PARTICLE ARRANGEMENT SYSTEM, PARTICLE ARRANGEMENT METHOD, AND PARTICLE ARRANGEMENT PROGRAM

Abstract

To suppress the calculation cost of particle arrangement even when the number of particles to be simulated increases.SOLUTION: A particle arrangement system 10, which is a system for arranging particles to be simulated in a space for simulation, includes a block generation part 11 for generating a block having a shape capable of combining a plurality of blocks without a gap in the space, having all boundaries as periodic boundaries and having the particles arranged therein, and an arrangement part 12 for arranging the particles by combining the plurality of generated blocks so that the periodic boundaries corresponding to each other are adjacent to each other in the space.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a particle arrangement system, a particle arrangement method, and a particle arrangement program for arranging particles to be simulated in a space for simulation. [Background technology]

[0002] The behavior of multiple particles is analyzed by particle method simulations such as DEM (Discrete Element Method). To perform a simulation, it is first necessary to arrange the particles to be simulated in a simulation space. Conventionally, methods for automatically arranging particles have been proposed. For example, Patent Document 1 shows that after arranging particles in a way that allows overlapping, the particles are moved to obtain a state in which there is no overlapping between the particles. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Laid-Open No. 2006-259910 Summary of the Invention [Problem to be solved by the invention]

[0004] However, the method disclosed in Patent Document 1 requires information processing such as simulation or judgment for the initial placement of each particle, and the calculation cost increases as the number of particles to be simulated increases.

[0005] Other particle placement methods include, for example, a drop-type filling method, which generates an arbitrary initial particle group in a simulation space, simulates the particles falling into a predetermined frame by gravity, and fills the frame with particles. Another method involves randomly generating particles sequentially in a simulation space, and discarding, moving, growing, and adopting particles based on predetermined constraints. These methods, like the method described in Patent Document 1, also require high computational costs as the number of particles to be simulated increases. Furthermore, the procedure for filling particles into an arbitrary shape becomes complicated.

[0006] The present invention has been made in consideration of the above, and aims to provide a particle arrangement system, a particle arrangement method, and a particle arrangement program that can reduce the calculation cost of particle arrangement and can appropriately arrange particles, even when the number of particles to be simulated is large. [Means for solving the problem]

[0007] In order to achieve the above object, the particle placement system of the present invention is a particle placement system that places particles to be simulated in a simulation space, and is equipped with: a block generation means that generates blocks having a shape that can be combined in multiple places in space without gaps, all of whose boundaries are periodic boundaries, and in which particles are placed; and a placement means that places particles by combining multiple blocks generated by the block generation means so that corresponding periodic boundaries are adjacent to each other in space.

[0008] In the particle placement system according to the present invention, all boundaries are periodic boundaries, and particles are placed by combining blocks within which particles are placed. Therefore, even if the number of particles increases, particles can be placed by combining blocks in the area where the particles are to be placed. The process of combining blocks is simple, so the computational cost is low. Furthermore, the number of particles handled when creating a block can be made small compared to the number of particles to be placed. Therefore, the computational cost of creating blocks is also small compared to conventional particle placement. Therefore, according to the particle placement system according to the present invention, even if the number of particles to be simulated increases, the computational cost of particle placement can be reduced and particles can be placed appropriately.

[0009] The block generation means is Particles are arranged inside A region in which the boundary other than the one in the preset direction is a periodic boundary In the area Hey Teichi Thickness in the direction And two consecutive lines in that direction Set the subregion 、 The relevant Two partial area On the other hand The particles contained in , at one end of the region in one direction, so that the surface where the two subregions were in contact is on the outside. Moved Then, particles outside the other of the two partial regions are removed, and the surface where the other partial region was in contact is set as the other end of the region in one direction. Generate a block do. The block generating means may also place the particles inside the region by applying a force in one direction to the particles to move them. This configuration makes it possible to easily and appropriately generate blocks. As a result, it is possible to easily and reliably place particles.

[0010] Or, The block generation means performs a process of homogenizing the arrangement of particles inside the block. cormorant. Furthermore, the block generation means performs the homogenization process as follows: In a block in which particles are arranged and whose boundary is a periodic boundary, two partial regions that have a thickness in one direction and are continuous in that direction are set, and the particles contained in the two partial regions are moved in one direction while keeping the positional relationship between the particles fixed so that they are located at one end and the other end of the block in that direction, respectively.The positional relationship of the particles contained in the two partial regions moved to one end and the other end with respect to each partial region is fixed, and the movement of particles in the region sandwiched between the two partial regions is simulated while the other particles are allowed to move freely.The above process is performed on the two partial regions. Repeat while changing the position of cormorant. According to this configuration, it is possible to suppress unevenness in the arrangement of particles in each block, and to achieve a uniform arrangement of particles.

