Gravitational effect finite element simulation method based on solving partial differential equations of gravitational field
By constructing a gravitational field interface plugin in COMSOL software and performing mesh generation, the complexity of calculating the self-gravity effect of spacecraft was solved, enabling gravitational calculations for objects of arbitrary shapes and improving calculation accuracy and efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-31
- Publication Date
- 2026-03-24
AI Technical Summary
Existing technologies are insufficient to effectively simplify the calculation of spacecraft self-gravity effects, especially for the calculation of self-gravity effects for non-standard cube mass testing. Furthermore, experimental methods are difficult to measure the overall self-gravity effects of spacecraft, and simulation schemes are complex and contain errors.
A finite element simulation method based on solving partial differential equations of the gravitational field is adopted. By constructing a gravitational field interface plugin in COMSOL software, the spacecraft model is input and meshed. Combined with the boundary conditions, the gravitational field strength of the spacecraft and the surrounding space is calculated, and the gravitational force and gravitational torque are calculated by integrating over the verification mass.
The process of calculating self-gravity has been simplified, the calculation difficulty has been reduced, and gravity calculations can be performed on objects of arbitrary shapes. It balances calculation accuracy and efficiency, and achieves accurate calculation of the self-gravity effect of standard and non-standard objects.
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Figure CN120217795B_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of space gravitational wave detection technology, and more specifically, relates to a finite element simulation method for gravitational effects based on solving partial differential equations of the gravitational field. Background Technology
[0002] The space-based gravitational wave detection mission employs three drag-free spacecraft, each equipped with two test masses (TMs) as inertial references. Inter-satellite laser interferometry (IIFI) is used to measure the distance changes between the test masses, thereby detecting gravitational waves. Ideally, the test masses move along geodesics, and the spacecraft follow them using drag-free control. However, the test masses are susceptible to various disturbances from both inside and outside the spacecraft, affecting the accuracy of gravitational wave detection. One significant disturbance is the gravitational pull of the spacecraft itself on the test masses, known as spacecraft self-gravity. This influences the acceleration noise level of the test masses in multiple ways and must therefore be analyzed to meet the design requirements of the spacecraft for gravitational wave detection.
[0003] The self-gravitational effect can be obtained through two methods: simulation calculation and experimental measurement. Simulation methods typically involve discretizing the spacecraft model into a mesh, approximating each mesh as a point mass, and writing a program to calculate the self-gravitational effect of the point mass on the cubic test mass. The result is then summed over all meshes to obtain the overall self-gravitational effect of the spacecraft on the test mass. Experimental methods utilize a torsion balance as a force sensor to measure the magnitude of self-gravitation. Rotation or translation of the spacecraft is used to measure its gravitational acceleration or gradient. Researchers have proposed a self-gravitational effect measurement scheme based on a torsion balance. The principle of torsion balance measurement is analyzed, the external gravitational multipole moment required to obtain the self-gravitational effect is identified, and two different torsion balance configurations are constructed to measure different external gravitational multipole moments. A mass source simulating the spacecraft's gravitational field is also built, and the principle of the measurement scheme is verified. Because the experimental design is based on a torsion pendulum suspension, requiring a torsion wire suspension to check the mass, and since the mass is located inside the spacecraft surrounded by multiple spacecraft components, this design makes it difficult to measure the overall self-gravity effect of the spacecraft; it can only measure the self-gravity of specific components. Previous self-gravity effect simulation schemes required programming to calculate the spacecraft's self-gravity, a complex process. Furthermore, because the mass needs to be locked and released, the actual mass is a non-standard cube with grooves; calculating based on a standard cube would introduce errors. Summary of the Invention
[0004] In view of the shortcomings of the prior art, the purpose of this application is to reduce the computational difficulty of self-gravity effect and to realize the gravitational calculation of objects of arbitrary shapes.
[0005] To achieve the above objectives, in a first aspect, this application provides a finite element simulation method for gravitational effects based on solving partial differential equations of the gravitational field, the method comprising:
[0006] Input the weak form of the partial differential equation of the gravitational field into the physics field developer of the simulation software COMSOL, and build the gravitational field interface plugin.
[0007] Import the spacecraft model into the simulation software COMSOL and construct the space around the spacecraft;
[0008] Enter the boundary value conditions in the gravitational field interface plugin;
[0009] The gravitational potential is determined by mesh generation and gravitational field interface plugin, and the gravitational field strength of the spacecraft and the surrounding space is determined based on the gravitational potential.
