Particle discrete simulation method, device and equipment
Through the non-uniform rational B-spline method, and combined with the contact judgment algorithm, the problem of low accuracy of non-regular particle shape description and non-universal contact algorithm in the prior art is solved, and higher simulation accuracy and application scope are achieved.
Patent Information
- Application Number
- CN202311451442.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2023-11-02
- Publication Date
- 2025-05-06
AI Technical Summary
The existing discrete simulation methods have low accuracy in describing irregular particle shapes, and the contact algorithms between particles with different shapes are not universal, resulting in reduced simulation accuracy.
The non-uniform rational B-spline method is used to describe the particle shape, and combined with the particle contact judgment algorithm, the virtual particle information and nearest distance point calculation can be achieved to achieve accurate simulation of regular or irregular particles.
It improves the application range and accuracy of the particle discrete simulation method, can accurately describe particles of different sizes and shapes, and effectively detect contact collisions between particles.
Smart Images
Figure CN119939840A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the field of computational simulation technology, and relates to a discrete simulation method, and in particular to a particle discrete simulation method, device and equipment. Background Art
[0002] Industrial production processes widely involve the storage, transportation and processing of different granular materials. Due to the lack of understanding of the particle flow mixing mechanism and rheological transformation process, the granular material processing process often relies heavily on the experience of practitioners, the final product quality is difficult to precisely control, and the processing process wastes energy seriously. However, a large number of experimental and simulation results show that the shape of granular materials will greatly affect the flow and stacking state of the particle system. Ignoring the influence of particle shape effects will lead to the inability to accurately predict the feeding rate of granular materials and cause pipeline blockages due to particle orientation and intersection.
[0003] Discrete simulation method is the mainstream method for particle flow simulation, and it can track the motion state and position information of all particles in the particle system, which greatly promotes the understanding of the rheological state of particles. However, the traditional discrete element simulation method has limited description accuracy for particles, and the contact algorithm between particles of different shapes is not universal, which greatly reduces the accuracy of discrete simulation method for simulating complex industrial particle systems. Therefore, the lack of high-precision description methods for irregular particle shapes and efficient detection methods for contact and collision between irregular particles has become a bottleneck and constraint for further improving the application scope and accuracy of discrete simulation methods.
[0004] Therefore, in view of the shortcomings of the existing technology, it is necessary to provide a particle discrete simulation method, device and equipment. Summary of the invention
[0005] The purpose of the present invention is to provide a particle discrete simulation method, device and equipment to solve the defects of the discrete simulation method in the prior art, that is, the low accuracy in describing the irregular particle shape and the non-universal algorithm for determining the contact between particles.
[0006] In order to achieve the purpose of the invention, the present invention adopts the following technical solutions:
[0007] In a first aspect, the present invention provides a particle discreteness simulation method, the particle discreteness simulation method comprising the following steps:
[0008] S110: Description of particle shape based on non-uniform rational B-spline method;
[0009] S120: performing particle contact determination;
[0010] S130: Update the position and / or movement information of the particle.
[0011] The particle discrete simulation method provided by the present invention accurately describes particles of different sizes and shapes through the non-uniform rational B-spline method, and combines particle contact and collision detection to establish a universal discrete simulation method for regular or irregular particles, thereby improving the application scope and accuracy of the discrete simulation method.
[0012] Preferably, the method for describing the particle shape comprises constructing closed-shape discrete particles using a non-uniform rational B-spline method.
[0013] Preferably, when describing the particle shape, the number of particle control points is not less than 5, and the corresponding spline order is not less than 2.
[0014] When the non-uniform rational B-spline method is used to describe the particle shape, the number of control points required for describing the particle shape is reduced by shifting and merging the surface control points.
[0015] Preferably, the particle contact judgment includes: shrinking the particle shape to obtain virtual particle information, and then sequentially calculating the closest distance points between particles and the force state between particles.