[0011] Incidentally, the present invention can be described not only as an invention of a particle arrangement system as described above, but also as an invention of a particle arrangement method and a particle arrangement program as described below. These are essentially the same inventions, just in different categories, and have similar functions and effects.

[0012] That is, the particle arrangement method according to the present invention comprises: The particle placement system is Place the particles to be simulated in the simulation space. Grain A child placement method, comprising: The particle placement system is a block generation step of generating a block having a shape that can be combined in a space without gaps, all of whose boundaries are periodic boundaries, and in which particles are arranged; The particle placement system is an arrangement step of arranging particles by combining a plurality of blocks generated in the block generation step so that corresponding periodic boundaries are adjacent to each other in space; Execute . In the block generation step, two partial regions having a thickness in one direction and continuous in that direction are set in a region in which particles are arranged and boundaries other than a predetermined one direction are periodic boundaries, and particles contained in one of the two partial regions are moved, while fixing their positional relationship, to one end of the region in one direction so that the surface where the two partial regions were in contact is on the outside, and particles outside the other of the two partial regions are removed, and the surface where the other partial region was in contact is set as the other end of the region in one direction, thereby generating a block. Alternatively, in the block generation step, a process for homogenizing the particle arrangement inside the block is performed, and as the homogenization process in the block generation step, in a block in which particles are arranged and whose boundary is a periodic boundary, two partial regions that have a thickness in one direction and are continuous in that direction are set, and all of the particles of the block are moved in one direction while keeping the positional relationship between the particles fixed so that the particles included in the two partial regions are located at one end and the other end of the block in that direction, respectively, and the positional relationship of the particles included in the two partial regions moved to one end and the other end with respect to each partial region is fixed, and the movement of particles in the region sandwiched between the two partial regions is simulated while the other particles are allowed to move freely, and the above process is repeated while changing the positions of the two partial regions.

[0013] Furthermore, the particle placement program according to the present invention is a particle placement program that causes a computer to operate as a particle placement system that places particles to be simulated in a space for simulation, and causes the computer to function as: a block generation means that generates blocks having shapes that can be combined in multiple places in space without gaps, all of whose boundaries are periodic boundaries, and in which particles are placed; and a placement means that places particles by combining multiple blocks generated by the block generation means so that corresponding periodic boundaries are adjacent to each other in space. The block generating means sets two partial regions that have a thickness in one direction and are continuous in that one direction in an area in which particles are arranged and whose boundaries other than a predetermined one direction are periodic boundaries, moves the particles contained in one of the two partial regions, while fixing their positional relationship, to one end of the area in one direction so that the surface where the two partial regions were in contact is on the outside, removes the particles that are outside the other of the two partial regions, and sets the surface where the other partial region was in contact at the other end of the area in one direction, thereby generating a block. Alternatively, the block generation means performs a process of homogenizing the arrangement of particles within the block, and as the homogenization process, the block generation means sets two partial regions that have a thickness in one direction and are continuous in that direction in a block in which particles are arranged and whose boundary is a periodic boundary, moves all of the particles of the block in one direction while keeping the positional relationship between the particles fixed so that the particles included in the two partial regions are located at one end and the other end of the block in that direction, fixes the positional relationship of the particles included in the two partial regions moved to one end and the other end with respect to each partial region, and simulates the movement of particles in the region sandwiched between the two partial regions while allowing the other particles to move freely, and repeats the above process while changing the positions of the two partial regions. [Effects of the Invention]

[0014] According to the present invention, even when the number of particles to be simulated increases, it is possible to reduce the calculation cost for particle placement and to place the particles appropriately. [Brief explanation of the drawings]

[0015] [Figure 1]FIG. 1 is a diagram illustrating a functional configuration of a particle placement system according to an embodiment of the present invention. [Figure 2] FIG. 1 is a diagram showing an outline of particle arrangement. [Figure 3] FIG. 10 is a diagram for explaining block generation. [Figure 4] 1 is a flowchart showing a particle arrangement method which is a process executed by the particle arrangement system according to an embodiment of the present invention. [Figure 5] FIG. 2 is a diagram showing the configuration of a particle placement program according to an embodiment of the present invention, together with a recording medium. DETAILED DESCRIPTION OF THE INVENTION

[0016] Hereinafter, embodiments of a particle arrangement system, a particle arrangement method, and a particle arrangement program according to the present invention will be described in detail with reference to the drawings. In the description of the drawings, the same elements are given the same reference numerals, and duplicated explanations will be omitted.

[0017] FIG. 1 shows the functional configuration of a particle placement system 10 according to this embodiment. The particle placement system 10 is a system (device) that places particles to be simulated in a simulation space (computational domain). The simulation analyzes the behavior of multiple particles in a three-dimensional simulation space. The particles are, for example, spherical (shapes with a constant distance from the center to the surface). The particles may also have shapes other than those mentioned above.

