JP7730538B2 - PARTICLE ARRANGEMENT SYSTEM, PARTICLE ARRANGEMENT METHOD, AND PARTICLE ARRANGEMENT PROGRAM - Google Patents

Description

The present invention relates to a particle placement system, a particle placement method, and a particle placement program for placing particles to be simulated in a simulation space.

The behavior of multiple particles is analyzed using particle-based simulations such as the Discrete Element Method (DEM). To perform a simulation, the particles to be simulated must first be placed in the simulation space. Methods for automatically placing particles have been proposed. For example, Patent Document 1 shows a method in which particles are placed in a way that allows them to overlap, and then the particles are moved to eliminate any overlap.

Japanese Patent Application Laid-Open No. 2006-259910

However, methods such as those described in Patent Document 1 require information processing such as simulation or judgment for the initial placement of each particle, and the computational cost increases as the number of particles to be simulated increases.

Other methods for arranging particles include, for example, drop-filling, which involves generating an arbitrary initial group of particles in a simulation space, simulating the particles falling into a preset frame due to gravity, and filling the frame with particles. Another method involves randomly generating particles sequentially in a simulation space, and then discarding, moving, growing, and adopting particles based on preset constraints. As with the method described in Patent Document 1, these methods also incur high computational costs as the number of particles to be simulated increases. Furthermore, the procedure becomes complicated when packing particles into an arbitrary shape.

The present invention was made in consideration of the above, and aims to provide a particle placement system, particle placement method, and particle placement program that can reduce the calculation cost of particle placement and properly place particles, even when the number of particles to be simulated is large.

To achieve the above objective, the particle placement system of the present invention is a particle placement system that places simulation target particles in a simulation space, and includes: a block generation means that generates blocks with shapes that can be combined 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 in space.

In the particle placement system of 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 is large, particles can be placed by combining blocks in the area where the particles are to be placed. Because the process of combining blocks is simple, 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, with the particle placement system of the present invention, even when the number of particles to be simulated is large, the computational cost of particle placement can be kept low and particles can be placed appropriately.

The block generating means generates a block by setting two partial regions having a thickness in one direction and continuous in the one direction in a region in which particles are arranged and boundaries other than a predetermined one direction are periodic boundaries , moving particles included in one of the two partial regions to one end of the region in one direction while fixing their positional relationship so that the surface where the two partial regions contact each other is on the outside , removing particles outside the other of the two partial regions, and setting the surface where the other partial region contacted as the other end of the region in the one direction . The block generating means may also arrange particles within the region by applying a force to the particles in one direction to move them. This configuration allows blocks to be generated easily and appropriately. As a result, particles can be arranged easily and reliably.

Alternatively, the block generation means performs a process of homogenizing the particle arrangement within the block. Furthermore, as the homogenization process, the block generation means sets two partial regions having a thickness in one direction and continuous in that direction in a block having particles arranged therein and 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, respectively, fixes the positional relationship of the particles included in the two partial regions moved to one end and the other end with respect to the respective partial regions, and performs a simulation of 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 . This configuration makes it possible to suppress bias in the particle arrangement within each block and achieve a homogenized particle arrangement.

Incidentally, in addition to being described as a particle placement system invention as described above, the present invention can also be described as a particle placement method and particle placement program invention as described below. These are essentially the same inventions, just in different categories, and achieve similar functions and effects.

[0013] That is, a particle placement method according to the present invention is a particle placement method in which a particle placement system places particles to be simulated in a simulation space, the particle placement system performing the following steps: a block generation step in which the particle placement system generates blocks having a shape that can be combined in multiple blocks without gaps in space, all of whose boundaries are periodic boundaries, and in which particles are placed inside; and an placement step in which the particle placement system combines multiple blocks generated in the block generation step so that corresponding periodic boundaries in space are adjacent to each other. In the block generation step, two partial regions having a thickness in one direction and being continuous in the one direction are set in a region in which particles are placed inside and whose boundaries other than a predetermined one direction are periodic boundaries, and particles included in one of the two partial regions are moved, while fixing their positional relationship, to one end of the one direction of the region so that the surface where the two partial regions 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 contacted is set as the other end of the one direction of the region, thereby generating a block. Alternatively, in the block generation step, a process for homogenizing the arrangement of particles 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.

