A method of simulating a debris cloud impact on a spacecraft

Abstract

The application provides a simulation method for debris cloud impacting a spacecraft, and relates to the technical field of dynamic numerical simulation. First, the displacement migration speed of the moving particles is calculated based on the displacement state of the SPH particles; then, the left and right states of the contact particle pairs, including the migration speed, are high-precision WENO reconstructed based on the ALE-SPH framework; then, the reconstructed left and right states are substituted into the newly proposed migration amount Riemann solver to obtain the Riemann solution of the migration speed. By introducing the particle migration mechanism based on the high-order reconstructed Riemann solution, the present application can effectively alleviate the uneven distribution phenomenon in the particle simulation process, realize clear capture of the multi-medium interface, significantly reduce the numerical dissipation, improve the fidelity and stability of the numerical simulation under the high-speed impact and large deformation scene, and provide more reliable numerical support tools for the extreme dynamics process such as space debris protection and defense equipment design.

Description

Technical Field

[0001] This invention relates to the field of dynamic numerical simulation, and in particular to a method for simulating the impact of a debris cloud on a spacecraft. Background Technology

[0002] Currently, numerous studies have proposed particle migration methods for the motion of weakly compressible and incompressible fluids. These methods aim to effectively overcome the anisotropy of particle distribution along streamlines by migrating the non-uniformly distributed particle displacements during computation, while also mitigating volume non-conservation issues in long-term simulations of incompressible motion. Some researchers have introduced the ALE method into the SPH particle migration technique for incompressible flows, improving the computational accuracy of the migration method.

[0003] However, existing particle migration methods lack systematic solutions for simulating motion processes such as low Mach number gas shock waves, weakly compressible fluids, and solid impacts. The application of the ALE-SPH migration method is also limited to incompressible flow conditions, and its numerical stability is only achieved through traditional artificial viscosity methods with manual parameter tuning. In the field of space protection engineering and defense equipment design, the application of shock wave effects and damage effects from high-speed impacts also poses new challenges to the stability and accuracy of numerical simulation methods.

[0004] Therefore, a simulation method for debris cloud impacting spacecraft is provided, which enables a self-verification method for dynamic, real-time, and quantitative quality assessment and feedback. Summary of the Invention

[0005] The purpose of this invention is to provide a simulation method for debris cloud impacting spacecraft. The Riemann solution obtained by reconstructing migration velocity and pressure using WENO can adaptively introduce implicit dissipation, reduce numerical instability caused by migration, and eliminate the need to introduce artificial viscosity that requires manual parameter tuning.

[0006] To achieve the above objectives, the present invention provides a method for simulating the impact of a debris cloud on a spacecraft, comprising the following steps:

[0007] S1: Obtain the displacement state of the SPH particle and get the Cartesian coordinates of the particle displacement state;

[0008] S2: Calculate the displacement migration velocity of the moving particle based on the Cartesian coordinates of the displacement state of the SPH particle obtained in S1.

[0009] S3: Based on the displacement migration velocity obtained in S2 and the pressure among the known physical quantities, for any pair of particles in the domain, the left and right reconstruction values ​​of migration velocity and pressure are obtained by using the WENO reconstruction method.

[0010] S4: Based on the left and right states of the reconstructed particle pair obtained in S3, use them as parameters for the Riemann solver to obtain the Riemann solution for the particle pair migration velocity.

[0011] S5: The migration velocity obtained in S4 is substituted into the migration part of the ALE-SPH framework governing equations to correct the change in physical flux caused by the Lagrange particle shift and suppress numerical dissipation during the migration process.

[0012] Preferably, S2 calculates the displacement migration velocity of the moving particle by substituting the Cartesian coordinates of the particle displacement state obtained in S1 into the following formula for discretization and summation:

[0013] ;

[0014] ;

[0015] In the formula, Represents the migration displacement of particle i. h For the smooth length of the particle, To calculate the maximum velocity within the domain, For particles i Supports the maximum velocity difference between particles within the domain. For particle pairs ij coordinate distance, For particle pairs ij smooth length and The arithmetic mean, For particle pairs ij Corresponding kernel function , κ This is the ratio of smooth length to initial particle size. For particles i Spatial differentiation, Represents particles j volume, For particles i migration speed, Indicates the time step.