[0018] The simulation, for example, calculates the positions and velocities of multiple particles for each time step, which is the time in the simulation. In the simulation, the force applied to each particle is calculated, and the position and velocity of the particle are calculated based on the calculated force. The force applied to each particle is, for example, an interaction force generated by interaction between particles, such as a contact force due to contact (collision). The simulation is performed based on, for example, DEM. Alternatively, the simulation may be performed based on other particle methods such as SPH (Smoothed Particle Hydrodynamics) or MPS (Moving Particle Semi-implicit method). The simulation may handle many particles, i.e., perform large-scale particle method calculations.

[0019] The particles to be simulated, i.e., the particles to be placed by particle placement system 10, include any particles that have been the subject of conventional particle simulations. For example, soil or powder may be the subject of the simulation. Alternatively, a fluid or solid may be assumed to be composed of multiple particles and used as the subject of the simulation.

[0020] The above simulation is used to simulate natural phenomena such as landslides in terrain. In this case, a collection of particles corresponds to a geological layer (e.g., a sedimentary layer, a rock layer, or a sand layer). The above simulation may also be used in any field, such as academia, industry, games, and CG (computer graphics). For example, it may be used to simulate the behavior of powder structures in sandbox games, or to represent the erosion and weathering of structures in movies or animations.

[0021] To perform a simulation, particles must be arranged in space as the initial state of the simulation. The particle arrangement system 10, for example, arranges particles in space as the initial state of the simulation. When the particles are arranged in space as the initial state, the arrangement must appropriately represent the object to be simulated. For example, when simulating a landslide, the arranged particles must be uniformly packed in an area corresponding to the geological layer so as to appropriately correspond to the geological layer.

[0022] Specifically, the particle placement system 10 is configured by a computer including hardware such as a CPU (Central Processing Unit), a GPU (Graphics Processing Unit), and a memory. Each function of the particle placement system 10, which will be described later, is realized by these components operating by programs or the like. The particle placement system 10 may be realized by a single computer, or may be realized by a computer system configured by connecting multiple computers to each other via a network. The particle placement system 10 does not necessarily need to include a GPU as a computing device, and may be configured to include only a CPU.

[0023] An overview of particle placement by the particle placement system 10 according to this embodiment will now be described. The particle placement system 10 first generates a block 20 as shown in FIG. 2(a). The block 20 is a rectangular parallelepiped, and particles are placed inside it. Next, the particle placement system 10 combines and places the blocks 20 in an area in space where particles are to be placed, as shown in FIG. 2(b), to generate a block assembly 30. Next, the particle placement system 10 deletes particles not used in the simulation from the block assembly 30, as shown in FIG. 2(c), to create an initial particle placement 40.

[0024] Next, the functions of the particle placement system 10 according to this embodiment will be described. As shown in FIG.

[0025] The block generation unit 11 is a block generation means that generates a block 20 having a shape that can be combined in space without gaps, all boundaries of which are periodic boundaries, and particles disposed therein. The block generation unit 11 may dispose particles inside a region whose boundaries other than a predetermined direction are periodic boundaries, set a partial region in the region having a thickness in the predetermined direction, and move the particles included in the partial region while fixing their positional relationship, thereby generating a block 20 with the boundary of the partial region as a periodic boundary. The block generation unit 11 may dispose particles inside the region by applying a force to the particles in one direction to move them. The block generation unit 11 may perform a process of homogenizing the particle arrangement inside the block 20. As the homogenization process, the block generation unit 11 may fix the positions of particles near a predetermined position in the block 20 in one predetermined direction, and repeatedly perform a simulation of the movement of particles whose positions are not fixed while changing the predetermined position.

[0026] The boundaries of the blocks 20 generated by the block generator 11, i.e., each face constituting the rectangular parallelepiped block 20, are periodic boundaries (boundaries that satisfy the periodic boundary condition). That is, the block 20 is a full-surface periodic boundary particle block. Of the faces constituting the rectangular parallelepiped block 20, the faces facing each other form corresponding periodic boundaries. Furthermore, because the blocks 20 are rectangular parallelepipeds as described above, two blocks 20 can be combined by closely contacting their corresponding periodic boundary faces with no gaps. Furthermore, because the faces of two blocks 20 that are in close contact form corresponding periodic boundaries, there is no bias in the particles that are arranged due to the presence of the faces. Furthermore, because all faces of the block 20 are periodic boundaries, another block 20 can be combined by closely contacting its periodic boundary in the direction of any face of the block 20. This allows the generation of a block assembly 30 that includes an arbitrary initial state arrangement 40, as described above.

