JP5668373B2 - Simulation apparatus, program, and method - Google Patents

Description

  The present specification relates to a visualization technique for fluid simulation by a computer.

  Recent advances in computer technology have increased the number of cases where large-scale numerical calculations are performed on a physical phenomenon and the results are displayed on a high-resolution display device to understand the physical phenomenon. Furthermore, more objects can be displayed simultaneously on a display device, and the objects can be displayed in real time while interactively specifying enlargement / reduction and rotation of the objects.

  On the other hand, as a display method when the calculation result is a vector field, there is a method called particle flow. Particle flow is a technique for expressing a flow by moving massless microparticles called particles along the direction of a surrounding vector placed at an arbitrary time. Thanks to the improved performance of computers, it has become possible to distribute a larger number of particles in a wider range and to check the flow of very fine areas.

JP-A-4-320589 JP-T-2001-502097 JP 2007-188502 A

Avizo Online Help, [on line], [Search August 16, 2010], Internet <http://docs.drabba.net/avizo/6.1.0/hxvectorfieldanimation/HxParticlesCompute.html>

  Even if a large number of particles can be displayed simultaneously, human vision and recognition are limited. For example, consider a case where a vertical vortex in a turbulent boundary layer is simulated and the result is observed by particle flow. In this case, while a large number of particles that do not represent a vortex move macroscopically, particles move around a number of small vortices, while particles that move as if walking around the vortex are also displayed. As a result, the particles show complex movements, which are not likely to be followed by the eyes and are likely to cause misrecognition.

  Therefore, it is difficult to track the three-dimensional behavior of the particles due to the complicated behavior of the particles. Further, since the particles do not indicate a region, it is difficult to display the shape of a part such as a vortex region.

  In view of the above problems, the present specification provides a simulation apparatus, the program, and the method that can track the three-dimensional behavior of particles.

  An example of the simulation apparatus described in this specification includes a speed calculation unit, a grouping unit, and a drawing information generation unit. The velocity calculation unit calculates the velocity of the particle at each position based on simulation result information regarding the physical quantity of the particle for each hour calculated by simulation of the fluid flow.

  The grouping unit calculates a distance between the two particles based on the position of the particles. The grouping unit calculates a speed difference between the two particles based on the speed of the particles. The grouping unit groups the two particles when the distance between the particles is smaller than a first threshold and the speed difference between the particles is smaller than a second threshold.

  The drawing information generation unit generates drawing information for drawing a display object indicating the behavior of the two grouped particles based on the velocity vector of the two grouped particles.

  According to an example of the simulation apparatus described in this specification, it becomes easy to track the three-dimensional behavior of particles.

It is a figure which shows an example of a particle flow. It is a figure for demonstrating the grouping visualization of a particle flow. It is a figure which shows the color classification regulation (color classification by the front and back of a surface) at the time of visualization of the grouped particle. It is a figure which shows the color classification regulation (color classification by the amount of twist of a vector) at the time of visualization of the grouped particle. It is a figure which shows an example of a function structure of the simulation system which performs the simulation of the flow of the fluid in 1st Embodiment. It is a figure which shows an example of the particle position table. It is a figure which shows an example of the particle position speed table. It is a figure which shows an example of the grouping table. It is a figure which shows the whole flow of the grouping visualization process of a particle flow. It is a figure which shows the detailed flow of the group search process of S11 of FIG. It is a figure which shows the detailed flow of the visualization process of S14 of FIG. 9 in 1st Embodiment. It is a figure for demonstrating visualization of the grouped particle in 2nd Embodiment. It is a figure which shows an example of a function structure of the simulation system which performs the simulation of the flow of the fluid in 2nd Embodiment. 3 is a diagram illustrating an example of a line drawing table 21. FIG. It is a figure which shows the detailed flow of the visualization process of S14 of FIG. 9 in 2nd Embodiment. It is a block diagram of the hardware environment of the simulation system.

<First Embodiment>
FIG. 1 shows an example of a particle flow. FIG. 1A shows a particle flow that forms two adjacent vortices. An arrow drawn in a curve indicates the direction of the vortex. Other small arrows drawn with straight lines indicate the direction of the particles. In order to make it easy to recognize the shape of the vortex, a contour line on the side surface for forming a substantially cylindrical shape having an upper surface and a bottom surface with arrows drawn by a pair of curves is drawn for convenience.

  When only particles are displayed, there is no sense of depth in the displayed content, and the movement of the particles is difficult to understand. For example, in the right vortex, the particles are turning counterclockwise. In the vortex on the left, the particles are turning clockwise.

  If the depth cannot be recognized in the display content, the movement of the particles on the front side and the back side of the outer edge of the substantially cylindrical vortex may be recognized as the movement on the same plane. In this case, the vortex shape cannot be recognized.

FIG. 1B shows a plurality of generated particle flows. As shown in FIG. 1B, when a plurality of particle flows are generated, it is difficult to recognize an area only with particles.
By the way, as a trap of human recognition, there is a tendency to try to understand a large number of objects as “lumps”, which is called “grouping” in the field of psychology. A random and complex arrangement of points is automatically divided into clusters in the observer's brain and recognized as "one point in a grouped group". For example, in the above vortex particle visualization example, if there are particles that you want to see and have similar movements in the vicinity, it is quite natural to recognize them as a lump. is there.

  Therefore, particles that are close in position and move at a specific speed are grouped and visualized from a large number of particles that move in a complicated manner. This will be described with reference to FIG.

  FIG. 2 is a diagram for explaining grouped visualization of particle flows. FIG. 2A is a grouped visualization of the particle flow of FIG. FIG. 2B is a grouped visualization of the particle flow of FIG.

  In FIGS. 2A and 2B, a surface is generated by grouping particles that are close in position and moving at a specific speed from a large number of particles that move in a complex manner. It is color-coded according to the side, back side, and vortex boundary region. 2A and 2B are diagrams in which surface generation for one step is performed in the process described later.

  Compared to FIGS. 1A and 1B, in FIGS. 2A and 2B, the display content has a sense of depth, and visually, the front side, the back side, and the boundary region between the vortices It is easy to understand the behavior of the particles. Note that if a surface for an arbitrary step is generated according to the flow characteristics, the boundary surface can also be expressed approximately.