[0016] The particle contact judgment method provided by the present invention has good versatility and is not only applicable to the non-uniform rational B-spline method, but can also be further extended to collision detection of irregular particle discrete simulation described by superquadratic surfaces and other CAE methods.
[0017] Preferably, the shrinkage ratio is 0.9800-0.9999, and the virtual particles formed are not in contact with each other.
[0018] The shrinkage ratio of the particle shape is adjusted according to the physical parameters of the particle, illustratively including Young's modulus.
[0019] Preferably, the method for calculating the shortest distance point between particles includes a momentum gradient descent method and / or a Newton-Raphson method.
[0020] When calculating the closest distance point between particles, the gradient descent method requires up to 20-30 loop iterations, while the NR (Newton-Raphson) iteration or momentum gradient descent method can significantly reduce the number of iterations. It should be noted that the NR iteration method needs to ensure that the order of the particles described is not less than 3 to ensure that the irregular rational B-spline curve has second-order or higher continuity.
[0021] Preferably, the method for calculating the inter-particle force state includes using a Hertz-Mindlin model and / or a linear contact force model.
[0022] Preferably, the process of updating the position and / or movement information of the particles is performed with respect to the orientation of the local space coordinate axis carried by each particle.
[0023] The translational and rotational states and position information of the particles are iteratively updated through the force state. During the updating process, the orientation of the local space coordinate axis carried by each particle is updated without the need to perform separate translational and rotational calculations on each control point.
[0024] In a second aspect, the present invention provides a device for particle discrete simulation, the device comprising:
[0025] The particle shape description module is used to construct discrete particle shapes using the non-uniform rational B-spline method;
[0026] The particle contact judgment module is used to detect particle collisions and calculate the force state between particles;
[0027] The particle information updating module is used to iteratively calculate the position and / or motion information of the particles.
[0028] In a third aspect, the present invention provides an electronic device, the electronic device comprising:
[0029] at least one processor; and
[0030] a memory communicatively connected to the at least one processor; wherein,
[0031] The memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor so that the at least one processor can perform the particle discreteness simulation method described in the first aspect.
[0032] Compared with the prior art, the present invention has the following beneficial effects:
[0033] The particle discrete simulation method provided by the present invention accurately describes particles of different sizes and shapes through the non-uniform rational B-spline method, and combines particle contact and collision detection to establish a universal discrete simulation method for regular or irregular particles, thereby improving the application scope and accuracy of the discrete simulation method. BRIEF DESCRIPTION OF THE DRAWINGS
[0034] Figure 1 This is a flow chart of the particle discreteness simulation method provided in Example 1.
[0035] Figure 2 Schematic diagram of two-dimensional irregular particles described by non-uniform rational B-spline method.
[0036] Figure 3 It is a schematic diagram of three-dimensional irregular particles described by non-uniform rational B-spline method.
[0037] Figure 4 It is a schematic diagram of the shrinkage and collision detection of irregular particles.
[0038] Figure 5 This is a schematic diagram of the accumulation state of spherical particles in Example 2.
[0039] Figure 6 This is a comparison diagram of the packing density distribution state of spherical particles in Example 2.
[0040] Figure 7 This is a simulation diagram of the stacking state of ellipsoidal particles in Example 3.
[0041] Figure 8 This is a comparison chart of the results of the ellipsoidal particle dropping process in Example 4.
[0042] Fig. 9 This is a schematic diagram of the device structure for particle discrete simulation provided in Example 5.
[0043] Fig.10 It is a schematic diagram of the electronic device structure for particle discrete simulation provided in Example 6. DETAILED DESCRIPTION
[0044] The technical solution of the present invention is further described below by specific implementation methods. It should be understood by those skilled in the art that the embodiments are only to help understand the present invention and should not be regarded as specific limitations of the present invention.
[0045] Example 1
[0046] This embodiment provides a particle discreteness simulation method, which can realize accurate simulation of irregular particle discrete states. The method can be executed by a particle discreteness simulation device, which can be implemented in the form of hardware and / or software, and the device can be configured in an electronic device with particle discreteness simulation capabilities.