[0027] The block generator 11 generates a block 20 as follows. The block generator 11 arranges particles inside a region in which boundaries other than one preset direction are periodic boundaries. For example, as shown in FIG. 3(a), the block generator 11 forms a region in which four faces 21 perpendicular to the x direction (x axis) and y direction (y axis) of space are periodic boundaries. Note that the diagram shown in FIG. 3 is a view seen from a direction parallel to the xy plane of space, and the vertical direction is the z direction. Some of these faces 21 become faces of the block 20. The process of setting the faces of a region as periodic boundaries may be performed in the same manner as in conventional methods (the same applies below).

[0028] As shown in FIG. 3( a), the block generator 11 generates a non-periodic boundary surface 22 perpendicular to the z direction (z axis) of space in an area surrounded by the four surfaces 21. When viewed from above in the z direction, the area is a rectangle formed by the four surfaces 21 perpendicular to the x and y directions. The block generator 11 generates particles of arbitrary size and shape at random positions above the area in the z direction. The block generator 11 stores particle parameters used for particle placement, such as particle radius, in advance, and generates particles based on this information. As described below, the block generator 11 also simulates particle behavior for particle placement. This simulation may be performed in the same manner as a conventional DEM-based simulation. The block generator 11 also stores parameters for the simulation, such as the friction coefficient, elastic coefficient, viscous damping coefficient, and restitution coefficient, in advance, and uses these parameters in the simulation.

[0029] The block generation unit 11 performs a simulation in which a downward force in the z direction, for example, gravity, is applied to the generated particles. The particles subjected to gravity fall to the bottom surface 22, which is a surface perpendicular to the z direction. The block generation unit 11 generates a large number of particles and performs the above simulation. As a result of this simulation, the particles are packed onto the bottom surface 22, as shown in FIG. 3(a). That is, the block generation unit 11 performs gravity-drop type packing of particles into the above region (a box whose sides are periodic boundaries). The block generation unit 11 continues the above packing until the length from the bottom surface 22 of the region to be packed with particles reaches a certain length that is longer than the length of the block 20 in the z direction.

[0030] In this way, the block generation unit 11 applies a force in the z direction to the generated particles to move them inside the region whose periodic boundaries are the surfaces 21 in the x and y directions other than the preset z direction, thereby placing the particles inside the region.

[0031] Next, the block generation unit 11 sets two partial regions 23, 24 having a thickness in the z direction in the region. The two partial regions 23, 24 are set so as to include particles located in the thickness portion in the z direction. The positions of the two partial regions 23, 24 are positions whose length from the bottom surface 22 is a predetermined length that is longer than the length of the block 20 in the z direction. Furthermore, the thickness in the z direction of the two partial regions 23, 24 is, for example, sufficiently smaller than the z direction of the block 20 to be finally generated, and is a thickness such that the particles included in the partial regions 23, 24 form at least one layer.

[0032] The two partial regions 23 and 24 are continuous in the z direction. The block generation unit 11 moves particles included in the partial region 23, for example, particles whose center of gravity is included in the partial region 23, to below the surface 22 as shown in FIG. 3(b) while keeping their positional relationship with the partial region 23 fixed. This movement is only in the z direction, and their positions in the x and y directions are not changed. At this time, among the particles that are not moved, particles that are located a certain distance in the z direction from the bottom surface 22 of the region may be deleted. The certain distance related to the particle deletion may be adjusted so that the number of particles or particle volume fraction of the particles included in the finally generated block 20 is a predetermined value. In this way, the block generation unit 11 can arbitrarily adjust the number of particles or particle volume fraction of the particles included in the block 20. Furthermore, particles above the partial region 23 in the z direction are not used in subsequent processing.

[0033] When moving particles in partial region 23 downward, the block generator 11 moves them to a position where a gap is created between them and particles that are not to be moved (a position where the particles that are not to be moved and the particles that are to be moved do not overlap). As shown in FIG. 3(b), in the particle collection configured in this manner, the particles of partial region 24 are located on the upper side in the z direction, and the particles of partial region 23 are located on the lower side. As described above, since the two partial regions 23 and 24 are continuous in the z direction, the boundary surface between partial regions 23 and 24 can be considered a periodic boundary. The block generator 11 considers the upper and lower surfaces in the z direction of the region where the particles shown in FIG. 3(b) are located to be periodic boundaries.

[0034] Next, the block generation unit 11 fixes the positional relationship of particles included in the partial region 23, for example, particles whose center of gravity is included in the partial region 23, with respect to the partial region 23. Furthermore, the block generation unit 11 fixes the positional relationship of particles included in the partial region 24, for example, particles whose center of gravity is included in the partial region 24, with respect to the partial region 24. The other particles are allowed to move freely in space. In this state, the block generation unit 11 performs a simulation to move the particles included in the partial region 23 closer to the partial region 24 in the z direction. In other words, the block generation unit 11 performs a simulation to compress the block at this point in time in the z direction. This simulation is a simulation of the movement of particles in the region sandwiched between the partial regions 23 and 24. Note that during this simulation, gravity may or may not be applied to the particles.