As described above, the grouping visualization enables to display the “cluster” of the particles as a surface, so that the three-dimensional behavior of the particles can be easily traced.
In addition, if the distance from the vortex center of the particles moving in a vortex is the same, the speed of the particles will be about the same. Therefore, particles moving around the outer periphery of the vortex region can be extracted by extracting the particles with a certain speed threshold. Of the extracted particles, if particles that are close to each other and move at a specific speed are drawn so as to be connected, the vortex region appears to be circular along the outer edge when viewed as a whole even though it is cut finely . Therefore, the shape of a part like a vortex is displayed and the vortex is easily recognized.

  Furthermore, grouped visualization of particle flows will be described. As a specific particle flow grouping visualization method, two triangles are formed between two vectors formed by two particles in a certain range, and grouping visualization is performed by drawing the triangles.

  FIG. 3 shows color-coding restrictions (color-coding by the front and back of a surface) at the time of visualization of the grouped particle. The direction of the normal vector on each surface side is different between the front side and the back side of the outer periphery of the vortex. Paying attention to this, the surface formed by the grouped particles on the front side of the outer periphery of the vortex and the surface formed by the grouped particles on the back side are colored differently. .

For example, the start point and end point of the velocity vector P ₀ P ₁ of the first particle and the start point and end point of the velocity vector Q ₀ Q ₁ of the second particle, which are close in position and move at a specific speed, Create two triangular faces from four points.

  Then, when the direction of the normal vector of the triangular surface is in the line-of-sight direction (that is, the front side of the surface) (FIG. 3A), and when the direction is opposite (that is, the back side of the surface) (FIG. 3 (B)), different colors are displayed for each surface (color coding).

FIG. 3A shows a surface when the normal is facing forward (the normal direction is based on the line segment P ₀ P ₁ ), that is, a surface on the front side of the outer periphery of the vortex. FIG. 3B shows a surface in the case where the normal is away (the normal direction is based on the line segment P ₀ P ₁ ), that is, a surface on the back side of the outer periphery of the vortex. In this way, color coding is performed according to the direction of the surface in the normal direction.
Thereby, as shown in FIG. 2, it becomes easy to recognize whether the particle passes the near side of the vortex or the far side.

  FIG. 4 shows color-coding restrictions (color-coding based on the amount of vector twist) when visualizing grouped particles. Particles at the boundary between vortices behave in such a way that adjacent particles are divided into separate vortex centers. Therefore, when attention is paid to the direction of the velocity vector of the particles, they are directed to twisted directions.

Therefore, when the velocity vector P ₀ P ₁ of the first particle and the velocity vector Q ₀ Q _{1 of} the second particle are in the same plane (FIG. 4A), or when they are twisted (FIG. 4B )) And a different display (for example, color-coded).

As a method for detecting this twist, for example, the following method can be considered. First, the start point and end point of the velocity vector P ₀ P ₁ of the first particle and the start point and end point of the velocity vector Q ₀ Q ₁ of the second particle, which are close in position and move at a specific speed, Create two triangular faces from four points. Then, the normal directions of the triangular surfaces are compared.

As shown in FIG. 4A, the direction of the normal line a of the triangle P ₀ P ₁ Q _{0 and} the normal line b of the triangle Q ₀ Q ₁ P ₁ are aligned at the outer periphery of the vortex. From this, it can be seen that the triangle P ₀ P ₁ Q ₀ and the triangle Q ₀ Q ₁ P ₁ are not twisted. On the other hand, as shown in FIG. 4B, the direction of the normal line a and the direction of the normal line b are twisted in the vortex boundary region. From this, it can be seen that the triangle P ₀ P ₁ Q ₀ and the triangle Q ₀ Q ₁ P ₁ are twisted.

In this way, it is possible to show not only the vortex region but also the boundary between vortices according to the angle of the two normals.
Incidentally, here, as a rule for determining the direction of the normal line, for example, “trace the vertex of the triangle in the direction of the vector above the vector P ₀ P ₁ and the vector Q ₀ Q ₁ (in the positive direction on the y-axis). , The direction of facing up in the left hand system ".

  There are two reasons why such a technique has not existed in the past. First, as a first reason, it is considered that it has been several years that a large number of vortex regions can be output by a large-scale simulation. As a second reason, when a calculation that outputs many vortex regions by large-scale simulation is not performed as in the first reason, generally, an isosurface display by vorticity and an absolute value of velocity are used. It is conceivable to use isosurface display or vortex region extraction such as the λ2 method.

  With respect to the first reason, for example, longitudinal vortices in the velocity boundary can finally be analyzed by the development of computers. In this visualization, for example, vertical vortices in a large number of velocity boundary layers are displayed, and the vertical vortices each move in the wake direction and have alternate rotation directions. Until now, very large vortex areas that encompass these areas have been visualized by the method mentioned in the second reason above, or by isosurface display based on the size of the vector. .

  On the other hand, in general visualization by particle flow, the user controls the number of particles in the space and the movement (step size of time step), and as a result, the complicated flow has been expressed in an easy-to-understand manner. Although there was a method of adding the rotational motion of one particle to the trajectory, the result was that the number of visualization objects was increased in the space, and the user still had to be controlled by parameters.

  In the present embodiment, it is possible to control the number of particles by grouping particles that are close in speed and similar in direction within an arbitrary time, thereby making observation easier to understand. Moreover, a boundary shape is discretely expressed by generating a surface between a pair of particles.

  FIG. 5 shows an example of a functional configuration of a simulation system that executes a fluid flow simulation in the present embodiment. The simulation system includes a simulation device 1, an input unit 2, and a display device 15. The simulation apparatus 1 includes a simulation result storage unit 3, a grouping visualization execution unit 10, a storage unit 11, a particle flow drawing processing unit 12, a drawing instruction unit 13, and a graphic processing unit 14.

  In the simulation result storage unit 3, a physical quantity for each time of the fluid calculated by a simulation process on the fluid flow is stored as a particle position result. The storage unit 11 stores information related to other objects.

  The grouping visualization execution unit 10 executes grouping visualization of particle flows. The grouping visualization execution unit 10 includes a speed calculation unit 5, a grouping determination unit 7, a grouping visualization processing unit 9, and a storage unit 16. The storage unit 16 stores a particle position table 4, a particle position speed table 6, a grouping table 8, and information such as threshold values and rendering setting conditions described later.

  The speed calculation unit 5 reads the simulation result from the simulation result storage unit 3 and stores the particle position information in the particle position table 4 based on the simulation result. Then, the velocity calculation unit 5 calculates the particle velocity using the particle position table 4. The particle position table 4 will be described with reference to FIG.

