Gravitational effect finite element simulation method based on solution of gravitational field partial differential equation

Abstract

The invention belongs to the technical field of space gravitational wave detection, and particularly discloses a gravitational effect finite element simulation method based on solving a gravitational field partial differential equation, and the method comprises the steps: inputting a weak form of the gravitational field partial differential equation in a physical field developer of simulation software COMSOL, and constructing a gravitational field interface plug-in; importing a spacecraft model into the simulation software COMSOL, and constructing a space around the spacecraft; inputting definite solution conditions in the gravitational field interface plug-in; gravitational potential is determined through grid subdivision and a gravitational field interface plug-in, and the gravitational field intensity of the spacecraft and the surrounding space is determined based on the gravitational potential; and for the test mass in the spacecraft, on the basis of the field intensity of the gravitational field of the spacecraft and the surrounding space, integral operation is executed, and the gravitational force and gravitational moment borne by the test mass are determined. According to the method, the self-gravity effect calculation process can be effectively simplified; meanwhile, the gravitation borne by the object in any shape can be calculated.

Description

Technical Field

[0001] This application belongs to the technical field of space gravitational wave detection. More specifically, it relates to a finite element simulation method for gravitational effects based on solving partial differential equations of the gravitational field. Background Art

[0002] The space gravitational wave detection plan uses three drag-free spacecraft, and each spacecraft is equipped with two test masses (TM) inside as inertial references. Through the inter-satellite laser interferometry ranging technology, the distance change between the test masses on the spacecraft is measured, so as to achieve the detection of gravitational waves. Ideally, the test mass moves along the geodesic, and the spacecraft follows the test mass through drag-free control. However, the test mass will be affected by various disturbing forces inside and outside the spacecraft, which affects the detection accuracy of gravitational waves. An important disturbing force is the gravitational force of the spacecraft itself on the test mass, called the spacecraft self-gravitation. It will affect the acceleration noise level of the test mass in many aspects. Therefore, it must be analyzed to meet the design requirements of the space gravitational wave detection spacecraft.

[0003] The self-gravitation effect value can be obtained by two methods: simulation calculation and experimental measurement. The simulation method generally uses the discretization method to mesh the spacecraft model, then approximates the mesh as point masses, writes a program to calculate the self-gravitation effect of the point masses on the cubic test mass, and then sums all the meshes to obtain the self-gravitation effect of the entire spacecraft on the test mass. The experimental method uses a torsion pendulum balance as a force sensor to measure the self-gravitation, and rotates or translates the spacecraft to measure the gravitational acceleration or gradient of the spacecraft. Relevant researchers have proposed a set of self-gravitation effect measurement schemes based on torsion balances, analyzed the principle of measuring the self-gravitation effect by torsion balances, given the gravitational outer multipole moments that need to be measured to obtain the self-gravitation effect, built two different configurations of torsion balances to measure different gravitational outer multipole moments, and also constructed a mass source that simulates the gravitational field of the spacecraft and carried out the principle verification of this measurement scheme. Since the basic principle of the experimental scheme is torsion pendulum suspension, a torsion wire is needed to suspend the test mass, and the test mass is located inside the spacecraft with multiple layers of spacecraft components outside. Therefore, it is very difficult to measure the overall self-gravitation effect of the spacecraft by this test scheme, and only the self-gravitation of some components can be measured. And the previous self-gravitation effect simulation scheme requires programming to calculate the self-gravitation of the spacecraft, and the process is complex. At the same time, since the test mass needs to be locked and released, the actual test mass is a non-standard cube with grooves, and calculating according to the standard cube will introduce certain errors. Summary of the Invention

[0004] Aiming at the defects of the prior art, the purpose of this application is to reduce the calculation difficulty of the self-gravitation effect and be able to realize the gravitational calculation of objects with arbitrary shapes.

[0005] To achieve the above object, in a first aspect, the present application provides a finite element simulation method for gravitational effects based on solving partial differential equations of the gravitational field. The method includes: Input the weak form of the partial differential equation of the gravitational field into the physics field developer of the simulation software COMSOL to construct a gravitational field interface plug-in; Import the spacecraft model into the simulation software COMSOL and construct the space around the spacecraft; Input the definite solution conditions into the gravitational field interface plug-in; Determine the gravitational potential through mesh generation and the gravitational field interface plug-in, and determine the gravitational field strength of the spacecraft and the surrounding space based on the gravitational potential; For the test mass in the spacecraft, perform an integration operation based on the gravitational field strength of the spacecraft and the surrounding space to determine the gravitational force and gravitational torque received by the test mass.