[0010] For the inspection mass in the spacecraft, based on the gravitational field strength of the spacecraft and the surrounding space, an integral operation is performed to determine the gravitational force and gravitational torque acting on the inspection mass.
[0011] In one possible implementation, the weak form of the above gravitational field partial differential equations is determined by the following formula:
[0012] ;
[0013] in, Let G represent the gravitational potential at all points in space, and G be the gravitational constant. Let be the density function at various points in space. Describes the differential operator. This represents the test function. Represents the domain space surrounding the spacecraft. S Representation domain space The boundary surface, where the integral term of the first term is in the domain space. The weak form of the gravitational field equations satisfied on the boundary surface, where the integral term of the second term is in the domain space. The weak form of the gravitational field equations satisfied in the equations.
[0014] In one possible implementation, the space around the spacecraft is simulated by creating geometry.
[0015] In one possible implementation, the outermost layer of space surrounding the spacecraft is configured with a spherical space of finite thickness, which is set as an infinite meta-domain. The role of the infinite meta-domain is to use finite space to simulate infinite space.
[0016] In one possible implementation, the boundary conditions include: the density function of the spacecraft model and the gravitational potential under initial conditions.
[0017] In one possible implementation, the above mesh partitioning includes:
[0018] The target object whose gravity is to be calculated and the space close to the target object are finely divided, while the space far from the target object is roughly divided.
[0019] The distance between a nearby object and the target object is less than or equal to the distance threshold, while the distance between a distant object and the target object is greater than the distance threshold. The mesh size used for fine meshing is smaller than the mesh size used for coarse meshing.
[0020] In one possible implementation, the determination of the gravitational field strength of the spacecraft and its surrounding space based on the gravitational potential includes determining the gravitational field strength using the following formula;
[0021] ;
[0022] in, This indicates the strength of the gravitational field. Represents the gravitational potential at various points in space. This represents a differential operator.
[0023] In one possible implementation, the above-mentioned inspection mass in the spacecraft, based on the gravitational field strength of the spacecraft and the surrounding space, performs an integration operation to determine the gravitational force and gravitational torque acting on the inspection mass, including:
[0024] If we calculate gravity, then the gravitational field strength is integrated over the entire test mass over each infinitesimal element. With gravitational field strength The relationship is represented as:
[0025] ;
[0026] If we calculate the gravitational torque, then we integrate the gravitational torque caused by each infinitesimal element over the entire test mass. Represented as:
[0027] ;
[0028] in, It refers to the distance from the infinitesimal element of the inspection quality to the centroid of the inspection quality. This represents the mass of each infinitesimal element. This represents the volume of each infinitesimal element. Let be the density function at various points in space. This refers to the space surrounding a spacecraft.
[0029] Secondly, this application provides a finite element simulation device for gravitational effects based on solving partial differential equations of the gravitational field, comprising:
[0030] The first configuration module is used to input the weak form of the partial differential equation of the gravitational field into the physics field developer of the simulation software COMSOL, and to build the gravitational field interface plugin.
[0031] The second configuration module is used to import spacecraft models into the simulation software COMSOL and construct the space around the spacecraft;
[0032] The third configuration module is used to input boundary value conditions in the gravitational field interface plugin;
[0033] The gravitational field strength determination module is used to determine the gravitational potential through mesh generation and gravitational field interface plug-in, and to determine the gravitational field strength of the spacecraft and the surrounding space based on the gravitational potential.
[0034] The integration module is used to perform integration operations on the inspection mass in the spacecraft based on the gravitational field strength of the spacecraft and the surrounding space to determine the gravitational force and gravitational torque acting on the inspection mass.
[0035] Thirdly, this application provides an electronic device, comprising: at least one memory for storing a program; and at least one processor for executing the program stored in the memory, wherein when the program stored in the memory is executed, the processor is configured to execute the method described in the first aspect or any possible implementation thereof.
[0036] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art:
[0037] (1) By constructing a weak form of the partial differential equation of the gravitational field and developing a gravitational field interface with the help of the finite element simulation software COMSOL, the gravitational field can be directly calculated by inputting a spacecraft model, thereby effectively simplifying the self-gravity calculation process and significantly reducing the calculation difficulty of the self-gravity effect.