  FIG. 6 shows an example of the particle position table 4. There are two particle position tables 4. One particle position table 4 is a work table in which particle position data is stored at times T = t, t + 1, t + 2,. The other particle position table 4 is a work table in which particle position data is stored at times T = t + 1, t + 2, t + 3,. Each particle position table 4 stores a particle ID for identifying a particle and a particle position (x, y, z) corresponding to the particle ID. Returning to the description of FIG.

  The velocity calculator 5 calculates the velocity of the particles using the two particle position tables 4 and stores the result in the particle position velocity table 6. The particle position speed table 6 will be described with reference to FIG.

  FIG. 7 shows an example of the particle position velocity table 6. The particle position velocity table 6 stores a particle ID, a particle position (x, y, z) and a velocity vector (velocity x, velocity y, velocity z) corresponding to the particle ID. Returning to the description of FIG.

  The grouping determination unit 7 uses the particle position velocity table 6 to determine which particles can be grouped together. The grouping determination unit 7 stores the particle IDs of the pair of particles determined to be grouped in the grouping table 8. The grouping table 8 will be described with reference to FIG.

  FIG. 8 shows an example of the grouping table 9. The grouping table 9 stores a particle ID (particle ID1, particle ID2) of a pair of particles determined to be grouped and a grouping ID for identifying the pair of particles. Returning to the description of FIG.

The grouping visualization processing unit 9 uses the grouping table 9 to perform visualization processing on the grouped particles. Thereby, grouped drawing data is generated.
The particle flow drawing processing unit 12 performs processing for drawing a normal particle flow based on the input information from the input unit 2, the simulation result, and other object data stored in the storage unit 11. Thereby, particle flow drawing data is generated.

The drawing adjustment unit 13 performs adjustment to superimpose and display the grouped drawing data output from the grouping visualization execution unit 10 and the particle flow drawing data output from the particle flow drawing processing unit 12.
The graphic processing unit 14 performs graphic processing on the drawing data adjusted by the drawing adjusting unit 13 and outputs the processed graphic data to the display device 15.

  FIG. 9 shows an overall flow of particle flow grouping visualization processing. FIG. 9 shows a processing flow executed by the grouping visualization execution unit 10 (speed calculation unit 5, grouping determination unit 7, grouping visualization processing unit 9) in FIG.

  The speed calculator 5 first initializes the time t with 0 (S1). The speed calculation unit 5 acquires the position of the particle at a certain time (this time is set as time t = 0) from the simulation result storage unit 3, and stores it in one particle position table 4 (S2).

  The speed calculation unit 5 increments the time t (S3). The speed calculation unit 5 acquires the position of the particle at time t = 1 from the simulation result storage unit 3 and stores it in the other particle position table 4 (S4).

  The velocity calculation unit 5 calculates the velocity field of the particles (S5). That is, the velocity calculation unit 5 uses the two particle position tables 4 to calculate the movement amount (Δx, Δy, Δz) of the particle position at Δt (Δt = 1-0). The speed calculation unit 5 calculates the speed of the particle from (movement amount of the particle position) / Δt. The velocity calculation unit 5 stores the particle position at the time t = 1 and the calculated velocity in the particle position velocity table 6 together with the particle ID.

  Next, the grouping determination unit 7 performs a filtering process on the speed of the particles stored in the particle position speed table 6. That is, the grouping determination unit 7 deletes the particles stored in the particle position / velocity table 6 that are out of the predetermined speed range, and selects only the particles within the predetermined speed range as the particle position / speed. It remains in the table 6 (S6).

  The grouping determination unit 7 assigns a particle number n = 1 to an arbitrary particle among particles included in the particle position speed table 6 after the filtering process in S6 (S7). Hereinafter, the particles to which n is assigned are referred to as target particles or target particles n.

  The grouping determination unit 7 determines whether or not the target particles are already grouped using the grouping table 8 (S8). When the target particles are already stored in “Particle ID1” or “Particle ID2” of the grouping table 8, the grouping determination unit 7 determines that the target particles are grouped.

When the target particles are already grouped (“Yes” in S8), the grouping determination unit 7 determines whether the particles paired with the target particles are in the vicinity of the target particles even at the current time. (S9). That is, the grouping determination unit 7 determines whether or not the value of the distance Δd between the target particle and the particle paired with the target particle is smaller than the threshold value d _q .

When _{dq of} Δd <(“Yes” in S9), the grouping determination unit 7 determines whether the speed of the particle paired with the target particle is close to that of the target particle even at the current time ( S10). The grouping determination unit 7 determines whether or not the value of the speed difference Δv between the target particle and the particle paired with the target particle is smaller than the threshold value v _q . When the value of the speed difference Δv between the target particle and the particle paired with the target particle is smaller than the threshold value v _q (“No” in S10), the process proceeds to S12.

When the target particles are not grouped (“No” in S8), or the paired particles are excluded from the grouping target (that is, _{dq of} Δd ≧ (“No” in S9)) or Δv ≧ In the case of v _q (“No” in S10)), the grouping determination unit 7 performs the following. That is, the grouping determination unit 7 searches for particles that are paired with the target particles (grouping search process) (S11). The grouping search process in S11 will be described later.

  When there is an unprocessed particle in the particle position speed table 6 after the filtering process in S6 (“Yes” in S12), the grouping determination unit 7 performs the following. That is, the grouping determination unit 7 increments n (S13), and performs the processing of S8-S11 using the unprocessed particles as target particles.

  When all the particles included in the particle position / velocity table 6 after the filtering process in S6 have been processed in S8-S11 (“No” in S12), the grouping visualization processing unit 9 performs the visualization process (S14). ). The process of S14 will be described later.

  If the simulation result storage unit 3 has a simulation result at the next t (that is, t + 1) after the visualization process (S14) ends (“Yes” in S15), the grouping visualization processing unit 9 increments t ( Steps S16) and S4-S14 are performed.

Note that the particle position table 4 used in S4 is alternately changed every time the loop processing (S4-S15) is performed. The grouping table 8 is rewritten every time t is incremented.
The process of S4-S14 is repeated until the process is completed for the simulation result for the final time stored in the simulation result storage unit 3.

  FIG. 10 shows a detailed flow of the group search process in S11 of FIG. The grouping determination unit 7 first sets a search area (S21). Here, the search area refers to a predetermined three-dimensional search range centered on the target particle for searching for a particle that is paired with the target particle.

  Next, the grouping determination unit 7 determines the particle number m (m ≠ n) for an arbitrary particle different from the target particle n among the particles included in the particle position speed table 6 after the filtering process in S6. Is set (S22). Unless the particle number n of the target particle is 1, the initial value is m = 1. When the particle number n of the target particle is 1, m = 2 is set as an initial value. Hereinafter, a particle having the particle number m of a particle to be searched for the target particle is referred to as a particle m.