[0006] In a possible implementation, the weak form of the above partial differential equation of the gravitational field is determined by the following formula: ; Where, represents the gravitational potential at various places in space, G is the universal gravitational constant, is the density function at various places in space, represents the differential operator, represents the test function, represents the domain space around the spacecraft, S represents the domain space of the boundary surface. The integral term of the first item in the formula is the weak form of the gravitational field equation satisfied on the boundary surface of the domain space , and the integral term of the second item in the formula is the weak form of the gravitational field equation satisfied in the domain space .

[0007] In a possible implementation, the space around the spacecraft is simulated by creating a geometric body.

[0008] In a possible implementation, the outermost layer of the space around the spacecraft is configured with a spherical space with a finite thickness, and the spherical space is set as an infinite element domain. The role of the infinite element domain is to use a finite space to simulate an infinite space.

[0009] In a possible implementation, the definite solution conditions include: the density function of the spacecraft model and the gravitational potential in the initial situation.

[0010] In a possible implementation, the above mesh generation includes: Perform a fine mesh generation on the target object for which the gravitational force is to be calculated and the space relatively close to the target object, and perform a rough mesh generation on the space relatively far from the target object; The distance between the nearer space and the target object is less than or equal to the distance threshold, the distance between the farther space and the target object is greater than the distance threshold, and the grid size used for fine meshing is less than the grid size used for coarse meshing.

[0011] In a possible implementation, determining the gravitational field strength of the spacecraft and the surrounding space based on the gravitational potential includes determining the gravitational field strength through the following formula; ; where, represents the gravitational field strength, represents the gravitational potential at various locations in space, represents the differential operator.

[0012] In a possible implementation, for the test mass in the spacecraft, based on the gravitational field strength of the spacecraft and the surrounding space, performing an integration operation to determine the gravitational force and gravitational torque acting on the test mass includes: If calculating the gravitational force, integrate the gravitational field strength of each infinitesimal element over the entire test mass, and the gravitational force and the gravitational field strength are related as: ; If calculating the gravitational torque, integrate the gravitational torque caused by each infinitesimal element over the entire test mass, and the gravitational torque is expressed as: ; where, refers to the distance from the infinitesimal element on the test mass to the centroid of the test mass, represents the mass of each infinitesimal element, represents the volume of each infinitesimal element, is the density function at various locations in space, represents the domain space around the spacecraft.

[0013] In a second aspect, the present application provides a finite element simulation device for gravitational effects based on solving partial differential equations of the gravitational field, including: A first configuration module, configured to input the weak form of the partial differential equation of the gravitational field into the physics field developer of the simulation software COMSOL to construct a gravitational field interface plug-in; A second configuration module, configured to import a spacecraft model into the simulation software COMSOL and construct the surrounding space of the spacecraft; A third configuration module, configured to input the definite solution conditions into the gravitational field interface plug-in; A gravitational field strength determination module, configured to determine the gravitational potential through grid meshing and the gravitational field interface plug-in, and determine the gravitational field strength of the spacecraft and the surrounding space based on the gravitational potential; An integration module is configured to perform an integration operation on a test mass in a spacecraft based on the gravitational field strength of the spacecraft and the surrounding space, and determine the gravitational force and gravitational torque exerted on the test mass.

[0014] In a third aspect, the present application provides an electronic device, including: at least one memory for storing a program; at least one processor for executing the program stored in the memory, and 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 manner of the first aspect.

[0015] Generally speaking, compared with the prior art, the above technical solution conceived by the present application has the following beneficial effects: (1) By constructing the weak form of the gravitational field partial differential equation and developing a gravitational field interface with the help of the finite element simulation software COMSOL, it is possible to directly calculate the gravitational field by inputting the spacecraft model, thereby effectively simplifying the self-gravitational calculation process and significantly reducing the calculation difficulty of the self-gravitational effect.

[0016] (2) By integrating relevant physical quantities on the test mass, it is possible not only to calculate the self-gravitational effect of a standard cubic test mass, but also to verify the gravitational force of a standard part object with a regular shape or effectively calculate the gravitational force of an object with an arbitrary shape.