[0038] (2) By integrating the relevant physical quantities on the inspection quality, it is possible not only to calculate the self-gravitation effect of the inspection quality of a standard cube, but also to verify the gravitational force of a standard object of regular shape, or to effectively calculate the gravitational force of an object of arbitrary shape.
[0039] (3) Fine meshing is performed on the object whose gravity needs to be calculated, while coarse meshing is performed on the distant space, which can effectively balance the calculation accuracy and calculation efficiency. Attached Figure Description
[0040] Figure 1 This is a flowchart illustrating the principle of the finite element simulation method for gravitational effects based on solving partial differential equations of the gravitational field provided in this application embodiment.
[0041] Figure 2This is a schematic diagram of the geometric structure constructed for calculating the self-gravity of the solar panel of a gravitational wave detection spacecraft and the test mass, provided in an embodiment of this application.
[0042] Figure 3 This is a schematic diagram of a grooved inspection quality structure provided in an embodiment of this application;
[0043] Figure 4 This is a schematic diagram of geometric mesh generation provided in an embodiment of this application;
[0044] Figure 5 This is a schematic diagram of the simulation results of the self-gravity of the gravitational wave detection spacecraft solar panel and the test mass provided in the embodiments of this application;
[0045] Figure 6 This is a schematic diagram of the structure of the finite element simulation device for gravitational effects based on solving partial differential equations of the gravitational field provided in this application embodiment;
[0046] Figure 7 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation
[0047] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.
[0048] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.
[0049] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.
[0050] The embodiments of this application are described below with reference to the accompanying drawings.
[0051] Figure 1 This is a flowchart illustrating the principle of the finite element simulation method for gravitational effects based on solving partial differential equations of the gravitational field, as provided in the embodiments of this application. Figure 1 As shown, it includes the following steps.
[0052] The first step is to construct the weak form of the partial differential equations of the gravitational field.
[0053] The weak form of partial differential equations of gravitational fields is an important method for dealing with field equations in mathematical physics. It relaxes the requirements for the continuity and smoothness of the solution by transforming the partial differential equations into integral forms. In the finite element method, the weak form can be directly discretized into a system of algebraic equations, making it applicable to complex geometries and material properties.
[0054] The second step is to input the weak form in the physics field developer of the COMSOL software and develop the gravitational field interface plugin.
[0055] COMSOL Multiphysics is a multiphysics simulation software based on finite element analysis (FEA) technology. It supports coupled multiphysics simulation, allowing multiple physical phenomena to be considered simultaneously in the same model.
[0056] The third step is to establish a spacecraft model (specifically, a three-dimensional structural model of the spacecraft) and obtain the density functions of each component of the spacecraft.
[0057] The fourth step involves importing the spacecraft model into the COMSOL software to construct the space surrounding the spacecraft.
[0058] Fifth, input the boundary conditions in the gravitational field interface.
[0059] The sixth step is to mesh the spacecraft and calculate the gravitational field strength of the spacecraft and the surrounding space.
[0060] The seventh step is to integrate the relevant physical quantities on the quality of the inspection to calculate the gravitational force and gravitational torque acting on it.
[0061] Furthermore, the partial differential equations of the gravitational field can be expressed as:
[0062] ;
[0063] Where V represents the gravitational potential at any point in space, G is the gravitational constant, and ρ is the density function at any point in space. The weak form of the differential operator can be expressed as:
[0064] ;
[0065] Where v is the test function. Refers to the space surrounding a spacecraft. S Referential domain The boundary surface. The first term in the formula... The integral term is the weak form of the gravitational field equations satisfied on the boundary surface, the second term... The integral term is the weak form of the gravitational field equations satisfied in the domain.
[0066] Furthermore, the aforementioned process involves inputting the weak form of the gravitational field equations into the COMSOL physics developer to develop a gravitational field interface plugin. Following the relevant operating instructions of the COMSOL physics developer, the weak form of the gravitational field equations is input to form the gravitational field interface plugin. The gravitational field interface plugin (a single file) is then placed in the COMSOL plugin folder, allowing direct use of the gravitational field interface for gravitational calculations when the COMSOL software is opened.
[0067] Furthermore, the aforementioned construction of the space surrounding the spacecraft refers to creating geometry to simulate the space around the spacecraft. Since the space around the spacecraft is theoretically infinite, to improve computational accuracy, a thin spherical space can be constructed on the outer layer and set as an infinite meta-domain. The function of the infinite meta-domain is to simulate infinite space using finite space.