[0047] like Figure 1 As shown, the method provided in this embodiment includes:
[0048] S110. Describing particle shape based on non-uniform rational B-spline method.
[0049] In step S110, the non-uniform rational B-spline method uses control points, node vectors, curve degrees and weights to describe the shape of irregular particles, and reduces the number of control points required for describing the particle shape by shifting and merging surface control points, such as Figure 2 and Figure 3 shown.
[0050] The non-uniform rational B-spline representation of a two-dimensional curve is:
[0051]
[0052] The non-uniform rational B-spline representation method of three-dimensional curves is:
[0053]
[0054] Where P is the coordinate of the control point, w is the weight of the control point, N(u) is the B-spline basis function of p and q times, and the basis function can be iteratively calculated by the de-Boor-Cox equation.
[0055] S120, performing particle contact judgment, including:
[0056] The required number of particles is randomly generated in the calculation space, and the particles are shrunk according to a certain ratio. The shrinkage ratio is between 0.9800-0.9999. This value is appropriately adjusted according to the physical parameters such as the Young's modulus of the particles to ensure that the particles are in a non-contact state after shrinkage. The closest distance between two non-uniform rational B-spline surfaces is solved by iterative calculation. The closest value of the distance between the virtual particle surfaces is solved, that is, the minimum value of the following function:
[0057] dist(u,v,t,s)=(g(u,v)-f(t,s)) 2
[0058] Among them, g(u,v) represents the wall position information of the shrunk virtual particle i, and f(t,s) represents the wall position information of the actual particle j adjacent to particle i.
[0059] Then, by comparing the size difference between the actual size and the contracted size of the particles with the distance between the closest points, the collision state between the particles and the corresponding overlap between the particles can be determined, such as Figure 4 As shown, the inter-particle force state is calculated by Hertz-Mindlin.
[0060] For three-dimensional irregular particles, when the order of the surface is not less than 3, the NR iteration can be used for solution. The NR equation is as follows:
[0061]
[0062]
[0063]
[0064]
[0065] The iterative equation is of the form:
[0066]
[0067] Among them, u i 、v i ,t i and i Respectively represent the position weight values of the NURBS surfaces u, v, t and s obtained after i iterations.
[0068] When the surface order is less than 3, the second derivative of the surface may be zero or undifferentiable, so the NR iterative method will produce unknown errors.
[0069] When the surface order is less than 3, the momentum gradient descent method is used to solve it, and the iterative equation is as follows:
[0070] Δx0=0
[0071]
[0072] x k+1 =x k -(γΔx k-1 +(1-γ)Δx k )
[0073] Δx k =γΔx k-1 +(1-γ)Δx k
[0074] Among them, Δx0 represents the displacement of the weight value updated by the momentum gradient descent method in the initial state, and its value is usually directly set to zero; Δx k represents the displacement of the weight value updated by the momentum gradient descent method for the kth time; α represents the value of the descending gradient weight; γ represents the influence weight of the previous level momentum retained by the momentum gradient descent method; x k Indicates the weight value of the NURBS surface after the kth update.
[0075] The iterative equation of the stochastic gradient descent method is as follows:
[0076]
[0077]
[0078]
[0079]
[0080] This embodiment does not use the stochastic gradient descent method. Using the stochastic gradient descent method for iterative solution will affect the convergence speed and accuracy. The reason is that if the value of α is greater than 0.1, the value will not converge, and if its value is too low, the convergence speed will be slow.
[0081] S130: Update the position and / or movement information of the particle.
[0082] The translation, rotation and position information of the particles are iteratively updated through the force state between the particles to achieve continuous simulation of the particle motion process. In the process of updating the particle position and motion state information, only the orientation of the local space coordinate axis carried by each particle is updated, without performing separate translation and rotation calculations for each control point.
[0083] Example 2
[0084] This embodiment takes the stacking of spherical particles as an example to further explain the specific technical solution.