[0017] (3) By performing a fine mesh dissection on the object where the gravitational force needs to be calculated and a rough mesh dissection on the distant space, it is possible to effectively balance the calculation accuracy and calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a flowchart of the principle of a finite element simulation method for gravitational effects based on solving the gravitational field partial differential equation provided by an embodiment of the present application; Figure 2 is a schematic diagram of a geometric structure constructed for calculating the self-gravitation of a solar panel and a test mass of a gravitational wave detection spacecraft provided by an embodiment of the present application; Figure 3 is a schematic diagram of the structure of a grooved test mass provided by an embodiment of the present application; Figure 4 is a schematic diagram of the mesh dissection of a geometric body provided by an embodiment of the present application; Figure 5 is a schematic diagram of the simulation result of the self-gravitation of a solar panel and a test mass of a gravitational wave detection spacecraft provided by an embodiment of the present application; Figure 6 is a schematic diagram of the structure of a finite element simulation device for gravitational effects based on solving the gravitational field partial differential equation provided by an embodiment of the present application; Figure 7It is a schematic structural diagram of an electronic device provided by an embodiment of the present application. Detailed implementation manners

[0019] In order to make the objectives, technical solutions and advantages of the present application clearer and more understandable, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0020] In the embodiments of the present application, words such as "exemplary" or "for example" are used to indicate examples, illustrations or explanations. Any embodiment or design solution described as "exemplary" or "for example" in the embodiments of the present application should not be construed as being more preferred or having more advantages than other embodiments or design solutions. Rather, the use of words such as "exemplary" or "for example" is intended to present related concepts in a specific manner.

[0021] In the description of the embodiments of the present application, unless otherwise specified, the meaning of "a plurality of" refers to two or more. For example, a plurality of processing units refers to two or more processing units, etc.; a plurality of elements refers to two or more elements, etc.

[0022] The embodiments of the present application will be described below with reference to the accompanying drawings in the embodiments of the present application.

[0023] Figure 1 It is a principle flowchart of a finite element simulation method for gravitational effects based on solving partial differential equations of the gravitational field provided by an embodiment of the present application. As Figure 1 shown, it includes the following steps.

[0024] The first step is to construct the weak form of the partial differential equation of the gravitational field.

[0025] The weak form of the partial differential equation of the gravitational field 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 equation into an integral form. In the finite element method, the weak form can be directly discretized into a system of algebraic equations, which is applicable to complex geometries and material properties.

[0026] The second step is to input the weak form into the physics field developer of the software COMSOL to develop a gravitational field interface plug-in.

[0027] COMSOL Multiphysics is a multi-physics simulation software. Based on finite element analysis (FEA) technology, it supports multi-physics coupled simulation and can consider multiple physical phenomena simultaneously in the same model.

[0028] The third step is to establish a spacecraft model (specifically referring to the three-dimensional structural model of the spacecraft) and obtain the density functions of each component of the spacecraft.

[0029] In the fourth step, import the spacecraft model into the software COMSOL to construct the space around the spacecraft.

[0030] In the fifth step, input the definite solution conditions in the gravitational field interface.

[0031] In the sixth step, perform mesh generation and calculate the gravitational field strength of the spacecraft and the surrounding space.

[0032] In the seventh step, integrate the relevant physical quantities on the test mass to calculate the gravitational force and gravitational torque it receives.

[0033] Furthermore, the partial differential equation of the gravitational field can be expressed as: ; where V represents the gravitational potential at various points in space, G is the universal gravitational constant, ρ is the density function at various points in space, represents the differential operator, and its weak form can be expressed as: ; where v is the test function, refers to the domain space around the spacecraft. S refers to the domain of the boundary surface. The first integral term is the weak form of the gravitational field equation satisfied on the boundary surface, and the second integral term is the weak form of the gravitational field equation satisfied in the domain.

[0034] Furthermore, input the weak form in the physical field developer of the software COMSOL, develop the gravitational field interface plug-in, input the weak form of the gravitational field equation according to the relevant operation instructions of the physical field developer of the software COMSOL to form the gravitational field interface plug-in, and then place the gravitational field interface plug-in (a file) in the plug-in folder of the software COMSOL, so that the gravitational field interface can be directly used for gravitational calculation when the software COMSOL is opened.

[0035] Furthermore, the above-mentioned construction of the space around the spacecraft refers to creating a geometric body to simulate the space around the spacecraft. And since the space around the spacecraft is theoretically infinite, in order to improve the calculation accuracy, a thin spherical space can be constructed on the outer layer and set as an infinite element domain. The function of the infinite element domain is to use a finite space to simulate an infinite space.

[0036] Furthermore, the above-mentioned definite solution conditions refer to the density function of the spacecraft model and the gravitational potential of each component (spacecraft model, space around the spacecraft) in the initial situation.