[0016] Preferably, in S3, WENO uses parameter values ​​of four equally spaced template points within a third-order reconstruction framework. , , ,in , Corresponding particles , The physical parameters, and the missing template point particles within the WENO template. Left side ,particle right side The parameter values ​​are expanded using a second-order Taylor series and the particle... ,particle its own physical parameters and its spatial derivative The expression is as follows:

[0017]

[0018] Self-physical parameters Migration speed Vector and known physical parameters pressure The derivatives in all directions are:

[0019] ;

[0020] ;

[0021] In the formula, , These represent the velocity gradient and pressure gradient, respectively. express The unit direction vector of the direction. Represents the Kronecker product;

[0022] Reconstructing the left state of particle pairs using WENO and right state ,in This represents the density in the left-hand state. This represents the migration speed in the left state. This indicates the pressure in the left-hand state. This represents the density in the right-hand state. This indicates the migration speed in the right state. This represents the pressure in the right-hand state, and the template point during the WENO higher-order format reconstruction process. For particles According to the template points , , Its own physical parameters, the left state through two candidate templates and Weighted average yields:

[0023] ;

[0024] , ;

[0025] In the formula, , These represent the weight functions for the corresponding templates, respectively. The optimal order weight function is obtained within the WENO framework, determined by the smoothness of the numerical solution. It is calculated in the following way:

[0026] , , ;

[0027] Among them, parameters For any non-zero value, The parameters are the optimal weights obtained using the traditional WENO method:

[0028] , ;

[0029] and This is a smoothness index, calculated as follows:

[0030] ;

[0031] ;

[0032] Obtain the left state of the particle pair ; where the right state of the ion pair The method for obtaining the left state is the same.

[0033] Preferably, in S4, the left state of the particle pair is... and right state Substituting into the Riemann solver, the Riemann solution for the migration velocity is obtained as follows:

[0034] ;

[0035] .

[0036] Preferably, in S5, the following calculation operations are specifically performed to update the changes in volume, mass, momentum, and energy caused by particle migration:

[0037] ;

[0038] ;

[0039] ;

[0040] ;

[0041] ;

[0042] In the formula, The mass derivative of volume with respect to time. The mass derivative of mass with respect to time. The mass derivative of momentum with respect to time. The mass derivative of internal energy with respect to time; Represents particle pairs ij Riemann solution for migration velocity Represents particle pairs ij The average density; This represents the average value of the product of density and velocity. This represents the average value of the product of density and internal energy.

[0043] Therefore, the present invention employs the above-mentioned simulation method for debris cloud impacting a spacecraft, and the technical effects are as follows:

[0044] (1) The present invention uses the migration speed and pressure of WENO reconstruction to obtain the Riemann solution, which can adaptively introduce implicit dissipation, reduce the numerical instability caused by migration, and eliminate the need to introduce artificial viscosity that requires manual parameter tuning.

[0045] (2) The particle distribution in the calculated results after migration is more uniform, and the density cloud map eliminates non-physical numerical oscillations. In engineering scenarios such as high-speed gas dynamics, the position and intensity of the shock wave surface directly determine the design load of the protective structure. The cloud map of the particle distribution after migration can accurately output the shock wave arrival time and peak pressure, avoiding design overload or underload caused by interface dispersion.

[0046] (3) In multi-medium coupling scenarios, the position of the phase interface determines the process parameters or disaster prediction results. The particle distribution cloud map after migration accurately outputs the distribution range and evolution law of each medium, and optimizes the engineering scheme. Attached Figure Description

[0047] Figure 1 This is a diameter-density curve generated after placing unmigrated ion pairs and velocity-migrated particle pairs into a two-dimensional shock tube in an embodiment of the present invention.

