JP3048794B2 - Trajectory calculation method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a trajectory calculation method for calculating a trajectory from vector field data, and more particularly to a trajectory calculation method for calculating a trajectory of virtual particles in an analysis area based on a flow velocity vector value of a fluid.

[0002]

2. Description of the Related Art Continuous distribution of physical quantities in physical space
It is assumed that experiments and numerical analysis have been performed on. Physical quantity
If it is a vector quantity (eg fluid velocity)
Vector values at a finite number of points set in (for example,
Flow velocity vector). In vector-valued space
Of distribution characteristics, that is, regularity of size and direction
Virtual, without size and mass in space to capture
Conventionally, the trajectory is calculated by setting a typical particle
That it has (for example, JP-A-4-264958).

Referring to FIG. 6, in the conventional trajectory calculation method, a trajectory calculation start point setting step 10 for setting a start point for calculating a trajectory, and a vector value and a vector value calculation point from a vector value storage unit 60 are referred to. Segment end point calculation step 20 for calculating the end point of the trajectory line segment, and the trajectory point sequence calculated by judging the end of the trajectory calculation is stored in the trajectory point sequence storage unit 8
And a trajectory calculation end determination step 50 to be stored in 0.

First, in a trajectory calculation start point setting step 10, a trajectory calculation start point P0 and a trajectory calculation step width t are inputted, and a trajectory calculation start point P0 is set as a trajectory line segment tip point Pn, and the trajectory calculation start point P0 is set. The start point P0 is stored in the locus point sequence storage unit 80.

Next, in a trajectory line segment end point calculation step 20, a vector value V (Pn) at the trajectory line segment tip point Pn is calculated with reference to the vector value at each vector value calculation point from the vector value storage unit 60. . Further, the trajectory line segment tip point Pn, the vector value V at this trajectory segment tip point Pn
Using (Pn) and the calculation step width t, the trajectory segment end point Pn + 1 is calculated.

Next, in a trajectory calculation end determination step 50, the trajectory segment end point Pn + 1 is stored in the trajectory point sequence storage section 80. As a result of determining the end of the trajectory calculation, if the trajectory creation is to be continued, the trajectory segment end point Pn is set to the trajectory segment end point P
Then, the process returns to the processing of the trajectory line segment end point calculating step 20, and the calculation of the next trajectory line segment is continued.

[0007]

However, according to the above-described conventional trajectory calculation method, for example, as shown in FIG. 7, in the analysis area 720, there is no fluid, and therefore there is no need to calculate the flow velocity vector value in the obstacle area 710. In this case , there is a problem that an accurate trajectory cannot be calculated near the obstacle because the obstacle is not considered.

Referring to FIG. 8A, in a two-dimensional analysis area, a vector value calculation point 810, which is a numerical analysis result, is located on each grid point in the space, and a trajectory segment tip point Pn8
V (Pn) 830 representing the vector value at 20 and the trajectory segment end point Pn + 1 84 calculated by the above-described method.
0 is shown.

On the other hand, referring to FIG. 8B, the trajectory segment end point Pn + 1 840 calculated by the above method is
Despite the presence of the obstacle area 850, it is calculated in the same place as in FIG. 8A, and does not reflect the actual physical space.

On the other hand, at the stage of the numerical analysis, the influence of the obstacle on the physical quantity is considered, and the vector value obtained as a result is such that there is no trajectory passing through the obstacle near the obstacle. Should be distributed.

When an obstacle is set at the time of numerical analysis, a physical quantity on the boundary between the analysis area and the obstacle may be calculated according to the nature of the obstacle. For example, when calculating a flow velocity vector value by fluid analysis, the property of an obstacle such as "slip" or "no slip" may be specified depending on the presence or absence of friction on the obstacle surface when the obstacle is set. In such a case, it is necessary to calculate the flow velocity vector value on the boundary depending on the type of the obstacle surface also at the time of calculating the trajectory.

[0012]

Means for Solving the Problems In order to solve the above-described problems, the present invention employs a vector at each point in the physical space.
A trajectory calculation method for calculating a trajectory line segment at an arbitrary point from a torque value, a trajectory calculation start point setting step of setting a calculation start point of the trajectory segment and storing the calculated start point in a trajectory point sequence storage unit; A trajectory segment end point calculating step of calculating an end point of the trajectory segment by referring to a vector value at each point in the analysis space to obtain the trajectory segment; and obtaining an obstacle in the analysis space from the obstacle boundary data storage unit. An obstacle passage determining step of determining whether or not the trajectory line segment calculated in the trajectory line segment end point calculating step with reference to an obstacle boundary intersects with an obstacle boundary; If it is determined that
An obstacle boundary processing step of generating again a trajectory line segment that does not intersect with the harmful object boundary, and determining the end of the trajectory calculation, and if ending as a result, the calculated trajectory line segment is stored in the trajectory point sequence storage unit. Trajectory calculation end determination step for storing.