[0068] Furthermore, the aforementioned boundary conditions refer to the density function of the spacecraft model and the gravitational potential of each component (spacecraft model and the space surrounding the spacecraft) under the initial conditions.
[0069] In finite element simulation, boundary conditions are additional conditions that need to be specified to ensure that the mathematical model (described by partial differential equations) has a unique solution.
[0070] Furthermore, the aforementioned mesh generation process refers to meshing all geometries (including those corresponding to the spacecraft and the surrounding space) (the resulting mesh is a micro-element). To balance computational accuracy and efficiency, the target object whose gravity is to be calculated (e.g., a solar panel and a test mass) and the space closest to it are finely meshed, while the space farther away is coarsely meshed. The distance between the closer space and the target object is less than or equal to a distance threshold, while the distance between the farther space and the target object is greater than the distance threshold. The mesh size used for fine meshing is smaller than the mesh size used for coarse meshing.
[0071] Furthermore, the aforementioned gravitational field strength The relationship with gravitational potential is .
[0072] Furthermore, the integration of the relevant physical quantities in relation to inspection quality refers to:
[0073] If gravity needs to be calculated, it is the integral of the gravitational field strength over each infinitesimal element over the entire test mass. With gravitational field strength The relationship can be represented as:
[0074] ;
[0075] If it is necessary to calculate the gravitational torque, it is to integrate the gravitational torque caused by each infinitesimal element over the entire inspection mass. It can be represented as:
[0076] ;
[0077] in It refers to the displacement vector from the infinitesimal element of the inspection quality to the centroid of the inspection quality. This represents the mass of each infinitesimal element. This represents the volume of each infinitesimal element.
[0078] Furthermore, the gravitational field strength or gravitational torque integral for each infinitesimal element can be automatically achieved using the volume integral nodes of the finite element software COMSOL.
[0079] In COMSOL software, the "volume integral node" is a mathematical node used to perform volume integral operations. The volume integral node allows users to calculate the integral of a specified physical field over the entire volume region or a specific sub-region.
[0080] The following example illustrates the finite element simulation method for gravitational effects based on solving partial differential equations of the gravitational field provided in this application.
[0081] by Figure 2 Taking the solar panel and test mass model of the gravitational wave detection spacecraft as an example, the self-gravitational force of the solar panel on the test mass is calculated by solving the partial differential equations of the gravitational field using the finite element method. The steps of the embodiment are as follows.
[0082] Implementation steps (1): Construct the weak form of the partial differential equation of the gravitational field; Implementation steps (2): Input the weak form into the physics field developer of the software COMSOL and develop the gravitational field interface plugin; Implementation steps (3): Establish the solar panel and the inspection mass model with grooves, and obtain the density of the solar panel and the inspection mass; Implementation steps (4): Import the solar panel and the inspection mass model into the finite element software COMSOL, and construct the space around the spacecraft in COMSOL.
[0083] like Figure 2 As shown, a sphere that completely encloses the solar panel and the test mass is defined as the space surrounding the solar panel and the test mass. Since the gravitational field exists in all spaces, a thin shell of finite thickness is added to the outermost layer as an infinite element field, that is, the finite thickness represents the infinite thickness of the outer layer; optionally, the thickness of the thin shell of the infinite element field is one-tenth of the thickness of the inner space.
[0084] The quality inspection can be performed on objects of any shape, such as a non-standard cube with grooves. Figure 3This is a schematic diagram of a grooved inspection quality structure provided in an embodiment of this application.
[0085] Implementation step (5): Input the boundary conditions in the gravitational field interface. In this gravitational field calculation process, the boundary conditions include the density of each component, the gravitational potential of each component under the initial condition, and the initial value of the gravitational potential at infinity. In this implementation case, the solar panel and the test mass can be assigned values according to their actual densities, the density of the surrounding space and the infinite element domain is 0, the gravitational potential of each component under the initial condition is 0, and the gravitational potential at infinity, i.e., the boundary surface of the infinite element domain, is also 0.
[0086] Implementation step (6): Mesh generation and calculation of the gravitational field strength of the spacecraft and its surrounding space. For example... Figure 4 As shown, since it is necessary to calculate the gravitational force of the solar panel on the inspection mass, both the solar panel and the inspection mass are finely meshed, while the surrounding space only needs to be coarsely meshed; and the infinite element field should be aligned with the direction of gravitational propagation, so the infinite element field should be divided into outward-extending grids by sweeping meshes. Figure 5 The calculations show the gravitational field strength distribution of the solar panel and the test mass.