[0048] Figure 2 This is a diameter-pressure curve generated after placing unmigrated ion pairs and velocity-migrated particle pairs into a two-dimensional shock tube in an embodiment of the present invention.

[0049] Figure 3 This is a density result and a magnified view of a portion of the data obtained by placing unmigrated ion pairs into a two-dimensional impact Taylor bar in an embodiment of the present invention.

[0050] Figure 4 This is the density result and a magnified view of the particle pairs after velocity migration placed into a two-dimensional impact Taylor bar calculation in an embodiment of the present invention.

[0051] Figure 5The figures show the simulation and experimental results of the high-speed impact problem of the ball-shaped plate in Embodiment 2 of the present invention. Detailed Implementation

[0052] The method of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0053] Unless otherwise defined, the methodological or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0054] The terms "comprising" or "including" as used in this invention mean that the element preceding the term encompasses the element listed after the term, and do not exclude the possibility of encompassing other elements. Terms such as "inner," "outer," "upper," and "lower" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. When the absolute position of the described object changes, the relative positional relationship may also change accordingly. In this invention, unless otherwise explicitly specified and limited, the term "attached" and similar terms should be interpreted broadly. For example, it can refer to a fixed connection, a detachable connection, or an integral part; it can refer to a direct connection or an indirect connection through an intermediate medium; it can refer to the internal communication of two elements or the interaction relationship between two elements. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0055] Example

[0056] like Figure 1 As shown, the present invention provides a method for simulating the impact of a debris cloud on a spacecraft, comprising the following steps:

[0057] S1: Obtain the displacement state of the SPH particle and get the Cartesian coordinates of the particle displacement state;

[0058] S2: Calculate the displacement migration velocity of the moving particle based on the Cartesian coordinates of the displacement state of the SPH particle obtained in S1; calculate the displacement migration velocity of the moving particle by substituting the Cartesian coordinates of the particle displacement state obtained in S1 into the following formula for discretization and summation:

[0059] ;

[0060] ;

[0061] In the formula, Represents the migration displacement of particle i. h For the smooth length of the particle, To calculate the maximum velocity within the domain, For particles i Supports the maximum velocity difference between particles within the domain. For particle pairs ij coordinate distance, For particle pairs ij smooth length and The arithmetic mean, For particle pairs ij Corresponding kernel function , κ This is the ratio of smooth length to initial particle size. For particles i Spatial differentiation, Represents particles j volume, For particles i migration speed, Indicates the time step.

[0062] S3: Based on the displacement migration velocity obtained in S2 and the pressure among the known physical quantities, for any pair of particles in the domain, the left and right reconstruction values ​​of migration velocity and pressure are obtained by using the WENO reconstruction method.

[0063] In S3, WENO uses a three-order reconstruction framework with four equally spaced template points as parameter values. , , ,in , Corresponding particles , The physical parameters, and the missing template point particles within the WENO template. Left side ,particle right side The parameter values ​​are expanded using a second-order Taylor series and the particle... ,particle its own physical parameters and its spatial derivative The expression is as follows:

[0064]

[0065] Self-physical parameters Migration speed Vector and known physical parameters pressure The derivatives in all directions are:

[0066] ;

[0067] ;

[0068] In the formula, , These represent the velocity gradient and pressure gradient, respectively. express The unit direction vector of the direction. Represents the Kronecker product;

[0069] Reconstructing the left state of particle pairs using WENO and right state ,in This represents the density in the left-hand state. This represents the migration speed in the left state. This indicates the pressure in the left-hand state. This represents the density in the right-hand state. This indicates the migration speed in the right state. This represents the pressure in the right-hand state, and the template point during the WENO higher-order format reconstruction process. For particles According to the template points , , Its own physical parameters, the left state through two candidate templates and Weighted average yields:

[0070] ;

[0071] , ;

[0072] In the formula, , These represent the weight functions for the corresponding templates, respectively. The optimal order weight function is obtained within the WENO framework, determined by the smoothness of the numerical solution. It is calculated in the following way:

[0073] , , ;

[0074] Among them, parameters For any non-zero value, The parameters are the optimal weights obtained using the traditional WENO method:

[0075] , ;

[0076] and This is a smoothness index, calculated as follows:

[0077] ;

[0078] ;

[0079] Obtain the left state of the particle pair ; where the right state of the ion pair The method for obtaining the left state is the same.