Furthermore, a 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 simulation space, and causes the computer to function as: a block generation means that generates blocks having a shape that can be combined in multiple blocks in space without gaps, all of whose boundaries are periodic boundaries, and in which particles are placed; and a placement means that arranges particles by combining multiple blocks generated by the block generation means so that corresponding periodic boundaries are adjacent in space. The block generation means sets two partial regions that have a thickness in one direction and are continuous in the one direction in a region in which particles are placed and whose boundaries other than a predetermined one direction are periodic boundaries, moves particles included in one of the two partial regions to one end in the one direction of the region while fixing their positional relationship so that the surface where the two partial regions contact is on the outside, removes particles that are outside the other of the two partial regions, and sets the surface where the other partial region contacted as the other end of the region in the one direction, thereby generating a block. Alternatively, the block generation means performs a process of homogenizing the arrangement of particles inside 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 the respective partial regions, 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.

According to the present invention, even when the number of particles to be simulated is large, it is possible to reduce the calculation cost for particle placement and to place the particles appropriately.

FIG. 1 is a diagram illustrating a functional configuration of a particle placement system according to an embodiment of the present invention. FIG. 1 is a diagram showing an outline of particle arrangement. FIG. 10 is a diagram for explaining block generation. 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. 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.

Embodiments of a particle placement system, particle placement method, and particle placement program according to the present invention will be described in detail below with reference to the drawings. Note that in the description of the drawings, identical elements will be given the same reference numerals, and duplicate explanations will be omitted.

Figure 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 (with a constant distance from the center to the surface). However, the particles may also have shapes other than those mentioned above.

A 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 the 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 also handle many particles, i.e., perform large-scale particle method calculations.

The particles that are the subject of the above simulation, i.e., the particles that are the subject of placement by the particle placement system 10, include any particles that have been the subject of conventional particle simulations. For example, soil or powder can be the subject. Alternatively, fluids or solids can be assumed to be made up of multiple particles and treated as the subject.

The above simulations are used to simulate natural phenomena such as landslides. In this case, collections of particles correspond to geological layers (e.g., sedimentary layers, rock, or sand layers). The above simulations may also be used in any field, such as academia, industry, games, and computer graphics (CG). For example, they 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.

To perform a simulation, particles must be placed in space as the initial state of the simulation. The particle placement system 10, for example, places particles in space as the initial state of the simulation. When placing particles in space as the initial state, the placement must appropriately represent the object to be simulated. For example, when simulating a landslide, the placed particles must be filled homogeneously in areas that appropriately correspond to the strata.

Specifically, the particle placement system 10 is configured by a computer including hardware such as a CPU (Central Processing Unit), GPU (Graphics Processing Unit), and memory. The functions of the particle placement system 10, which will be described later, are realized by these components operating through programs, etc. The particle placement system 10 may be implemented by a single computer, or by a computer system consisting of multiple computers connected 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 instead be configured to include only a CPU.

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 collection 30. Next, the particle placement system 10 deletes particles not used in the simulation from the block collection 30, as shown in FIG. 2(c), to create an initial particle placement 40.

Next, we will explain the functions of the particle placement system 10 according to this embodiment. As shown in FIG. 1, the particle placement system 10 is configured to include a block generation unit 11 and a placement unit 12.

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 place particles inside a region whose boundaries other than a predetermined one direction are periodic boundaries, set a partial region within the region that has a thickness in that one direction, and move the particles contained 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 place 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 a homogenization process, the block generation unit 11 may fix the positions of particles near a predetermined position in one predetermined direction in the block 20, and repeatedly simulate the movement of particles whose positions are not fixed while changing the predetermined position.

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 conditions). That is, the block 20 is a full-surface periodic boundary particle block. Of the faces constituting the rectangular parallelepiped block 20, the opposing faces form corresponding periodic boundaries. Furthermore, as described above, because the blocks 20 are rectangular parallelepipeds, 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 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, it is possible to combine another block 20 by closely contacting periodic boundaries in the direction of any face of the block 20. This makes it possible to generate a block assembly 30 that includes any initial state arrangement 40, as described above.

The block generator 11 generates blocks 20 as follows. The block generator 11 places particles inside a region whose boundaries other than one preset direction are periodic boundaries. For example, as shown in Figure 3(a), the block generator 11 forms a region whose periodic boundaries are four faces 21 perpendicular to the x direction (x-axis) and y direction (y-axis) of space. Note that the diagram shown in Figure 3 is a view parallel to the xy plane of space, with the vertical direction being the z direction. Some of these faces 21 become the faces of the block 20. The process of making the faces of a region periodic boundaries can be performed in the same way as in conventional methods (the same applies below).