[0037] In finite element simulation, the definite solution conditions are additional conditions that need to be specified to ensure the existence of a unique solution for a mathematical model (described by partial differential equations).

[0038] Furthermore, the above-mentioned mesh generation process refers to performing mesh generation on all geometric bodies (including the geometric bodies corresponding to the spacecraft and the geometric bodies corresponding to the surrounding space), and the meshes obtained from the mesh generation are micro-elements. In order to balance computational accuracy and computational efficiency, the target objects for which the gravitational force is to be calculated (such as solar panels and test masses) and the space relatively close to the target objects can be finely meshed, while the space relatively far from the target objects can be coarsely meshed. The distance between the relatively close space and the target object is less than or equal to the distance threshold, and the distance between the relatively far 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.

[0039] Furthermore, the above-mentioned gravitational field strength has the following relationship with the gravitational potential .

[0040] Furthermore, the above-mentioned integration of relevant physical quantities on the test mass refers to: If the gravitational force needs to be calculated, it is to integrate the gravitational field strength of each micro-element over the entire test mass. The gravitational force and the gravitational field strength have the following relationship: ; If the gravitational torque needs to be calculated, it is to integrate the gravitational torque caused by each micro-element over the entire test mass. The gravitational torque can be expressed as: ; where denotes the displacement vector from the micro-element on the test mass to the centroid of the test mass, represents the mass of each micro-element, represents the volume of each micro-element.

[0041] Furthermore, the integration of the gravitational field strength or gravitational torque of each micro-element can be automatically implemented using the volume integral node of the finite element software COMSOL.

[0042] In the 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.

[0043] Next, an example is used to provide an exemplary illustration of the finite element simulation method for gravitational effects based on solving partial differential equations of the gravitational field provided in this application.

[0044] Taking Figure 2 the gravitational wave detection spacecraft solar panel and the test mass model shown as an example, the self-gravity of the solar panel on the test mass is calculated by using the finite element method to solve the partial differential equation of the gravitational field. The steps of the embodiment are as follows.

[0045] Implementation step (1): Construct the weak form of the partial differential equation of the gravitational field; Implementation step (2): Input the weak form in the physical field developer of the software COMSOL to develop the gravitational field interface plug-in; Implementation step (3): Establish the solar panel and the grooved test mass model, and obtain the densities of the solar panel and the test mass; Implementation step (4): Import the solar panel and the test mass model into the finite element software COMSOL, and construct the space around the spacecraft in COMSOL.

[0046] As Figure 2 shown, a sphere that can completely enclose the solar panel and the test mass is defined as the space around the solar panel and the test mass. At the same time, since the gravitational field exists in all spaces, a thin shell with a finite thickness is added to the outermost layer as the infinite element domain, that is, the finite thickness represents the infinite thickness of the outer layer; optionally, the thickness of the thin shell of the infinite element domain is one-tenth of the thickness of the inner space.

[0047] The test mass can be an object of any shape, such as a non-standard cube with grooves. Figure 3 is a schematic diagram of the structure of the grooved test mass provided by the embodiment of the present application.

[0048] Implementation step (5): Input the definite solution conditions in the gravitational field interface. In this gravitational field calculation process, the definite solution conditions include the densities of each component, the gravitational potential of each component in the initial case, and the initial value of the gravitational potential at infinity. In this implementation case, the solar panel and the test mass can be assigned according to their actual densities, the densities of the surrounding space and the infinite element domain are 0, the gravitational potentials of each component in the initial case are all 0, and the gravitational potential at infinity, that is, the boundary surface of the infinite element domain, is also 0.

[0049] Implementation step (6): Mesh generation and calculation of the gravitational field strength of the spacecraft and the surrounding space. As Figure 4 shown, since the gravity of the solar panel on the test mass needs to be calculated, both the solar panel and the test mass are finely meshed, while the surrounding space only needs to be roughly meshed; and the infinite element domain should be consistent with the direction of gravitational propagation, so the infinite element domain should be swept into a grid extending outward by sweeping. Figure 5 shows the distribution of the gravitational field strength of the solar panel and the test mass after calculation.

[0050] Step (7) is to integrate relevant physical quantities in terms of inspection quality to calculate the gravitational force and gravitational torque it experiences. The inspection mass is an independent geometric body. By directly integrating the gravitational field strength of all micro-elements and the gravitational torque caused by the micro-elements on the inspection mass, the gravitational force and gravitational torque received by the entire inspection mass can be obtained.