[0080] S4: Based on the left and right states of the reconstructed particle pair obtained in S3, use them as parameters for the Riemann solver to obtain the Riemann solution for the particle pair migration velocity.

[0081] In S4, the left state of the particle pair and right state Substituting into the Riemann solver, the Riemann solution for the migration velocity is obtained as follows:

[0082] ;

[0083] .

[0084] S5: The migration velocity obtained in S4 is substituted into the migration part of the ALE-SPH framework governing equations to correct the flux changes in physical quantities caused by Lagrange particle migration, thus suppressing numerical dissipation during the migration process. The migration velocity optimized through high-precision reconstruction significantly suppresses numerical dissipation during the migration process, thereby improving the fidelity and accuracy of the simulation of complex dynamic processes. Specifically, S5 performs the following calculations to update the changes in volume, mass, momentum, and energy caused by particle migration:

[0085] ;

[0086] ;

[0087] ;

[0088] ;

[0089] ;

[0090] In the formula, The mass derivative of volume with respect to time. The mass derivative of mass with respect to time. The mass derivative of momentum with respect to time. The mass derivative of internal energy with respect to time; Represents particle pairs ij Riemann solution for migration velocity Represents particle pairsij The average density; This represents the average value of the product of density and velocity. This represents the average value of the product of density and internal energy.

[0091] In this embodiment, the SPH numerical simulation methods without and with the migration method described in this scheme are respectively applied to the two-dimensional shock tube example and the two-dimensional impact Taylor bar example. Figures 1-2 As shown, in the back segment of the shock wave, the density and pressure of the non-migrated method are not lower than the reference solution, while the error is well corrected after the migration method is used.

[0092] like Figures 3-4 As shown, the unmigrated computational results particles exhibit a distinct strip-like distribution in the bottom compression region, with significant anisotropy in their distribution, resulting in large non-physical oscillations in the density. The migrated computational results particles are more uniformly distributed, and the density cloud map eliminates the non-physical numerical oscillations.

[0093] Example 2

[0094] Hypervelocity impact (HVI) is a core issue in aerospace, disaster prevention, and mitigation. In space protection, spacecraft frequently face the risk of impacts from millimeter-sized space debris at extremely high speeds, potentially leading to wall perforation or disintegration. In the field of protection, studying the damage mechanisms and penetration processes of impacts on defensive equipment is crucial for improving survivability. This embodiment is a typical example of an HVI process, involving a 10mm diameter aluminum sphere impacting a 4mm thick aluminum plate perpendicularly at a speed of 6180m / s.

[0095] like Figure 5 As shown, the optimized program using this approach significantly improves the simulation accuracy of debris cloud morphology, successfully alleviating the inherent challenges of traditional SPH particle clustering. This breakthrough not only enhances the reliability of numerical simulations but also provides crucial technical support for the design of aerospace protection engineering and defense equipment.

[0096] Therefore, the present invention adopts the above-mentioned simulation method of debris cloud impacting spacecraft. The Riemann solution obtained by using the migration velocity and pressure reconstructed by WENO can adaptively introduce implicit dissipation, reduce the numerical instability caused by migration, and eliminate the need to introduce artificial viscosity that requires manual parameter tuning.