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 the above region is viewed from above in the z direction, it forms a rectangle composed of 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 region in the z direction. The block generator 11 pre-stores particle parameters used for particle placement, such as particle radius, 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 pre-stores parameters for the simulation, such as the friction coefficient, elastic coefficient, viscous damping coefficient, and restitution coefficient, and uses these parameters in the simulation.

The block generation unit 11 performs a simulation in which a downward force in the z direction, such as 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 Figure 3(a). In other words, the block generation unit 11 performs gravity-fall 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.

In this way, the block generation unit 11 applies a z-direction force to the generated particles to move them within the region whose periodic boundaries are the x-direction and y-direction surfaces 21 other than the pre-set z-direction, thereby placing the particles within the region.

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 portion of the thickness in the z direction. The positions of the two partial regions 23, 24 are such that the 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 contained in the partial regions 23, 24 form at least one layer.

The two partial regions 23, 24 are continuous in the z direction. The block generation unit 11 moves particles contained in the partial region 23, for example, particles whose center of gravity is contained in the partial region 23, to the bottom of the surface 22 as shown in FIG. 3(b), while keeping their position relative to the partial region 23 fixed. This movement is only in the z direction; their positions in the x and y directions remain unchanged. At this time, of 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 for particle deletion may be adjusted so that the number of particles or particle volume fraction of the particles contained in the final 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 contained in the block 20. Furthermore, particles above the partial region 23 in the z direction are not used in subsequent processing.

When moving particles in partial region 23 downward, the block generation unit 11 moves them to a position where there is a gap 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 Figure 3(b), in the particle collection configured in this way, 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 generation unit 11 considers the upper and lower surfaces in the z direction of the region where the particles shown in Figure 3(b) are located to be periodic boundaries.

Next, the block generation unit 11 fixes the positional relationship of particles contained in partial region 23, for example, particles whose center of gravity is in partial region 23, relative to partial region 23. The block generation unit 11 also fixes the positional relationship of particles contained in partial region 24, for example, particles whose center of gravity is in partial region 24, relative to partial region 24. Other particles are allowed to move freely in space. In this state, the block generation unit 11 performs a simulation to move the particles contained in partial region 23 closer to 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 simulates the movement of particles in the region sandwiched between partial region 23 and partial region 24. Note that during this simulation, gravity may or may not be applied to the particles.

The block generation unit 11 moves the particles until the distance between the outer surface of the partial region 23 (lower in the z direction) and the outer surface of the partial region 24 (upper in the z direction) after the movement reaches the preset length of the block 20 to be finally generated. Figure 3(c) shows the 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 Figure 3(b)). Note that the distance between the outer surface of the partial region 23 (lower in the z direction) and the outer surface of the partial region 24 (upper in the z direction) before the movement 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 moving the partial region 23, the greater 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 by treating the particles contained in the moved partial region 23 as the lower lid in the z direction and the particles contained in the moved partial region 24 as the upper lid in the z direction.

The above process allows for the generation of blocks with each face of a rectangular parallelepiped as a periodic boundary. However, the generated blocks have biased particle placement. This bias in particle placement is due to partial regions 23 and 24, where the particle positions were fixed. The block generation unit 11 homogenizes the particle placement to remove the bias in particle placement in the block as follows:

The block generated as 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 the particles as a whole can be moved (shifted) in the z direction while the positional relationships between particles remain fixed.

When the block is in the state shown in Figure 3(c), the block generation unit 11 sets two partial regions 25, 26 in the block, each having a thickness in the z direction. The two partial regions 25, 26 may be the same size as the two partial regions 23, 24 described above. The two partial regions 25, 26 are located at predetermined positions other than the two partial regions 23, 24 described above. The two partial regions 25, 26 are continuous in the z direction.

As shown in Figure 3(d), the block generation unit 11 moves (shifts) all of the particles in the z direction while keeping the positional relationship between the particles fixed so that the particles contained 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 Figure 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 Figure 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.

Next, the block generation unit 11 fixes the positional relationship of particles contained in partial region 25, for example, particles whose center of gravity is in partial region 25, relative to partial region 25. The block generation unit 11 also fixes the positional relationship of particles contained in partial region 26, for example, particles whose center of gravity is in partial region 26, relative to 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 between partial regions 25 and 26. Note that during this simulation, gravity may or may not be applied to the particles. In this simulation, particles contained in the two partial regions 23 and 24, whose positional relationships were fixed in the above-mentioned processing, are also moved. In other words, this simulation is a relaxation calculation that relieves the load on the particles. This relaxation reduces bias in the particle placement.