[0051] The beneficial effects of this application are as follows: By constructing the weak form of the gravitational field partial differential equation and developing the gravitational field interface with the help of the finite element simulation software COMSOL, the direct calculation of the gravitational field can be realized by inputting the spacecraft model, thus effectively simplifying the self-gravitation calculation process and significantly reducing the calculation difficulty of the self-gravitation effect; By integrating relevant physical quantities on the inspection mass, not only can the self-gravitation effect of the standard cube inspection mass be calculated, but also the gravitational force of standard parts with regular shapes can be verified, or the gravitational force of objects with arbitrary shapes can be effectively calculated; By performing fine mesh dissection on the object where the gravitational force needs to be calculated and rough mesh dissection on the distant space, the calculation accuracy and calculation efficiency can be effectively balanced.

[0052] The following describes the finite element simulation device for gravitational effects based on solving the partial differential equation of the gravitational field provided by this application. The finite element simulation device for gravitational effects based on solving the partial differential equation of the gravitational field described below can be mutually referred to the finite element simulation method for gravitational effects based on solving the partial differential equation of the gravitational field described above.

[0053] Figure 6 It is a schematic structural diagram of the finite element simulation device for gravitational effects based on solving the partial differential equation of the gravitational field provided by the embodiment of this application. As Figure 6 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. Among them: The first configuration module 10 is used to input the weak form of the gravitational field partial differential equation in the physical field developer of the simulation software COMSOL to construct a gravitational field interface plug-in; The second configuration module 20 is used to import the spacecraft model into the simulation software COMSOL and construct the space around the spacecraft; The third configuration module 30 is used to input the definite solution conditions into the gravitational field interface plug-in; The gravitational field strength determination module 40 is used to determine the gravitational potential through mesh dissection and the gravitational field interface plug-in, and determine the gravitational field strength of the spacecraft and the surrounding space based on the gravitational potential; The integration module 50 is used to perform an integration operation 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 received by the inspection mass.

[0054] It can be understood that for the detailed function implementation of each of the above units / modules, reference can be made to the introduction in the foregoing method embodiments, which will not be elaborated here.

[0055] It should be understood that the above device is used to execute the method in the above embodiments. For the corresponding program modules in the device, their implementation principles and technical effects are similar to those described in the above method. The working process of the device can refer to the corresponding process in the above method, which will not be elaborated here.

[0056] Based on the method in the above embodiments, an embodiment of the present application provides an electronic device. Figure 7 is a schematic structural diagram of the electronic device provided by the embodiment of the present application. As Figure 7 shown, the electronic device may include: a processor (Processor) 810, a communication interface (Communications Interface) 820, a memory (Memory) 830, and a communication bus 840. Among them, the processor 810, the communication interface 820, and the memory 830 complete mutual communication through the communication bus 840. The processor 810 can call the logical instructions in the memory 830 to execute the method in the above embodiments.

[0057] In addition, when the logical instructions in the above memory 830 are implemented in the form of software function units and sold or used as an independent product, they can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions to enable a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present application.

[0058] Based on the method in the above embodiments, an embodiment of the present application provides a computer-readable storage medium. The computer-readable storage medium stores a computer program. When the computer program runs on the processor, the processor is enabled to execute the method in the above embodiments.

[0059] Based on the method in the above embodiments, an embodiment of the present application provides a computer program product. When the computer program product runs on the processor, the processor is enabled to execute the method in the above embodiments.

[0060] It can be understood that the processor in the embodiments of the present application may be a central processing unit (CPU), or may also be 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. The general-purpose processor may be a microprocessor or any conventional processor.

[0061] The method steps in the embodiments of the present application may be implemented in a hardware manner or by a processor executing software instructions. The software instructions may be composed of corresponding software modules, and the software modules may be stored in a random access memory (RAM), flash memory, read-only memory (ROM), programmable ROM (PROM), erasable PROM (EPROM), electrically erasable PROM (EEPROM), registers, hard disks, removable hard disks, CD-ROMs, or any other form of storage medium well known in the art. An exemplary storage medium is coupled to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium may also be a component of the processor. The processor and the storage medium may be located in an ASIC.

[0062] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of 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, the processes or functions described in the embodiments of the present application are generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. 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 in a wired manner (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or a wireless manner (such as infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server or a data center that includes one or more integrated available media. The available medium can be a magnetic medium (such as a floppy disk, a hard disk, a magnetic tape), an optical medium (such as a DVD), or a semiconductor medium (such as a solid state disk (SSD)), etc.

