysical parameter value of the abnormal field, calculating to obtain the abnormal field temperature of the space-wave number domain by combining a space-wave number domain abnormal field control equation;
s54: performing two-dimensional Fourier inverse transformation on the abnormal field temperature in the space-wave number domain to obtain the abnormal field temperature in the space domain;
s55: obtaining a new spatial domain total field temperature based on the spatial domain background field temperature and the spatial domain abnormal field temperature;
s56: judging whether the new space domain total field temperature meets the iteration convergence condition, if so, outputting the new space domain total field temperature as the space domain total field temperature of the current time node; otherwise, the new spatial domain total field temperature is taken as the current round of spatial domain total field temperature in the next round of iteration, and the step S53 is returned.
4. The anisotropic medium three-dimensional transient earth temperature field forward method of claim 3, wherein the background field control equation is expressed as follows:
the space-wavenumber domain abnormal field control equation is expressed as follows:
in the method, in the process of the invention,
for abnormal thermal conductivity +.>
Is abnormal heat capacity->
Abnormal field temperature for the space-wavenumber domain, +.>
Abnormal heat generation rate for space-wave number domain, < >>
Respectively->
Wave number in direction, +.>
For the two-dimensional Fourier transform symbol, i is the imaginary unit, T is the total field temperature, +.>
Is the heat capacity of the fluid, v x 、v y 、v z The flow rates of the fluid in the x, y, and z directions, respectively.
5. The anisotropic medium three-dimensional transient earth temperature field forward modeling method according to claim 3, wherein the iterative convergence condition is that an error is smaller than a preset value; the expression of the error is as follows:
6. The anisotropic medium three-dimensional transient earth temperature field forward method according to claim 3, 4 or 5, wherein the step S6 comprises:
s61: combining a ground temperature field recursion formula in an explicit differential format, and solving the space-wave number domain abnormal field temperature in the last iteration of the current time node by adopting a catch-up method to obtain the space-wave number domain abnormal field temperature of the next time node;
s62: performing two-dimensional Fourier inverse transformation on the abnormal field temperature of the space-wave number domain of the next time node to obtain the abnormal field temperature of the space domain of the next time node;
s63: obtaining an initial spatial domain total field temperature of the next time node based on the spatial domain abnormal field temperature and the spatial domain background field temperature of the next time node;
s64: calculating the total field temperature of the space domain of the next time node by using a space-wave number mixed domain iteration method;
s65: and (6) circularly executing the steps S61-S64 until the total field temperature of the space domain of all the time nodes is obtained by forward modeling.
7. The anisotropic medium three-dimensional transient earth temperature field forward method of claim 6, wherein the earth temperature field recurrence formula is expressed as follows:
8. The anisotropic medium three-dimensional transient earth temperature field forward modeling method according to claim 3, 4 or 5, wherein the total field temperature for the spatial domain between adjacent time nodes is obtained by the following method:
acquiring adjacent time nodes
And time node->
Is>
And->
And acquisition time node->
And time node->
Is +.f. in the space-wavenumber domain>
And->
；
Calculating adjacent time nodes using interpolation algorithm
And time node->
A spatial domain background field temperature at a time t' in between +.>
And space-wavenumber domain abnormal field temperature +.>
；
Performing two-dimensional Fourier inverse transformation on the abnormal field temperature of the space-wave number domain at the time t 'to obtain the abnormal field temperature of the space domain at the time t';
and adding the space domain background field temperature at the time t 'and the space domain abnormal field temperature to obtain the space domain total field temperature at the time t'.
9. An electronic device, comprising:
a memory storing a computer program;
a processor for loading and executing the computer program to implement the steps of the anisotropic medium three-dimensional transient earth temperature field forward method as claimed in any of claims 1 to 8.
10. A computer readable storage medium storing a computer program, wherein the computer program when executed by a processor implements the steps of the anisotropic medium three-dimensional transient earth temperature field forward method of any of claims 1 to 8.
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