The block generation unit 11 then sets two new partial regions 25 and 26 (the process shown in Figure 3(c)) and performs the above-mentioned relaxation calculation (the process shown in Figure 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 across the entire block becomes negligible in terms of simulation. For example, the relaxation calculation simulation is repeated until a globally uniform internal contact stress is generated in each particle. Alternatively, the above repetition may be performed a preset number of times.

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.

The block generation unit 11 outputs information indicating the block 20 generated as described above, specifically information indicating the placement positions of the particles included in the block (e.g., coordinate information in the block), to the placement unit 12.

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 in space. The placement unit 12 inputs information indicating the blocks 20 from the block generation unit 11. Using the input information, the placement unit 12 combines and places 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 the user and stored in the placement unit 12. The placement unit 12 combines multiple blocks 20 so that corresponding periodic boundaries are adjacent with no gaps.

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 the block collection 30 formed by combining blocks 20. Note that if there are no particles placed in positions that are not in those areas, no particles are deleted. In this way, the initial state placement 40 of particles in space is performed.

Before or after the placement unit 12 places the particles in their initial state 40, the physical properties of the block 20 itself or the combination of blocks 20 may be calculated to confirm whether the particle placement 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 and other 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.

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 are different. Particle arrangement 40 may be performed using the block 20 only if the block 20 can obtain macroscopically homogeneous properties.

The placement unit 12 may calculate the physical properties of the above-mentioned block 20 and determine whether the calculated physical properties are appropriate. In this case, the placement unit 12 pre-stores information for performing these calculations (e.g., criteria for making the above-mentioned determination). If the placement unit 12 determines that the calculated physical properties are appropriate, it performs an initial state placement 40 of particles in space. If the placement 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 placement unit 12 pre-stores how to change the conditions for generating the block 20.

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 particle simulation functionality and perform particle simulation. Alternatively, 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. These are the functions of the particle arrangement system 10 according to this embodiment.

Next, we will explain the particle placement method, which is the processing executed by the particle placement system 10 according to this embodiment (the operating method performed by the particle placement system 10), using the flowchart in Figure 4.

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

Next, the block generator 11 performs a simulation to move the particles contained in subregion 23 closer to subregion 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 described above, as shown in FIGS. 3(c) and 3(d). The above process (S01 to S04) generates a block 20 with a shape that can be combined in space without gaps, all boundaries of which are periodic, and particles arranged inside.

Then, the placement unit 12 places particles by combining multiple 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 in positions that are not in the area where particles used in the simulation are to be placed may be deleted. The generated initial particle placement 40 is used in the particle simulation. The above is the processing executed by the particle placement system 10 according to this embodiment.

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 is large, particles can be arranged by combining blocks in the area where the particles are to be arranged. Because the process of combining blocks 20 is simple, 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 arranged. Therefore, the computational cost of creating blocks 20 is also small compared to conventional particle arrangements. Therefore, according to this embodiment, even if the number of particles to be simulated is large, the computational cost of particle arrangement can be reduced and the particles can be arranged appropriately.

Also, as in this embodiment, particles may be placed inside a region whose boundaries in a direction other than a predetermined one (e.g., surfaces 21 in the x and y directions) are periodic boundaries, 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 contained 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 in one direction (e.g., gravity) to the particles to move them. With this configuration, blocks whose boundaries are all periodic boundaries can be easily and appropriately generated. As a result, particles can be placed easily and reliably.

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

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 preset direction in the block (e.g., the z direction), and repeatedly simulating the movement of particles whose positions are not fixed (relaxation calculation) while changing the predetermined position. With this configuration, it is possible to reduce bias in the particle arrangement within each block 20, resulting in a homogenized particle arrangement. However, the homogenization process does not necessarily have to be performed. Furthermore, even if the homogenization process is performed, it may be performed using a method other than the above.

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

Next, we will explain the 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 on a computer-readable recording medium 110 that is inserted into a computer and accessed, or that is provided on the computer. The recording medium 110 may also be a non-transitory recording medium.

The particle placement program 100 is composed of 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.

The particle placement program 100 may be configured so that 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. Furthermore, each module of the particle placement program 100 may be installed on one of multiple computers, rather than on a single computer. In this case, the above-described series of processes is performed by a computer system consisting of the multiple computers.

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 (7)

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. 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. 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 . A particle placement method in which a particle placement system places simulation target particles in a simulation space, the method 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 . A particle placement method in which a particle placement system places simulation target particles in a simulation space, the method 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 . 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 . 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 .