[0035] The block generation unit 11 moves the particles until the distance between the outer surface (lower side in the z direction) of the partial region 23 after the movement and the outer surface (upper side in the z direction) of the partial region 24 after the movement reaches a preset length of the block 20 to be finally generated. FIG. 3(c) shows a collection of particles after the partial region 23 has been moved (the distance between the partial region 23 and the partial region 24 is shorter than that shown in FIG. 3(b)). Note that the distance between the outer surface (lower side in the z direction) of the partial region 23 before the movement and the outer surface (upper side in the z direction) of the partial region 24 is longer than the length of the block 20. Note that the longer the z direction length of the region in which the particles are located before the movement of the partial region 23, the higher the particle density in the block 20 to be finally generated. As described above, the block generation unit 11 generates the block at this point in time by regarding the particles contained in the partial region 23 after the movement as the lower cover in the z direction and the particles contained in the partial region 24 as the upper cover in the z direction.

[0036] The above process makes it possible to generate a block in which each face of a rectangular parallelepiped serves as a periodic boundary. However, the generated block has a bias in the particle arrangement. The bias in the particle arrangement is caused by the partial regions 23 and 24 in which the particle positions were fixed. The block generation unit 11 homogenizes the particle arrangement to remove the bias in the particle arrangement in the block as follows.

[0037] The block generated as described above and shown in Figure 3(c) has periodic boundaries on its upper surface in the z direction (the surface outside partial region 24 (upper side in the z direction)) and its lower surface (the surface outside partial region 23 (lower side in the z direction)), so that the entire particle can be moved (shifted) in the z direction while keeping the positional relationship between particles fixed.

[0038] When the block is in the state shown in FIG. 3(c), the block generation unit 11 sets two partial regions 25 and 26, each having a thickness in the z direction, in the block. The two partial regions 25 and 26 may be the same size as the above-mentioned two partial regions 23 and 24. The positions of the two partial regions 25 and 26 are predetermined positions other than the above-mentioned two partial regions 23 and 24. The two partial regions 25 and 26 are continuous in the z direction.

[0039] As shown in Fig. 3(d), the block generation unit 11 moves (shifts) all of the particles in the z direction while fixing the positional relationship between the particles so that the particles included in the two partial regions 25, 26 are located at the bottom and top ends of the block, respectively. Note that when the block is in the state shown in Fig. 3(c), partial region 25 located at the top in the z direction is located at the bottom end of the block after the movement, as shown in Fig. 3(d), and partial region 26 located at the bottom in the z direction is located at the top end of the block after the movement.

[0040] Next, the block generation unit 11 fixes the positional relationship of particles included in the partial region 25, for example, particles whose centroids are included in the partial region 25, with respect to the partial region 25. Furthermore, the block generation unit 11 fixes the positional relationship of particles included in the partial region 26, for example, particles whose centroids are included in the partial region 26, with respect to the partial region 26. Other particles are allowed to move freely in space. In this state, the block generation unit 11 simulates the movement of particles in the region sandwiched between the partial regions 25 and 26. Note that, during this simulation, gravity may or may not be applied to the particles. In this simulation, particles included in the two partial regions 23 and 24, whose positional relationship was fixed in the above-described processing, are also moved. In other words, this simulation is a relaxation calculation that relieves the load acting on the particles. This relaxation reduces bias in the particle arrangement.

[0041] Next, the block generation unit 11 sets two new partial regions 25 and 26 (the process shown in FIG. 3(c)) and performs the above-mentioned relaxation calculation (the process shown in FIG. 3(d)). The block generation unit 11 repeats the setting of the two partial regions 25 and 26 and the relaxation calculation. This repetition is performed, for example, until the bias in particle placement throughout the entire block becomes negligible in terms of simulation. For example, the process is repeated until a globally uniform internal contact stress is generated in each particle in the simulation of the relaxation calculation. Alternatively, the above repetition may be performed a preset number of times.

[0042] As described above, the block generation unit 11 may fix the positions of particles (particles included in the two partial regions 23 and 24) near a predetermined position in one direction in the block as a process for homogenizing the particle arrangement within the block, and repeatedly simulate the movement of particles whose positions are not fixed while changing the predetermined position.

[0043] The block generating unit 11 outputs to the arranging unit 12 information indicating the block 20 generated as described above, specifically information indicating the arrangement positions of the particles included in the block (for example, information on coordinates in the block).