[0097] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for simulating the impact of a debris cloud on a spacecraft, characterized in that, The simulation employs ALE-SPH particle migration based on the WENO Riemann solution. ALE-SPH particles are space debris, and the simulation includes the following steps: S1: Obtain the displacement state of the SPH particle and get the Cartesian coordinates of the particle displacement state; S2: Calculate the displacement migration velocity of the moving particle based on the Cartesian coordinates of the displacement state of the SPH particle obtained in S1. S3: Based on the displacement migration velocity obtained in S2 and the pressure among the known physical quantities, for any pair of particles in the domain, the left and right reconstruction values ​​of migration velocity and pressure are obtained by using the WENO reconstruction method. WENO uses a three-order reconstruction framework with four equally spaced template points as parameters. , , ,in , Corresponding particles , The physical parameters, and the missing template point particles within the WENO template. Left side ,particle right side The parameter values ​​are expanded using a second-order Taylor series and the particle... ,particle its own physical parameters and its spatial derivative The expression is as follows: Self-physical parameters Migration speed Vector and known physical parameters pressure The derivatives in all directions are: ； ； In the formula, , These represent the velocity gradient and pressure gradient, respectively. express The unit direction vector of the direction. Represents the Kronecker product; Reconstructing the left state of particle pairs using WENO and right state ,in This represents the density in the left-hand state. This represents the migration speed in the left state. This indicates the pressure in the left-hand state. This represents the density in the right-hand state. This indicates the migration speed in the right state. This represents the pressure in the right-hand state, and the template point during the WENO higher-order format reconstruction process. For particles According to the template points , , Its own physical parameters, the left state through two candidate templates and Weighted average yields: ； ， ； In the formula, , These represent the weight functions for the corresponding templates, respectively. The optimal order weight function is obtained within the WENO framework, determined by the smoothness of the numerical solution. It is calculated in the following way: ， ， ； Among them, parameters For any non-zero value, The parameters are the optimal weights obtained using the traditional WENO method: ， ； and This is a smoothness index, calculated as follows: ； ； Obtain the left state of the particle pair ; where the right state of the ion pair The method for obtaining the left state is the same; S4: Based on the left and right states of the reconstructed particle pair obtained in S3, use them as parameters for the Riemann solver to obtain the Riemann solution for the particle pair migration velocity. S5: The migration velocity obtained in S4 is substituted into the migration part of the ALE-SPH framework governing equations to correct the change in physical flux caused by the Lagrange particle shift and suppress numerical dissipation during the migration process.

2. The method for simulating the impact of a debris cloud on a spacecraft according to claim 1, characterized in that, S2 calculates the displacement and migration velocity of the moving particle by substituting the Cartesian coordinates of the particle displacement state obtained in S1 into the following formula for discretization and summation: ； ； In the formula, Represents the migration displacement of particle i. h For the smooth length of the particle, To calculate the maximum velocity within the domain, For particles i Supports the maximum velocity difference between particles within the domain. For particle pairs ij coordinate distance, For particle pairs ij smooth length and The arithmetic mean, For particle pairs ij Corresponding kernel function , κ This is the ratio of smooth length to initial particle size. For particles i Spatial differentiation, Represents particles j volume, For particles i migration speed, Indicates the time step.

3. The method for simulating the impact of a debris cloud on a spacecraft according to claim 2, characterized in that, In S4, the left state of the particle pair and right state Substituting into the Riemann solver, the Riemann solution for the migration velocity is obtained as follows: ； 。 4. The method for simulating the impact of a debris cloud on a spacecraft according to claim 3, characterized in that, S5 specifically performs the following calculations to update the changes in volume, mass, momentum, and energy caused by particle migration: ； ； ； ； ； In the formula, The mass derivative of volume with respect to time. The mass derivative of mass with respect to time. The mass derivative of momentum with respect to time. The mass derivative of internal energy with respect to time; Represents particle pairs ij Riemann solution for migration velocity Represents particle pairs ij The average density; This represents the average value of the product of density and velocity. This represents the average value of the product of density and internal energy.

Images