[0085] This embodiment simulates the stacking process of 3000 spherical particles with a particle size of 6.0 mm in a cylindrical container with a diameter of 48.0 mm. During the simulation process, the initial position information of 3000 spherical particles that do not touch each other is randomly generated in the conical hopper, and then the particles fall freely under the action of gravity to form a dense stacking structure in the hopper where the particle speed is almost negligible. Then, the lower end of the hopper is opened to allow the granular material to gradually fall through the hopper into the cylindrical container with a diameter of 48.0 mm, forming a stable particle bed stacking structure.
[0086] Schematic diagram of the stacking state of spherical particles Figure 5 As shown, during the experiment, high-precision computer tomography technology was used to obtain the axial stacking density distribution state of the spherical particles in the experiment, and then the spherical particle discrete simulation method and the particle discrete simulation method provided in Example 1 of the present invention were used to simulate the spherical particle stacking structure formed by the same particle falling and stacking process, and the stacking density distribution state in the particle stacking bed was analyzed. The comparison results are shown in FIG. Figure 6 shown.
[0087] It can be seen that the simulation results provided by Example 1 of the present invention are consistent with the experimental results, and the simulation results are accurate.
[0088] Example 3
[0089] This embodiment takes the stacking of ellipsoidal particles as an example to further explain the specific technical solution.
[0090] The particle volume of the simulation process is controlled to be the same as that of spherical particles with a particle size of 6.0 mm, and the aspect ratio of the particles is adjusted to generate a series of ellipsoidal particles with different shapes. A random generation method is used to randomly generate 5,000 ellipsoidal particles with different orientations and no contact with each other in a cylindrical container with a diameter of 48 mm. Under the action of gravity, the ellipsoidal particles are allowed to fall freely to form a particle bed with different structures.
[0091] This example uses the particle discrete simulation method provided in Example 1 to simulate the accumulation state of ellipsoidal particles with aspect ratios of 0.5, 1.5, and 2.5 in a cylindrical container, representing the shape of ellipsoidal particles from flat to elongated. The blanking accumulation results are shown in Figure 7 As shown, it can be seen that the method provided by the present invention is applicable to irregular particles of different shapes and sizes.
[0092] Example 4
[0093] This embodiment takes the dropping process of ellipsoidal particles as an example to further explain the specific technical solution.
[0094] The process of 5500 ellipsoidal particles with 2a=2b=13.56mm and 2c=7.19mm falling into a rectangular hopper with a size of 290mm wide, 55mm thick and 1000mm high was simulated. The bottom of the hopper was open and the opening size was 55mm×54mm. The stacking process randomly generated 5500 ellipsoidal particles with different orientations and no contact with each other within the hopper, and the particles were allowed to fall freely under the action of gravity to form a dense stacking structure. Then, the bottom opening of the hopper was opened to allow the particles to fall through the hopper. The particle properties and parameters used in the simulation process are exactly the same as those in the experimental process.
[0095] The experimental results of the blanking process are from "Flow characteristics and discharge rate of ellipsoidal particles in a flat bottom hopper" (Powder Technology, 2014, 253: 70-79). The comparison between the simulation results and the experimental results is shown in Figure 2. Figure 8 As shown in the figure, it can be found that in the falling speed simulation, the simulation results of the particle falling speed are basically consistent with the experimental results, with only a small difference in the number of particles remaining in the final hopper, which further verifies the accuracy of the simulation method.
[0096] Example 5
[0097] This embodiment provides a device for simulating particle dispersion, such as Fig. 9 As shown, the device includes: a particle shape description module 110, a particle contact judgment module 120, and a particle information update module 130. Among them:
[0098] The particle shape description module 110 is used to construct discrete particle shapes using a non-uniform rational B-spline method;
[0099] The particle contact judgment module 120 is used to perform particle collision detection and calculate the force state between particles;
[0100] The particle information updating module 130 is used to iteratively calculate the position and / or motion information of the particles.