[0044] The placement unit 12 is a placement means that places particles by combining multiple blocks 20 generated by the block generation unit 11 so that corresponding periodic boundaries are adjacent to each other in space. The placement unit 12 receives information indicating the blocks 20 from the block generation unit 11. Using the received information, the placement unit 12 combines and places the blocks 20 containing particles in space so as to include an area where particles used in the simulation are to be placed. The area where particles used in the simulation are to be placed is set in advance by a user and stored in the placement unit 12. The placement unit 12 combines multiple blocks 20 so that corresponding periodic boundaries are adjacent to each other without any gaps.

[0045] The placement unit 12 deletes particles that are placed in areas that are not positions where particles used in the simulation are to be placed from a block collection 30 formed by combining blocks 20. Note that if there are no particles placed in positions that are not in the area, no particles are deleted. In this way, an initial state placement 40 of particles in space is performed.

[0046] Before or after the initial particle arrangement 40 by the arrangement unit 12, the physical properties of the block 20 itself or the combination of blocks 20 may be calculated to confirm whether the particle arrangement by the block 20 is appropriate for performing a simulation. That is, the performance of the block 20 may be verified. For example, the particle packing ratio, number of connections, compressibility, or fracture properties may be calculated as the physical properties (mechanical properties) of the block 20 itself or the combination of blocks 20. The number of connections is the number of connections between particles. The fracture properties can be performed by a numerical triaxial compression experiment. These physical properties can be calculated by conventional methods. The shape of the combination of blocks 20 when calculating the physical properties may be a predetermined shape for calculating the physical properties. For example, when performing a numerical triaxial compression experiment, the shape may be cylindrical.

[0047] If the calculated physical properties are not appropriate, the block generator 11 may generate the block 20 again. In this case, the conditions for generating the block 20 are changed so that the physical properties of the generated block 20 will be different. Only when the block 20 can obtain macroscopically uniform properties, the block 20 may be used to perform particle arrangement 40.

[0048] The arrangement unit 12 may calculate the physical properties of the block 20 and determine whether the calculated physical properties are appropriate. In this case, the arrangement unit 12 stores in advance information for performing these calculations (e.g., criteria for making the above-mentioned determination). If the arrangement unit 12 determines that the calculated physical properties are appropriate, it performs an arrangement 40 of the initial state of particles in space. If the arrangement unit 12 determines that the calculated physical properties are inappropriate, it instructs the block generation unit 11 to generate a new block 20 under different conditions. In this case, the arrangement unit 12 stores in advance how to change the conditions for generating the block 20.

[0049] A particle simulation is performed using the initial particle arrangement 40 in space generated by the arrangement unit 12. The particle arrangement system 10 may have a particle simulation function and perform the particle simulation. Alternatively, the particle simulation may be performed in a system other than the particle arrangement system 10. In this case, the arrangement unit 12 outputs (transmits) information indicating the initial particle arrangement 40 in space to that system. The above is the function of the particle arrangement system 10 according to this embodiment.

[0050] Next, a particle arrangement method, which is a process executed by the particle arrangement system 10 according to this embodiment (an operation method performed by the particle arrangement system 10), will be described with reference to the flowchart of FIG.

[0051] In this process, first, the block generator 11 fills particles into a region where the x and y directions are periodic boundaries but the z direction is not periodic (S01, block generation step). As described above, this filling results in the particles being in the state shown in FIG. 3(a). Next, the block generator 11 creates a block where the z direction is a periodic boundary (S02, block generation step). This process is performed by setting two partial regions 23 and 24 that are continuous in the z direction as shown in FIGS. 3(a) and 3(b) as described above, and moving the particles in the upper partial region 23 in the z direction to below the position where the particles are filled.

[0052] Next, the block generator 11 performs a simulation to move the particles contained in the partial region 23 closer to the partial region 24, i.e., a simulation to compress the block at this point in the z direction (S03, block generation step). This process is performed so that the particles change from the state shown in FIG. 3(b) to the state shown in FIG. 3(c). Next, the block generator 11 repeats a relaxation calculation for the block (S04, block generation step). The relaxation calculation homogenizes the particle arrangement and is performed as shown in FIGS. 3(c) and 3(d) as described above. The above processes (S01 to S04) generate a block 20 having a shape that can be combined in space without gaps, all boundaries of which are periodic, and particles arranged inside.

[0053] Next, the placement unit 12 places particles by combining a plurality of blocks 20 generated by the block generation unit 11 so that corresponding periodic boundaries are adjacent in space (S05, placement step). As described above, at this time, particles placed at positions other than the area where particles to be used in the simulation are to be placed may be deleted. The generated initial state placement 40 of particles is used for particle simulation. The above is the processing executed by the particle placement system 10 according to this embodiment.