  The grouping determination unit 7 determines whether or not the particles m to be searched are already grouped from the grouping table 8 (S23). That is, when the particle number m of the particle m exists in “Particle ID 1” or “Particle ID 2” of the grouping table 8 (“Yes” in S23), the grouping determination unit 7 determines that the particle m is grouped. It is determined that

  When the particle m does not exist in the grouping table 8 (“No” in S23), the grouping determination unit 7 determines whether the particle m is inside the search area (S24). That is, the grouping determination unit 7 acquires the position information (x, y, z) of the particle m from the particle position / velocity table 6 and determines whether the position indicated by the position information is within the search area. .

When it is determined that the particle m is inside the search area (“Yes” in S24), the grouping determination unit 7 subtracts the speed of the target particle n from the speed of the particle m, The speed difference Δv is calculated. Then, the grouping determination unit 7 determines whether the particles m, the value of the speed difference Δv of n is smaller than the threshold value v _g (S25).

Delta] v <v For _g ( "Yes" in S25), the grouping determination unit 7 determines that the particles whose particle m is subject particle n paired. In this case, the grouping determination unit 7 sets the particle number m of the particle m and the particle number n of the target particle n, and gives a grouping ID to the set. Then, the grouping determination unit 7 stores the grouping ID and the particle numbers m and n in the grouping table 8 (S26).

On the other hand, if the particles m are present in the grouping table 8 ( "Yes" in S23), if the particles m is not inside the search area ( "No" in S24), or Delta] v ≧ v For _q (S25 " No "), the grouping determination unit 7 performs the following. That is, if there is an unprocessed particle among the particles included in the particle position speed table 6 after the filtering process in S6 (“Yes” in S27), the grouping determination unit 7 increments m ( S28) and S23-S26 are performed. In addition, when m = n is obtained as a result of the increment in S28, the grouping determination unit 7 further increments m.

  When the grouping ID and the particle numbers m and n are stored in the grouping table 7 (S26), or when the next particle does not exist in the particle position / velocity table 6, the grouping determination unit 7 ends the grouping search process. To do.

  FIG. 11 shows a detailed flow of the visualization processing in S14 of FIG. 9 in the first embodiment. In this embodiment, the particles are visualized by rendering. Rendering here refers to a three-dimensional image observed when an object in a three-dimensional space illuminated from a predetermined direction is observed from a predetermined viewpoint, and a three-dimensional image taking shadows, hues, shades, etc. into consideration. It means to generate.

  The grouping visualization processing unit 9 first reads preset rendering setting conditions from the storage unit 16 of the simulation apparatus 1 (S31). The rendering setting conditions include conditions such as illumination direction and viewpoint position.

The grouping visualization processing unit 9 uses the two particle position tables 4 to set the start point of the velocity vector for the position of the target particle n moved between Δt as P ₀ and the end point as P ₁ . Here, the starting point P ₀ is the position of the target particle n at time t, and P ₁ is the position of the target particle n at time t + 1.

In addition, the grouping visualization processing unit 9 uses the two particle position tables to set the start point of the velocity vector for the position of the particle m moved between Δt as Q ₀ and the end point as Q ₁ . Here, the starting point Q ₀ is the position of the particle m at time t, and Q ₁ is the position of the particle m at time t + 1.

The grouping visualization processing unit 9 calculates the normal a of the triangle P ₀ P ₁ Q ₀ (S32). The grouping visualization processing unit 9 calculates the normal b of the triangle Q ₀ Q ₁ P ₁ (S33). Then, the grouping visualization processing unit 9 sets the triangle P ₀ P ₁ Q ₀ and the triangle Q ₀ Q ₁ P ₁ as faces (S34).

The grouping visualization processing unit 9 determines the twist of the normal vectors a and b from the angle φ formed by the normal vectors a and b (S45). When the angle φ is _{equal to} or larger than the threshold φ _t (“No” in S35), the grouping visualization processing unit 9 sets the third color as the drawing color C3 (S39). Here, the drawing color C3 is a drawing color representing the vortex region boundary (FIG. 4).

When the angle φ is smaller than the threshold φ _t (“Yes” in S35), the grouping visualization processing unit 9 determines the direction of the z component (a _z ) of the normal vector a (S36). When it is determined that the z component (a _z ) of the normal vector a is a _z ≧ 0, that is, in the positive direction (“Yes” in S36), the grouping visualization processing unit 9 sets the drawing color C1 to the first color The color 1 is set (S37). Here, the drawing color C1 is a drawing color representing the outer edge of the vortex, and is used to determine the front side of the surface formed by the triangle P ₀ P ₁ Q ₀ as described with reference to FIG.

On the other hand, when it is determined that the z component (a _z ) of the normal vector a is a _z <0, that is, in the negative direction (“No” in S36), the grouping visualization processing unit 9 displays the drawing color C2. The second color is set to (S38). Here, the drawing color C2 is a drawing color representing the outer edge of the vortex, and is used to determine the back side of the surface formed by the triangle P ₀ P ₁ Q ₀ as described with reference to FIG.

Then, the grouping visualization processing unit 9 draws the triangle P ₀ P ₁ Q ₀ and the triangle Q ₀ Q ₁ P ₁ by rendering based on the rendering setting condition. Further, the grouping visualization processing unit 9 uses the drawing color C1, the drawing color C2, or the drawing color C3 to form a surface formed by the drawn triangle P ₀ P ₁ Q ₀ and a surface formed by the triangle Q ₀ Q ₁ P _1. Coloring is then performed (S35). That is, the grouping visualization processing unit 9 performs rendering based on the illumination direction, the viewpoint position, and the positions and shapes of the triangles P ₀ P ₁ Q ₀ and the triangles Q ₀ Q ₁ P ₁ . At this time, when the first color is set as the drawing color C1, the grouping visualization processing unit 9 applies to the surface formed by the triangle P ₀ P ₁ Q ₀ and the surface formed by the triangle Q ₀ Q ₁ P ₁ . The first color is applied. In addition, when the second color is set as the drawing color C2, the grouping visualization processing unit 9 performs the following operations on the surface formed by the triangle P ₀ P ₁ Q ₀ and the surface formed by the triangle Q ₀ Q ₁ P ₁ . A second color is applied. In addition, when the third color is set as the drawing color C3, the grouping visualization processing unit 9 performs the following operation on the surface formed by the triangle P ₀ P ₁ Q ₀ and the surface formed by the triangle Q ₀ Q ₁ P ₁ . A third color is imparted.