[0087] Step (7) involves integrating the relevant physical quantities over the inspection mass to calculate the gravitational force and gravitational torque acting on it. Since the inspection mass is an independent geometric body, the gravitational force and gravitational torque acting on the entire inspection mass can be obtained by directly integrating the gravitational field strength of all infinitesimal elements and the gravitational torque caused by those elements over the inspection mass.
[0088] The beneficial effects of this application are as follows: By constructing a weak form of the partial differential equation of the gravitational field and developing a gravitational field interface using the finite element simulation software COMSOL, the gravitational field can be directly calculated by inputting a spacecraft model, thereby effectively simplifying the self-gravity calculation process and significantly reducing the calculation difficulty of the self-gravity effect; by integrating relevant physical quantities on the inspection mass, not only can the self-gravity effect of the inspection mass of a standard cube be calculated, but also the gravity of a standard object with a regular shape can be verified, or the gravity of an object of arbitrary shape can be effectively calculated; by performing fine meshing on the object on which gravity needs to be calculated and coarse meshing on distant space, the calculation accuracy and calculation efficiency can be effectively balanced.
[0089] The following describes the finite element simulation device for gravitational effects based on solving partial differential equations of the gravitational field provided in this application. The finite element simulation device for gravitational effects based on solving partial differential equations of the gravitational field described below can be referred to in correspondence with the finite element simulation method for gravitational effects based on solving partial differential equations of the gravitational field described above.
[0090] Figure 6This is a schematic diagram of the structure of the finite element simulation device for gravitational effects based on solving partial differential equations of the gravitational field provided in the embodiments of this application, as shown below. Figure 6 As shown, the device includes: a first configuration module 10, a second configuration module 20, a third configuration module 30, a gravitational field strength determination module 40, and an integration module 50. Wherein:
[0091] The first configuration module 10 is used to input the weak form of the partial differential equation of the gravitational field into the physics field developer of the simulation software COMSOL, and to build the gravitational field interface plugin.
[0092] The second configuration module 20 is used to import the spacecraft model into the simulation software COMSOL and construct the space around the spacecraft;
[0093] The third configuration module 30 is used to input definite solution conditions in the gravitational field interface plugin;
[0094] The gravitational field strength determination module 40 is used to determine the gravitational potential through mesh generation and gravitational field interface plug-in, and to determine the gravitational field strength of the spacecraft and the surrounding space based on the gravitational potential.
[0095] The integration module 50 is used to perform integration operations on the inspection mass in the spacecraft based on the gravitational field strength of the spacecraft and the surrounding space to determine the gravitational force and gravitational torque acting on the inspection mass.
[0096] It is understood that the detailed functional implementation of each of the above units / modules can be found in the description in the aforementioned method embodiments, and will not be repeated here.
[0097] It should be understood that the above-described device is used to execute the methods in the above embodiments. The implementation principle and technical effect of the corresponding program modules in the device are similar to those described in the above methods. The working process of the device can be referred to the corresponding process in the above methods, and will not be repeated here.
[0098] Based on the methods in the above embodiments, this application provides an electronic device. Figure 7 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application, such as... Figure 7 As shown, the electronic device may include a processor 810, a communications interface 820, a memory 830, and a communication bus 840, wherein the processor 810, the communications interface 820, and the memory 830 communicate with each other through the communication bus 840. The processor 810 can call logical instructions in the memory 830 to execute the methods in the above embodiments.
[0099] Furthermore, the logical instructions in the aforementioned memory 830 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application.
[0100] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.
[0101] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.
[0102] It is understood that the processor in the embodiments of this application can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.
[0103] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.
[0104] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).
[0105] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.
[0106] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.
Claims
1. A finite element simulation method for gravitational effects based on solving partial differential equations of the gravitational field, characterized in that, include: Input the weak form of the partial differential equation of the gravitational field into the physics field developer of the simulation software COMSOL, and build the gravitational field interface plugin. Import the spacecraft model into the simulation software COMSOL and construct the space around the spacecraft. The space around the spacecraft is simulated by creating a geometry, specifically a sphere. Enter the boundary value conditions in the gravitational field interface plugin; The gravitational potential is determined by mesh generation and gravitational field interface plugin, and the gravitational field strength of the spacecraft and the surrounding space is determined based on the gravitational potential. For the inspection mass in the spacecraft, based on the gravitational field strength of the spacecraft and the surrounding space, an integral operation is performed to determine the gravitational force and gravitational torque acting on the inspection mass.