[0054] In this embodiment, all boundaries are periodic boundaries, and particles are arranged by combining blocks 20 inside which particles are arranged. Therefore, even if the number of particles increases, the particles can be arranged by combining blocks in the area where the particles are to be arranged. The process of combining blocks 20 is simple, so the calculation cost is low. Furthermore, the number of particles handled when creating a block can be made small compared to the number of particles to be arranged. Therefore, the calculation cost of creating blocks 20 is also small compared to conventional particle arrangement. Therefore, according to this embodiment, even if the number of particles to be simulated increases, the calculation cost of particle arrangement can be reduced and the particles can be appropriately arranged.

[0055] Alternatively, as in this embodiment, particles may be placed inside a region in which boundaries other than a predetermined one direction (e.g., planes 21 in the x and y directions) are periodic boundaries, and a partial region 23 having a thickness in that one direction (e.g., the z direction) may be set in that region, and the particles included in that partial region 23 may be moved while maintaining a fixed positional relationship to generate a block with the boundary of that partial region 23 as a periodic boundary. Furthermore, in this case, the particles may be placed inside the region by applying a force (e.g., gravity) to the particles to move them. This configuration makes it possible to easily and appropriately generate blocks in which all boundaries are periodic boundaries. As a result, particles can be placed easily and reliably.

[0056] However, blocks in which all boundaries are periodic boundaries do not necessarily have to be generated in the manner described above, and may be generated by other methods.Furthermore, when arranging particles inside the above-described region, it is not necessarily necessary to use a method of applying a unidirectional force to the particles to move them, and for example, a method of randomly generating particles within the region may be used.

[0057] Furthermore, as in this embodiment, a process for homogenizing the particle arrangement within a block may be performed. Specifically, the homogenization process may involve fixing the positions of particles near a predetermined position in one direction (e.g., the z direction) in the block, and repeatedly simulating the movement of particles whose positions are not fixed (relaxation calculation) while changing the predetermined position. This configuration can suppress bias in the particle arrangement in each block 20, resulting in a homogenized particle arrangement. However, the homogenization process is not necessarily required. Furthermore, when the homogenization process is performed, it may be performed by a method other than the above.

[0058] In the above-described embodiment, the space in which the particles are arranged is a three-dimensional space, but it may be a space other than three-dimensional, for example, a two-dimensional space. In this case, the block 20 used to arrange the particles may have a dimensional shape corresponding to the space in which the particles are arranged.

[0059] Next, we will explain a particle placement program for executing the above-mentioned series of processes by the particle placement system 10. As shown in Fig. 5, the particle placement program 100 is stored in a program storage area 111 formed in a computer-readable recording medium 110 that is inserted into a computer and accessed, or that is provided in the computer. The recording medium 110 may be a non-transitory recording medium.

[0060] The particle placement program 100 is configured to include a block generation module 101 and a placement module 102. The functions realized by executing the block generation module 101 and the placement module 102 are similar to the functions of the block generation unit 11 and the placement unit 12 of the particle placement system 10 described above, respectively.

[0061] The particle placement program 100 may be configured so that a part or all of it is transmitted via a transmission medium such as a communication line, and is received and recorded (including installed) by another device. Also, each module of the particle placement program 100 may be installed not in one computer but in one of multiple computers. In that case, the above-mentioned series of processes are performed by a computer system consisting of the multiple computers. [Explanation of symbols]

[0062] 10...particle placement system, 11...block generation unit, 12...placement unit, 100...particle placement program, 101...block generation module, 102...placement module, 110...recording medium, 111...program storage area.

Claims

1. A particle placement system for placing particles to be simulated in a simulation space, a block generating means for generating a block having a shape that can be combined with a plurality of other shapes without gaps in the space, all of whose boundaries are periodic boundaries, and in which the particles are arranged; an arrangement means for arranging particles by combining a plurality of blocks generated by the block generation means so that corresponding periodic boundaries are adjacent to each other in the space; Equipped with The block generation means In a region in which particles are arranged and in which boundaries other than a predetermined one direction are periodic boundaries, two partial regions are set that have a thickness in the one direction and are continuous in the one direction; a particle included in one of the two partial regions is moved to one end of the region in the one direction while fixing the positional relationship, so that the surface where the two partial regions were in contact with each other faces outward; A particle placement system that generates the block by removing particles that are outside the other of the two partial regions and making the contacting surface of the other partial region the other end of the region in the one direction.

2. 2. The particle placement system according to claim 1, wherein the block generation means places the particles inside the region by applying the force in one direction to the particles to move them.