In this way, the grouping visualization processing unit 9 generates grouping drawing data. As a result, for example, for one step, grouped drawing data as shown in FIG. 2 can be obtained.
In FIG. 11, since colors are given to the front and back of the triangular surface within the range that can be seen from the fixed viewpoint position, if the viewpoint position is moved, the processing of S35 to S39 is performed again, and the drawing is performed. Add color. However, the present invention is not limited to this depending on the rendering setting environment, and colors may be given to both the front and back of the triangular surface even in a range invisible from a fixed viewpoint position.

  According to this embodiment, particles having similar positions and velocities are clustered (grouped, grouped) and displayed as a surface. This grouped display makes it easier to recognize particles as a mass. In addition, since the outer edge of the vortex region and the boundary between the vortices are displayed, particles moving in a vortex can be tracked without causing erroneous recognition.

  Further, by adjusting the filtering in S6, the threshold values in S9 and S10, and the search area in S21, the particles to be grouped can be adjusted. As a result, the display accuracy can be adjusted.

<Second Embodiment>
This embodiment is a modification of the visualization process in S14 of FIG. In the first embodiment, the particle flow is visualized by rendering. On the other hand, in the present embodiment, visualization is performed by drawing a plurality of line segments between the velocity vectors of two particles whose positions and velocities are close, and regarding the aggregate of the line segments as a surface. In the present embodiment, the same components as those in the first embodiment are denoted by the same reference numerals, and the description thereof is omitted.

FIG. 12 is a diagram for explaining visualization of grouped particles in the present embodiment. In the present embodiment, two particles in a certain range form one set, and a line segment connecting the two particles is considered. The particle velocity vectors P ₀ P ₁ and Q ₀ Q ₁ are each divided into unit length vectors, and a line segment connecting the start points (or end points) of the unit length vectors is drawn. A line segment connecting the start points (or end points) of unit length vectors is sequentially drawn from the start point to the end point of the velocity vectors of both particles. Then, as shown in FIG. 12, the assembly of line segments forms a plane by being arranged in the same plane. Thereby, grouping visualization between two particles can be performed.

  FIG. 13 shows an example of a functional configuration of a simulation system that executes a fluid flow simulation in the present embodiment. FIG. 13 is obtained by adding a line segment drawing table 21 to the grouping visualization execution unit 10 of FIG. The grouping visualization processing unit 9 uses the line segment drawing table 21 to perform grouping visualization between two particles.

FIG. 14 shows an example of the line segment drawing table 21. In the line segment drawing table 21, the coordinates P ₀ = r _po = (r _pox , r _poy , r _poz ) of the velocity vector P ₀ P ₁ (= v _p ) and the normalized vector v _p = r _p = (R _px , r _py , r _pz ), end point coordinates P ₁ = r _p1 = (r _p1x , r _p1y , r _p1z ) are stored. Further, the line segment drawing table 21 includes the coordinates Q ₀ = r _qo = (r _qox , r _qoy , r _qoz ) of the velocity vector Q ₀ Q ₁ (= v _q ), and the normalized vector v _q = r _q = (r _qx , r _qy , r _qz ), and end point coordinates Q ₁ = r _q1 = (r _q1x , r _q1y , r _q1z ) are stored.

FIG. 15 shows a detailed flow of the visualization process in S14 of FIG. The grouping visualization processing unit 9 first sets the line segment drawing table 21 (S41). Specifically, the grouping visualization processing unit 9 selects the target particle position P ₁ (r _px , r) from the particle position table 4 in which the particle position is stored most recently (T = t + 1) out of the two particle position tables 4. r _py , r _pz ). Then, the grouping visualization processing unit 9 stores the acquired position P ₁ (r _px , r _py , r _pz ) in the position x, y, z corresponding to the “v _p end point” of the line segment drawing table 21. .

In addition, the grouping visualization processing unit 9 acquires the position P ₀ (r _pox , r _poy , r _poz ) of the target particle from the other (T = t) particle position table 4, and _displays “v” in the line segment drawing table 21. Store in the position x, y, z corresponding to “ _p start point”.

Further, the grouping visualization processing unit 9 calculates the amount of movement (Δx, Δy, Δz) of the target particle n in the unit time Δt, that is, the velocity vector, from the two particle position tables 4. The grouping visualization processing unit 9 normalizes the velocity vector based on (Δx / | Δx |, Δy / | Δy |, Δz / | Δz |). The grouping visualization processing unit 9 stores the normalized velocity vector in the position x, y, z corresponding to “normalized v _p ” in the line segment drawing table 21.

In addition, the grouping visualization processing unit 9 of the two particle position tables 4 stores the position Q ₁ (r _qx , r _qy , r) of the particle m from the particle position table in which the particle position is stored most recently (T = t + 1). _qz ) to get. Then, the grouping visualization processing unit 9 stores the acquired position Q ₁ (r _qx , r _qy , r _qz ) in the position x, y, z corresponding to the “v _q end point” of the line segment drawing table 21. .

Further, the grouping visualization processing unit 9 _acquires the position Q ₀ (r _qox , r _qoy , r _qoz ) of the particle m from the other (T = t) particle position table 4, and _displays “v” in the line segment drawing table 21. Store in the position x, y, z corresponding to “ _q start point”.

Further, the grouping visualization processing unit 9 calculates the movement amount (Δx, Δy, Δz) of the position of the particle m in the unit time Δt, that is, the velocity vector, from the two particle position tables 4. The grouping visualization processing unit 9 normalizes the velocity vector based on (Δx / | Δx |, Δy / | Δy |, Δz / | Δz |). The grouping visualization processing unit 9 stores the normalized velocity vector at positions x, y, and z corresponding to “normalized v _q ” of the line segment drawing table 21.

Next, the grouping visualization processing unit 9 calculates the normal a of the triangle P ₀ P ₁ Q ₀ (S42). The grouping visualization processing unit 9 calculates the normal b of the triangle Q ₀ Q ₁ P ₁ (S43).
The grouping visualization processing unit 9 determines the twist of the normal vectors a and b from the angle φ formed by the normal vectors a and b (S44). When the angle φ is _{equal to} or larger than the threshold φ _t (“No” in S44), the grouping visualization processing unit 9 sets the third color as the drawing color C3 (S48). Here, the drawing color C3 is a drawing color representing the vortex region boundary (FIG. 4).