[0101] In the particle shape description module 110, a non-uniform rational B-spline method is used to construct closed-shape discrete particles. The number of control points required for particle shape description is reduced by shifting and merging surface control points. The number of particle control points is not less than 5, and the corresponding spline order is not less than 2.
[0102] In the particle contact judgment module 120 , the particle contact judgment includes: shrinking the particle shape to obtain virtual particle information, and then calculating the shortest distance point between particles and the force state between particles in sequence.
[0103] The shrinkage ratio is 0.9800-0.9999, the virtual particles are formed in a non-contact state, the momentum gradient descent method and / or the Newton-Raphson method are used to calculate the closest distance point between the particles, and the Hertz-Mindlin model is used to calculate the force state between the particles.
[0104] In the particle information updating module 130, the position and / or motion information of the particle is iteratively updated according to the force state.
[0105] The device provided in this embodiment can execute the particle discreteness simulation method provided in any embodiment of the present invention, and has the corresponding functional modules and beneficial effects of the execution method.
[0106] Example 6
[0107] This embodiment provides an electronic device for implementing a particle discrete simulation method, such as Fig.10 As shown, the electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device may also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices (such as helmets, glasses, watches, etc.), and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present application described and / or required herein.
[0108] like Fig.10As shown, the electronic device 10 includes at least one processor 11, and a memory connected to the at least one processor 11, such as a read-only memory (ROM) 12, a random access memory (RAM) 13, etc., wherein the memory stores a computer program that can be executed by at least one processor, and the processor 11 can perform various appropriate actions and processes according to the computer program stored in the read-only memory (ROM) 12 or the computer program loaded from the storage unit 18 to the random access memory (RAM) 13. In the RAM 13, various programs and data required for the operation of the electronic device 10 can also be stored. The processor 11, the ROM 12, and the RAM 13 are connected to each other through a bus 14. An input / output (I / O) interface 15 is also connected to the bus 14.
[0109] A number of components in the electronic device 10 are connected to the I / O interface 15, including: an input unit 16, such as a keyboard, a mouse, etc.; an output unit 17, such as various types of displays, speakers, etc.; a storage unit 18, such as a second storage area, an optical disk, etc.; and a communication unit 19, such as a network card, a modem, a wireless communication transceiver, etc. The communication unit 19 allows the electronic device 10 to exchange information / data with other devices through a computer network such as the Internet and / or various telecommunication networks.
[0110] The processor 11 may be a variety of general and / or special processing components with processing and computing capabilities. Some examples of the processor 11 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various special artificial intelligence (AI) computing chips, various processors running machine learning model algorithms, a digital signal processor (DSP), and any appropriate processor, controller, microcontroller, etc. The processor 11 executes the various methods and processes described above, such as the particle discrete simulation method.
[0111] In some embodiments, the particle discrete simulation method may be implemented as a computer program, which is tangibly contained in a computer-readable storage medium, such as a storage unit 18. In some embodiments, part or all of the computer program may be loaded and / or installed on the electronic device 10 via the ROM 12 and / or the communication unit 19. When the computer program is loaded into the RAM 13 and executed by the processor 11, one or more steps of the particle discrete simulation method described above may be performed. Alternatively, in other embodiments, the processor 11 may be configured to perform the particle discrete simulation method in any other appropriate manner (e.g., by means of firmware).
[0112] Various implementations of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs), systems on chips (SOCs), load programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various implementations can include: being implemented in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which can be a special purpose or general purpose programmable processor that can receive data and instructions from a storage system, at least one input device, and at least one output device, and transmit data and instructions to the storage system, the at least one input device, and the at least one output device.
[0113] Computer programs for implementing the methods of the present application may be written in any combination of one or more programming languages. These computer programs may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable target determination device, so that when the computer program is executed by the processor, the functions / operations specified in the flow chart and / or block diagram are implemented. The computer program may be executed entirely on the machine, partially on the machine, partially on the machine and partially on a remote machine as a stand-alone software package, or entirely on a remote machine or server.