2. The finite element simulation method for gravitational effects based on solving partial differential equations of the gravitational field as described in claim 1, characterized in that, The weak form of the partial differential equations for the gravitational field is determined by the following formula: ； in, Let G represent the gravitational potential at all points in space, and G be the gravitational constant. Let be the density function at various points in space. Describes the differential operator. This represents the test function. Represents the domain space surrounding the spacecraft. S Representation domain space The boundary surface, where the integral term of the first term is in the domain space. The weak form of the gravitational field equations satisfied on the boundary surface, where the integral term of the second term is in the domain space. The weak form of the gravitational field equations satisfied in the equations.
3. The finite element simulation method for gravitational effects based on solving partial differential equations of the gravitational field as described in claim 1, characterized in that, The outermost layer of the space surrounding the spacecraft is configured with a spherical space of finite thickness. The spherical space is set as an infinite meta-domain, and the function of the infinite meta-domain is to use finite space to simulate infinite space.
4. The finite element simulation method for gravitational effects based on solving partial differential equations of the gravitational field as described in claim 1, characterized in that, The boundary conditions include: the density function of the spacecraft model and the gravitational potential under initial conditions.
5. The finite element simulation method for gravitational effects based on solving partial differential equations of the gravitational field according to claim 1, characterized in that, The mesh partitioning includes: The target object whose gravity is to be calculated and the space close to the target object are finely divided, while the space far from the target object is roughly divided. The distance between a nearby object and the target object is less than or equal to the distance threshold, while the distance between a distant object and the target object is greater than the distance threshold. The mesh size used for fine meshing is smaller than the mesh size used for coarse meshing.
6. The finite element simulation method for gravitational effects based on solving partial differential equations of the gravitational field according to claim 1, characterized in that, The determination of the gravitational field strength of the spacecraft and its surrounding space based on gravitational potential includes determining the gravitational field strength using the following formula; ； in, This indicates the strength of the gravitational field. Represents the gravitational potential at various points in space. This represents a differential operator.
7. The finite element simulation method for gravitational effects based on solving partial differential equations of the gravitational field according to claim 1, characterized in that, The method for determining the inspection mass within a spacecraft involves performing an integration operation based on the gravitational field strength of the spacecraft and its surrounding space to ascertain the gravitational force and gravitational torque acting on the inspection mass, including: If we calculate gravity, then the gravitational field strength is integrated over the entire test mass over each infinitesimal element. With gravitational field strength The relationship is represented as: ； If we calculate the gravitational torque, then we integrate the gravitational torque caused by each infinitesimal element over the entire test mass. Represented as: ； in, It refers to the displacement vector from the infinitesimal element of the inspection quality to the centroid of the inspection quality. This represents the mass of each infinitesimal element. This represents the volume of each infinitesimal element. Let be the density function at various points in space. This refers to the space surrounding a spacecraft.
8. A finite element simulation device for gravitational effects based on solving partial differential equations of the gravitational field, characterized in that, include: The first configuration module is used to input the weak form of the partial differential equation of the gravitational field into the physics field developer of the simulation software COMSOL, and to build the gravitational field interface plugin. The second configuration module is used to import a spacecraft model into the simulation software COMSOL and construct the space around the spacecraft. The space around the spacecraft is simulated by creating a geometry, specifically a sphere. The third configuration module is used to input boundary value conditions in the gravitational field interface plugin; The gravitational field strength determination module is used to determine the gravitational potential through mesh generation and gravitational field interface plug-in, and to determine the gravitational field strength of the spacecraft and the surrounding space based on the gravitational potential. The integration module is used to perform integration operations on the inspection mass in the spacecraft based on the gravitational field strength of the spacecraft and the surrounding space to determine the gravitational force and gravitational torque acting on the inspection mass.
9. An electronic device, characterized in that, include: At least one memory for storing computer programs; At least one processor is configured to execute a program stored in the memory, wherein when the program stored in the memory is executed, the processor is configured to perform the method as described in any one of claims 1-7.