When the angle φ is smaller than the threshold φ _t (“Yes” in S44), the grouping visualization processing unit 9 determines the direction of the z component (a _z ) of the normal vector a (S45). When it is determined that the z component (a _z ) of the normal vector a is a _z ≧ 0, that is, in the positive direction (“Yes” in S45), the grouping visualization processing unit 9 sets the drawing color C1 to the first color The color 1 is set (S46). Here, the drawing color C1 is a drawing color representing the outer edge of the vortex, and is used to determine the front side of the surface formed by the triangle P ₀ P ₁ Q ₀ as described with reference to FIG.

On the other hand, when the z component (a _z ) of the normal vector a is determined to be a _z <0, that is, in the negative direction (“No” in S45), the grouping visualization processing unit 9 uses the drawing color C2. The second color is set to (S47). Here, the drawing color C2 is a drawing color representing the outer edge of the vortex, and is used to determine the back side of the surface formed by the triangle P ₀ P ₁ Q ₀ as described with reference to FIG.

In the visualization process of the present embodiment, as shown in FIG. 12, the end points of the normalized velocity vectors v _p and v _q are drawn from the start point to the end point of the two velocity vectors P ₀ P ₁ and Q ₀ Q _1. A drawing process that connects in minutes is performed. Therefore, the grouping visualization processing unit 9 initializes a counter i for determining the position of the drawing point with 0 (S49).

Grouping visualization processing unit 9 reads the line segment drawing table 21 (S50), the start point of the vector _{v p r po = (r pox} , r poy, r poz), the vector v _p = (r _px normalized, r _py , r _pz ), the end point r _p1 = (r _p1x , r _p1y , r _p1z ) of the vector v _p is acquired. Grouping visualization processing unit 9 is further from the origin r _po and end r _p1 Metropolitan vector v _p, calculates the length of a vector v _p, assigns a length that the calculated L _vp. Further, the grouping visualization processing unit 9 reads the line segment drawing table 21, starts the vector v _q starting point r _qo = (r _qox , r _qoy , r _qoz ), and the normalized vector v _q = (r _qx , r _qy , R _qz ).

The grouping visualization processing unit 9 calculates the drawing point r _p of the vector v _p from r _p = r _p0 + i × (normalized vector v _p ) (S51). Further, the grouping visualization processing unit 9 calculates the drawing point r _q of the vector v _q from r _q = r _q0 + i × (normalized vector v _q ) (S52).

The grouping visualization processing unit 9 draws a line segment r _p r _q connecting the calculated drawing point r _p and the drawing point r _q using the drawing color C1, the drawing color C2, or the drawing color C3 (S53). That is, when the first color is set as the drawing color C1, the grouping visualization processing unit 9 draws the line segment r _p r _q using the first color. When the second color is set as the drawing color C2, the grouping visualization processing unit 9 draws the line segment r _p r _q using the second color. When the third color is set as the drawing color C3, the grouping visualization processing unit 9 draws the line segment r _p r _q using the third color.

The grouping visualization processing unit 9 determines whether or not the length (L _vp ) of the vector v _p has been reached (S54). The grouping visualization processing unit 9 draws a line segment r _p r _q each time the drawing point is advanced by the unit length of both vectors, and repeats the length of the vector v _p (L _vp ). Two visualizations can be performed for one set. The grouping visualization processing unit 9 increments the counter i when i <L _vp and repeats the processing of S51 to S53. As a result, it is possible to perform visualization by drawing a plurality of line segments between the velocity vectors of particles whose positions and velocities are close, and regarding the aggregate of the line segments as a surface.

  By the above method, particles having close positions and velocities are connected by a plurality of line segments, whereby the aggregate of the line segments can be regarded as a surface. This makes it easier to recognize particles as a mass. Further, since the outer edge of the vortex region and the boundary between the vortices are displayed, it is possible to track the particles moving in a vortex without causing erroneous recognition.

  Further, by adjusting the filtering in S6, the threshold values in S9 and S10, and the search area in S21, the particles to be grouped can be adjusted. As a result, the display accuracy can be adjusted.

  FIG. 16 is a configuration block diagram of the hardware environment of the simulation system. The simulation apparatus 1 includes a CPU 32, a ROM 33, a RAM 36, a communication I / F 34, a storage device 37, an output I / F 31, an input I / F 35, a reading device 38, a bus 39, an output device 41, and an input device 42.

  Here, CPU indicates a central processing unit. ROM indicates a read-only memory. RAM indicates random access memory. I / F indicates a communication interface. A CPU 32, ROM 33, RAM 36, communication I / F 34, storage device 37, output I / F 31, input I / F 35, and reading device 38 are connected to the bus 39. The reading device 38 is a device that reads a portable recording medium. The output device 41 is connected to the output I / F 31. The input device 42 is connected to the input I / F 35.

As the storage device 37, various types of storage devices such as a hard disk, a flash memory, and a magnetic disk can be used.
The storage device 37 or the ROM 33 as the storage units 11 and 16 stores, for example, a program that realizes the processing described in the first or second embodiment. Further, the storage device 37 or the ROM 33 stores the particle position table 4, the particle position speed table 6, the grouping table 8, the line segment drawing table 21, the simulation result, the threshold value, the rendering setting condition, and other information related to the object. ing.

The CPU 82 reads out a program that realizes the processing described in the first or second embodiment, stored in the storage device 87 or the like, and executes the program.
The program for realizing the processing described in the first or second embodiment may be stored in, for example, the storage device 37 from the program provider side via the communication network 40 and the communication I / F 34. Moreover, the program which implement | achieves the process demonstrated in 1st or 2nd embodiment may be stored in the portable storage medium marketed and distribute | circulated. In this case, the portable storage medium may be set in the reading device 38 and the program read by the CPU 32 and executed. As the portable storage medium, various types of storage media such as a CD-ROM, a flexible disk, an optical disk, a magneto-optical disk, an IC card, and a USB memory device can be used. The program stored in such a storage medium is read by the reading device 38.

  As the input device 42, a keyboard, a mouse, an electronic camera, a web camera, a microphone, a scanner, a sensor, a tablet, or the like can be used. The output device 41 can be a display, a printer, a speaker, or the like. The network 40 may be a communication network such as the Internet, a LAN, a WAN, a dedicated line, a wired line, and a wireless line.

The simulation apparatus in the first and second embodiments includes a speed calculation unit, a grouping unit, and a drawing information generation unit.
The velocity calculation unit calculates the velocity of the particle at each position based on simulation result information regarding the physical quantity of the particle for each hour calculated by simulation of the fluid flow. For example, the speed calculation unit 5 is included in the speed calculation unit.