[0114] In the context of the present application, a computer readable storage medium may be a tangible medium that may contain or store a computer program for use by or in conjunction with an instruction execution system, device or equipment. A computer readable storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices or equipment, or any suitable combination of the foregoing. Alternatively, a computer readable storage medium may be a machine readable signal medium. A more specific example of a machine readable storage medium may include an electrical connection based on one or more lines, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.
[0115] To provide interaction with a user, the systems and techniques described herein may be implemented on an electronic device having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and a pointing device (e.g., a mouse or trackball) through which the user can provide input to the electronic device. Other types of devices may also be used to provide interaction with the user; for example, the feedback provided to the user may be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user may be received in any form (including acoustic input, voice input, or tactile input).
[0116] The systems and techniques described herein may be implemented in a computing system that includes backend components (e.g., as a data server), or a computing system that includes middleware components (e.g., an application server), or a computing system that includes frontend components (e.g., a user computer with a graphical user interface or a web browser through which a user can interact with implementations of the systems and techniques described herein), or a computing system that includes any combination of such backend components, middleware components, or frontend components. The components of the system may be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: a local area network (LAN), a wide area network (WAN), a blockchain network, and the Internet.
[0117] A computing system may include a client and a server. The client and the server are generally remote from each other and usually interact through a communication network. The client and server relationship is generated by computer programs running on the corresponding computers and having a client-server relationship with each other. The server may be a cloud server, also known as a cloud computing server or cloud host, which is a host product in the cloud computing service system to solve the defects of difficult management and weak business scalability in traditional physical hosts and VPS services.
[0118] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps recorded in this application can be executed in parallel, sequentially or in different orders, as long as the information expected by the technical solution of this application can be achieved, and this document is not limited here.
[0119] The applicant declares that the above is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Those skilled in the art should understand that any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention are within the protection scope and disclosure scope of the present invention.
Claims
1. A particle discrete simulation method, characterized in that: The particle discreteness simulation method comprises the following steps: S110: Description of particle shape based on non-uniform rational B-spline method; S120: performing particle contact determination; S130: Update the position and / or movement information of the particle.
2. The particle discreteness simulation method according to claim 1, characterized in that: The method for describing the particle shape includes constructing closed-shape discrete particles using a non-uniform rational B-spline method.
3. The particle discreteness simulation method according to claim 1 or 2, characterized in that: When describing the particle shape, the number of particle control points is not less than 5, and the corresponding spline order is not less than 2.
4. The particle discreteness simulation method according to any one of claims 1 to 3, characterized in that: The particle contact judgment includes: shrinking the particle shape to obtain virtual particle information, and then sequentially calculating the closest distance point between particles and the force state between particles.
5. The particle discreteness simulation method according to claim 4, characterized in that: The shrinkage ratio is 0.9800-0.9999, and the virtual particles formed are in a non-contact state with each other.
6. The particle dispersion simulation method according to claim 4 or 5, characterized in that: The method for calculating the shortest distance point between particles includes a momentum gradient descent method and / or a Newton-Raphson method.
7. The particle discreteness simulation method according to any one of claims 4 to 6, characterized in that: The method for calculating the inter-particle force state includes using a Hertz-Mindlin model and / or a linear contact force model.
8. The particle discreteness simulation method according to any one of claims 1 to 7, characterized in that: The process of updating the position and / or motion information of the particles is performed with respect to the orientation of the local space coordinate axis carried by each particle.
9. A device for particle discrete simulation, characterized in that: The device comprises: The particle shape description module is used to construct discrete particle shapes using the non-uniform rational B-spline method; The particle contact judgment module is used to detect particle collisions and calculate the force state between particles; The particle information updating module is used to iteratively calculate the position and / or motion information of the particles.
10. An electronic device, characterized in that: The electronic device comprises: at least one processor; and a memory communicatively connected to the at least one processor; wherein, The memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor so that the at least one processor can execute the particle discreteness simulation method according to any one of claims 1 to 8.