3. A particle placement system for placing particles to be simulated in a simulation space, a block generating means for generating a block having a shape that can be combined with a plurality of other shapes without gaps in the space, all of whose boundaries are periodic boundaries, and in which the particles are arranged; an arrangement means for arranging particles by combining a plurality of blocks generated by the block generation means so that corresponding periodic boundaries are adjacent to each other in the space; Equipped with the block generation means performs a process of homogenizing the arrangement of particles within the block; The block generation means performs the homogenization process by In a block in which particles are arranged and whose boundary is a periodic boundary, two partial regions are set that have a thickness in one direction and are continuous in the one direction, moving all of the particles of the block in the one direction while keeping the positional relationship between the particles fixed so that the particles included in the two partial regions are positioned at one end and the other end of the block in the one direction, a simulation of the movement of particles in a region sandwiched between the two partial regions, in which the positional relationships of the particles included in the two partial regions moved to the one end and the other end are fixed with respect to the respective partial regions, and the other particles are allowed to move freely; The particle placement system repeats the above process while changing the positions of the two partial regions.

4. A particle placement method in which a particle placement system places simulation target particles in a simulation space, comprising: a block generation step in which the particle arrangement system generates a block having a shape that can be combined with a plurality of other blocks in the space without gaps, all of whose boundaries are periodic boundaries, and in which the particles are arranged; an arrangement step in which the particle arrangement system arranges particles by combining a plurality of blocks generated in the block generation step so that corresponding periodic boundaries are adjacent to each other in the space; Run In the block generation step, In a region in which particles are arranged and in which boundaries other than a predetermined one direction are periodic boundaries, two partial regions are set that have a thickness in the one direction and are continuous in the one direction; a particle included in one of the two partial regions is moved to one end of the region in the one direction while fixing the positional relationship, so that the surface where the two partial regions were in contact with each other faces outward; A particle placement method for generating the block by removing particles that are outside the other of the two partial regions and making the contacting surface of the other partial region the other end of the region in the one direction.

5. A particle placement method in which a particle placement system places simulation target particles in a simulation space, comprising: a block generation step in which the particle arrangement system generates a block having a shape that can be combined with a plurality of other blocks in the space without gaps, all of whose boundaries are periodic boundaries, and in which the particles are arranged; an arrangement step in which the particle arrangement system arranges particles by combining a plurality of blocks generated in the block generation step so that corresponding periodic boundaries are adjacent to each other in the space; Run In the block generation step, a process of homogenizing particle arrangement within the block is performed; In the block generation step, the homogenization process is In a block in which particles are arranged and whose boundary is a periodic boundary, two partial regions are set that have a thickness in one direction and are continuous in the one direction, moving all of the particles of the block in the one direction while keeping the positional relationship between the particles fixed so that the particles included in the two partial regions are positioned at one end and the other end of the block in the one direction, a simulation of the movement of particles in a region sandwiched between the two partial regions, in which the positional relationships of the particles included in the two partial regions moved to the one end and the other end are fixed with respect to the respective partial regions, and the other particles are allowed to move freely; The particle placement method repeats the above process while changing the positions of the two partial regions.

6. A particle placement program that causes a computer to operate as a particle placement system that places particles to be simulated in a simulation space, The computer, a block generating means for generating a block having a shape that can be combined with a plurality of other shapes without gaps in the space, all of whose boundaries are periodic boundaries, and in which the particles are arranged; an arrangement means for arranging particles by combining a plurality of blocks generated by the block generation means so that corresponding periodic boundaries are adjacent to each other in the space; It functions as The block generation means In a region in which particles are arranged and in which boundaries other than a predetermined one direction are periodic boundaries, two partial regions are set that have a thickness in the one direction and are continuous in the one direction; a particle included in one of the two partial regions is moved to one end of the region in the one direction while fixing the positional relationship, so that the surface where the two partial regions were in contact with each other faces outward; a particle placement program that generates the block by removing particles that are outside the other of the two partial regions and setting the contacting surface of the other partial region as the other end of the region in the one direction.

7. A particle placement program that causes a computer to operate as a particle placement system that places particles to be simulated in a simulation space, The computer, a block generating means for generating a block having a shape that can be combined with a plurality of other shapes without gaps in the space, all of whose boundaries are periodic boundaries, and in which the particles are arranged; an arrangement means for arranging particles by combining a plurality of blocks generated by the block generation means so that corresponding periodic boundaries are adjacent to each other in the space; It functions as the block generation means performs a process of homogenizing the arrangement of particles within the block; The block generation means performs the homogenization process by In a block in which particles are arranged and whose boundary is a periodic boundary, two partial regions are set that have a thickness in one direction and are continuous in the one direction, moving all of the particles of the block in the one direction while keeping the positional relationship between the particles fixed so that the particles included in the two partial regions are positioned at one end and the other end of the block in the one direction, a simulation of the movement of particles in a region sandwiched between the two partial regions, in which the positional relationships of the particles included in the two partial regions moved to the one end and the other end are fixed with respect to the respective partial regions, and the other particles are allowed to move freely; A particle placement program that repeats the above process while changing the positions of the two partial regions.

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