  The grouping unit calculates a distance between the two particles based on the position of the particle, calculates a speed difference between the two particles based on the speed of the particle, and calculates a distance between the particles. When the value is smaller than the first threshold and the value of the speed difference between the particles is smaller than the second threshold, the two particles are grouped. For example, the grouping determination unit 7 is included in the grouping unit.

  The drawing information generation unit generates drawing information for drawing a display object indicating the behavior of the two grouped particles based on the velocity vector of the two grouped particles. For example, the grouping visualization processing unit 9 is included in the drawing information generation unit.

With this configuration, it becomes easy to track the three-dimensional behavior of particles by grouping visualization of particle flows.
The drawing information generation unit includes two triangles having, as vertices, a start point and an end point of a velocity vector of one particle and a start point or an end point of the other particle of the two grouped particle velocity vectors Is generated. Then, the drawing information generation unit calculates a normal vector of the surface forming each triangle. Then, the drawing information generation unit changes the display form of the display object according to the direction of the normal vector or the angle formed by the two normal vectors.

With this configuration, for example, the behavior of particles in turbulent flow can be easily determined.
In addition, the drawing information generation unit, when the value of the angle formed by the two normal vectors is smaller than a third threshold value and the direction of the component in a predetermined direction of one of the normal vectors is positive, the display object A first color is assigned to the. In addition, the drawing information generation unit is configured to display the display when the value of the angle formed by the two normal vectors is smaller than the third threshold value and the direction of a component in a predetermined direction of one of the normal vectors is negative. Give the object a second color. Further, the drawing information generation unit assigns a third color to the display object when an angle value formed by the two normal vectors is equal to or greater than the third threshold value.

With this configuration, for example, it is possible to easily determine the behavior of particles moving on the near side, the far side, or the boundary between vortices in the turbulent flow.
Further, the rendering information generation unit configures a surface forming the triangle in a virtual three-dimensional space by rendering, and the first color and the second color are formed on the surface forming the triangle. Or a third color can be applied.

By configuring in this way, it is possible to color the surface formed by the velocity vectors of the particles whose velocities are close to the grouped positions using rendering.
The drawing information generation unit divides each of the two particle velocity vectors into a unit length vector. The drawing information generation unit uses the first color, the second color, or the third color as a line segment connecting the start points or the end points of the velocity vectors of the two particles having the divided unit length. The display object is generated by drawing using.

By configuring in this way, particles having close positions and velocities are connected by a plurality of line segments, so that an aggregate of the line segments can be regarded as a surface.
The first and second embodiments are not limited to the above-described embodiments, and can take various configurations or embodiments without departing from the gist of the present embodiments.

Regarding the above embodiment, the following additional notes are disclosed.
(Appendix 1)
A speed calculation unit that calculates the speed of the particle at each position, based on simulation result information on the physical quantity of the particle for each time calculated by simulation of the flow of the fluid;
The distance between the two particles is calculated based on the position of the particle, the speed difference between the two particles is calculated based on the speed of the particle, and the distance value between the particles is a first value. A grouping unit that groups the two particles when the value of the velocity difference between the particles is smaller than a threshold and smaller than a second threshold;
A drawing information generating unit that generates drawing information for drawing a display object indicating the behavior of the two grouped particles based on the velocity vectors of the two grouped particles;
A simulation apparatus comprising:
(Appendix 2)
The drawing information generation unit includes two triangles having, as vertices, a start point and an end point of a velocity vector of one particle and a start point or an end point of the other particle of the two grouped particle velocity vectors Generating a normal vector of the surface forming each triangle, and changing the display form of the display object according to the direction of the normal vector or the angle formed by the two normal vectors. The simulation apparatus according to appendix 1, which is characterized.
(Appendix 3)
When the value of the angle formed by the two normal vectors is smaller than a third threshold value and the direction of the component in a predetermined direction of one of the normal vectors is positive, When the color of 1 is given, the angle value formed by the two normal vectors is smaller than the third threshold value, and the direction of the component in the predetermined direction of one of the normal vectors is negative, the display object The second color is given, and when the value of the angle formed by the two normal vectors is equal to or larger than the third threshold, the third color is given to the display object. Simulation equipment.
(Appendix 4)
The drawing information generation unit configures a surface forming the triangle in a virtual three-dimensional space by rendering, and the first color, the second color, or the surface forming the triangle The simulation apparatus according to appendix 3, wherein a third color is imparted.
(Appendix 5)
The drawing information generation unit divides each of the two particle velocity vectors into a unit length vector, and a line segment connecting the start points or end points of the two divided particle unit velocity vectors, The simulation apparatus according to appendix 3, wherein the display object is generated by drawing using the first color, the second color, or the third color.
(Appendix 6)
A simulation result display program for causing a computer to execute a process of displaying a simulation result of a fluid flow,
Based on simulation result information on the physical quantity of each particle calculated by the simulation, a speed calculation process for calculating the speed of the particle at each position;
The distance between the two particles is calculated based on the position of the particle, the speed difference between the two particles is calculated based on the speed of the particle, and the distance value between the particles is a first value. A grouping process for grouping the two particles when the value of the velocity difference between the particles is smaller than a threshold and smaller than a second threshold;
A drawing information generation process for generating drawing information for drawing a display object indicating the behavior of the two grouped particles based on the velocity vector of the two grouped particles;
A simulation result display program for causing a computer to execute.
(Appendix 7)
The drawing information generation process includes two triangles having apexes of the velocity vector start point and end point of one particle and the velocity vector start point or end point of the other particle among the grouped two particle velocity vectors. Generating a normal vector of the surface forming each triangle, and changing the display form of the display object according to the direction of the normal vector or the angle formed by the two normal vectors. The simulation result display program according to appendix 6, which is a feature.
(Appendix 8)
In the drawing information generation process, when the value of the angle formed by the two normal vectors is smaller than a third threshold value and the direction of a component in a predetermined direction of one of the normal vectors is positive, When the color of 1 is given, the angle value formed by the two normal vectors is smaller than the third threshold value, and the direction of the component in the predetermined direction of one of the normal vectors is negative, the display object The supplementary note 7 is characterized in that when a second color is given and an angle value formed by the two normal vectors is equal to or more than the third threshold value, a third color is given to the display object. Simulation result display program.
(Appendix 9)
The drawing information generation process includes rendering to form a surface forming the triangle in a virtual three-dimensional space, and the first color, the second color, or the surface forming the triangle, The simulation result display program according to appendix 8, wherein a third color is given.
(Appendix 10)
The drawing information generation process divides each of the two particle velocity vectors into a unit length vector, and a line segment connecting the start points or end points of the two divided unit length velocity vectors, The simulation result display program according to appendix 8, wherein the display object is generated by drawing using the first color, the second color, or the third color.
(Appendix 11)
A simulation result display method for causing a computer to execute a process of displaying a simulation result of a fluid flow, which is executed by a computer,
The computer
Based on the simulation result information about the physical quantity of each particle calculated by the simulation, the velocity of the particle at each position is calculated,
The distance between the two particles is calculated based on the position of the particle, the speed difference between the two particles is calculated based on the speed of the particle, and the distance value between the particles is a first value. If the value of the velocity difference between the particles is smaller than the threshold value and smaller than the second threshold value, the two particles are grouped,
Based on the velocity vectors of the two grouped particles, generating drawing information for drawing a display object indicating the behavior of the two grouped particles;
A simulation result display method characterized by that.
(Appendix 12)
When generating the drawing information for drawing the display object, the computer generates a start point and an end point of the velocity vector of one particle, and a start point of the velocity vector of the other particle among the two velocity vectors of the grouped particles. Alternatively, two triangles having vertices at the end points are generated, and normal vectors of surfaces forming the respective triangles are calculated, and depending on the direction of the normal vectors or the angle formed by the two normal vectors, The simulation result display method according to appendix 11, wherein the display form of the display object is changed.
(Appendix 13)
When generating the drawing information for drawing the display object, the computer has an angle value formed by the two normal vectors smaller than a third threshold value, and a direction of a component in a predetermined direction of one of the normal vectors. Is positive, the display object is given a first color, the angle value formed by the two normal vectors is smaller than the third threshold value, and the component of any normal vector in a predetermined direction When the direction is negative, the display object is given a second color, and when the angle between the two normal vectors is greater than or equal to the third threshold value, the display object is given a third color. The simulation result display method according to attachment 12, wherein the simulation result is displayed.
(Appendix 14)
When generating the drawing information for drawing the display object, the computer configures a surface forming the triangle in a virtual three-dimensional space by rendering, and the computer forms the first information on the surface forming the triangle. The simulation result display method according to appendix 13, wherein the first color, the second color, or the third color is assigned.
(Appendix 15)
When generating drawing information for drawing the display object, the computer divides each of the two particle velocity vectors into a unit length vector, and the start point of the divided two unit length velocity vectors 14. The simulation according to appendix 13, wherein the display object is generated by drawing a line segment connecting the end points or the end points using the first color, the second color, or the third color. Result display method.