[0063] It can be understood that the various digital numbers involved in the embodiments of the present application are only for the convenience of description and are not used to limit the scope of the embodiments of the present application.

[0064] Those skilled in the art can easily understand that the above is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A finite element simulation method for gravitational effect based on solving partial differential equations of gravitational field, characterized in that: include: Input the weak form of the gravitational field partial differential equation into the physical field developer of the simulation software COMSOL to build a gravitational field interface plug-in; Import the spacecraft model into the simulation software COMSOL and construct the space around the spacecraft; Enter the solution conditions in the gravitational field interface plug-in; Determine the gravitational potential through meshing and gravitational field interface plug-in, and determine the gravitational field strength of the spacecraft and the surrounding space based on the gravitational potential; For the test mass in the spacecraft, an integration operation is performed based on the gravitational field strength of the spacecraft and the surrounding space to determine the gravitational force and gravitational torque on the test mass.

2. The finite element simulation method of gravitational effect based on solving the partial differential equation of gravitational field according to claim 1 is characterized in that: The weak form of the partial differential equation of the gravitational field is determined by the following formula: ； in, represents the gravitational potential everywhere in space, G is the gravitational constant, is the density function everywhere in space, represents the differential operator, Represents the test function, represents the domain space around the spacecraft, S Representation domain space The boundary surface of the domain space is The weak form of the gravitational field equations satisfied on the boundary surface of , where the integral term of the second term is in the domain space The weak form of the gravitational field equations satisfied by .

3. The finite element simulation method of gravitational effect based on solving the partial differential equation of gravitational field according to claim 1 is characterized in that: The space around the spacecraft is simulated by creating geometric bodies.

4. The finite element simulation method of gravitational effect based on solving the partial differential equation of gravitational field according to claim 1, characterized in that: The outermost layer of the space around the spacecraft is configured with a spherical space of finite thickness, and the spherical space is set as an infinite element domain. The function of the infinite element domain is to use a finite space to simulate an infinite space.

5. The finite element simulation method of gravitational effect based on solving the partial differential equation of gravitational field according to claim 1, characterized in that: The solution conditions include: the density function of the spacecraft model and the gravitational potential under initial conditions.

6. The finite element simulation method of gravitational effect based on solving the partial differential equation of gravitational field according to claim 1, characterized in that: The mesh generation includes: Finely divide the target object to be calculated for gravity and the space close to the target object, and roughly divide the space far from the target object; The distance between the closer space and the target object is less than or equal to the distance threshold, the distance between the farther space and the target object is greater than the distance threshold, and the grid size used for fine subdivision is smaller than the grid size used for coarse subdivision.

7. The finite element simulation method of gravitational effect based on solving the partial differential equation of gravitational field according to claim 1, characterized in that: Determining the gravitational field strength of the spacecraft and the surrounding space based on the gravitational potential includes determining the gravitational field strength by the following formula; ； in, represents the gravitational field strength, represents the gravitational potential everywhere in space, represents a differential operator.

8. The finite element simulation method for gravitational effect based on solving the partial differential equation of gravitational field according to claim 1, characterized in that: The method of performing an integration operation on the test 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 on the test mass includes: If we calculate the gravitational force, we integrate the gravitational field strength of each microelement over the entire test mass. and gravitational field strength The relationship is expressed as: ； If the gravitational torque is calculated, the gravitational torque caused by each microelement is integrated over the entire test mass. It is expressed as: ； in, It refers to the displacement vector from the infinitesimal element on the test mass to the center of mass of the test mass, represents the mass of each microelement, represents the volume of each microelement, is the density function everywhere in space, Represents the domain space around the spacecraft.

9. A finite element simulation device for gravitational effect based on solving partial differential equations of gravitational field, characterized in that: include: The first configuration module is used to input the weak form of the gravitational field partial differential equation in the physical field developer of the simulation software COMSOL to build a gravitational field interface plug-in; The second configuration module is used to import the spacecraft model into the simulation software COMSOL and construct the space around the spacecraft; The third configuration module is used to input the solution conditions in the gravitational field interface plug-in; The gravitational field strength determination module is used to determine the gravitational potential through grid generation and the gravitational field interface plug-in, and 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 test 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 on the test mass.

10. An electronic device, characterized in that: include: at least one memory for storing a computer program; At least one processor is used to execute the program stored in the memory. When the program stored in the memory is executed, the processor is used to execute the method according to any one of claims 1 to 8.

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