DESCRIPTION OF SYMBOLS 1 Simulation apparatus 2 Input part 3 Simulation result storage part 4 Particle position table 5 Speed calculation part 6 Particle position speed table 7 Grouping determination part 8 Grouping table 9 Grouping visualization process part 10 Grouping visualization execution part 11, 16 Storage part 12 Particle Flow Drawing Processing Unit 13 Drawing Instruction Unit 14 Graphic Processing Unit 15 Display Device 21 Line Segment Drawing Table

Claims (7)

A speed calculation unit that calculates the speed of the particle at each position, based on simulation result information on the physical quantity of the particle for each time calculated by simulation of the flow of the fluid;
The distance between the two particles is calculated based on the position of the particle, the speed difference between the two particles is calculated based on the speed of the particle, and the distance value between the particles is a first value. A grouping unit that groups the two particles when the value of the velocity difference between the particles is smaller than a threshold and smaller than a second threshold;
A drawing information generating unit that generates drawing information for drawing a display object indicating the behavior of the two grouped particles based on the velocity vectors of the two grouped particles;
A simulation apparatus comprising: Three said drawing information generating unit of the velocity vectors of the two particles are the grouped, shall be the starting point or vertex and the end point of the start point and the end point and the other side of the particle velocity vector of the velocity vector of one particle Generates a square , a start point and an end point of the velocity vector of the other particle, and a triangle whose vertex is the start point or end point of the velocity vector of the one particle, and calculates a normal vector of the surface forming each triangle The simulation apparatus according to claim 1, wherein the display form of the display object is changed according to a direction of the normal vector or an angle formed by the two normal vectors. When the value of the angle formed by the two normal vectors is smaller than a third threshold value and the direction of the component in a predetermined direction of one of the normal vectors is positive, When the color of 1 is given, the angle value formed by the two normal vectors is smaller than the third threshold value, and the direction of the component in the predetermined direction of one of the normal vectors is negative, the display object The second color is given, and when the value of the angle formed by the two normal vectors is equal to or greater than the third threshold value, the third color is given to the display object. The simulation apparatus described. The drawing information generation unit configures a surface forming the triangle in a virtual three-dimensional space by rendering, and the first color, the second color, or the surface forming the triangle The simulation apparatus according to claim 3, wherein a third color is imparted. The drawing information generation unit divides each of the two particle velocity vectors into a unit length vector, and a line segment connecting the start points or end points of the two divided particle unit velocity vectors, The simulation apparatus according to claim 3, wherein the display object is generated by drawing using the first color, the second color, or the third color. A simulation result display program for causing a computer to execute a process of displaying a simulation result of a fluid flow,
Based on simulation result information on the physical quantity of each particle calculated by the simulation, a speed calculation process for calculating the speed of the particle at each position;
The distance between the two particles is calculated based on the position of the particle, the speed difference between the two particles is calculated based on the speed of the particle, and the distance value between the particles is a first value. A grouping process for grouping the two particles when the value of the velocity difference between the particles is smaller than a threshold and smaller than a second threshold;
A drawing information generation process for generating drawing information for drawing a display object indicating the behavior of the two grouped particles based on the velocity vector of the two grouped particles;
A simulation result display program for causing a computer to execute. A simulation result display method for causing a computer to execute a process of displaying a simulation result of a fluid flow, which is executed by a computer,
The computer
Based on the simulation result information about the physical quantity of each particle calculated by the simulation, the velocity of the particle at each position is calculated,
The distance between the two particles is calculated based on the position of the particle, the speed difference between the two particles is calculated based on the speed of the particle, and the distance value between the particles is a first value. If the value of the velocity difference between the particles is smaller than the threshold value and smaller than the second threshold value, the two particles are grouped,
Based on the velocity vectors of the two grouped particles, generating drawing information for drawing a display object indicating the behavior of the two grouped particles;
A simulation result display method characterized by that.