[0013]

[0014]

Next, an embodiment of a trajectory calculation method according to the first invention of the present application will be described in detail with reference to the drawings.

Referring to FIG. 1, a trajectory calculation method according to one embodiment of the present invention includes a trajectory calculation start point setting step 10 for setting a trajectory calculation start point, and a vector value storage unit 60.
Trajectory line end point calculating step 20 for calculating the trajectory line end point with reference to the vector value and the vector value calculation point from
And referring to the boundary position between the obstacle and the obstacle in the analysis space from the obstacle boundary data storage unit 70 to determine whether the trajectory segment calculated in the trajectory segment end point calculation step 20 intersects with the obstacle boundary. Obstacle passing judgment step 30
And an obstacle boundary processing step 40 for generating a trajectory segment again so as not to intersect with the obstacle boundary, and a trajectory calculation for storing the trajectory point sequence calculated by determining the end of the trajectory calculation in the trajectory point sequence storage unit 80 An end determination step 50 is provided.

First, a locus calculation start point setting step 10
Inputs the trajectory calculation start point P0 and the trajectory calculation step width t, sets P0 as the trajectory segment end point Pn, and stores P0 in the trajectory point sequence storage unit 80.

Next, a trajectory line segment end point calculation step 20
Inputs a trajectory segment tip point Pn, and calculates a vector V (Pn) at Pn from vector values at each vector value calculation point stored in the vector value storage unit 60. Then, the trajectory line segment end point Pn + 1 is calculated as a value obtained by adding a value obtained by multiplying the vector value V (Pn) by t (calculation step width) to the trajectory line segment end point Pn.

Next, the obstacle passage determination step 30 is a step of determining the line segment connecting the trajectory segment end point Pn and the trajectory segment end point Pn + 1 and the analysis area stored in the obstacle boundary data storage unit 70. The presence / absence of intersection with the obstacle boundary position data Lm representing the boundary with the obstacle in the inside is checked. If there is an obstacle boundary intersecting the trajectory line segment PnPn + 1, the process proceeds to the obstacle boundary processing step 40. If they do not intersect, the process proceeds to a locus calculation end determination step 50.

In the obstacle boundary processing step 40 performed when there is an intersection, the end point of the trajectory line segment is corrected so as not to pass through the obstacle. Details of the processing will be described later. After the end point of the trajectory line segment is corrected, the flow returns to the obstacle passing determination step 30 again, and it is checked whether or not the trajectory line segment intersects with the obstacle boundary position data Lm. If not, the process proceeds to the trajectory calculation end determination step 50.

In the trajectory calculation end determination step 50, the trajectory segment end point Pn + 1 calculated by the processing so far is stored in the trajectory point sequence storage unit 80. Then, the end of the trajectory calculation is determined, and as a result, when it is determined that the trajectory creation is to be continued, the trajectory line segment end point Pn + 1 is replaced with the trajectory line segment end point Pn + 1, and the trajectory segment end point calculation is performed. It returns to the process of step 20.

Next, the processing of the obstacle boundary processing step 40 will be described. Referring to FIG. 2, in the flowchart of the processing before and after the obstacle boundary processing step 40, step 2 is performed.
Step 10 and step 220 are the trajectory line segment end point calculation step 2
0, steps 230 and 250 correspond to the obstacle passing determination step 30, and step 240 corresponds to the obstacle boundary processing step 40. First, step 2
After calculating Pn + 1 in step 10, Pn + 1 is set as the initial value of the adaptation end point Pa in step 220, and the calculation step width t of the trajectory is set as the initial value of the adaptation calculation step width ta. Then, in step 230, the line segment PnPa
It is checked whether there is an intersection with the obstacle boundary position data Lm in the analysis area stored in the obstacle boundary data storage unit 70, and if there is an obstacle boundary that intersects the line segment PnPa, the process proceeds to step 240. If not, step 2
Go to 50.

In step 240, the adaptive calculation process
Set the step width ta to be smaller than t and do not pass an obstacle.
Correct the end point of the trajectory line segment as follows. For this purpose, the adaptive calculation step width ta is halved, that is, ta is set to 1
/ Ta, and a value obtained by adding the vector value V (Pn) multiplied by the adaptation calculation step width ta to the trajectory line segment end point Pn is calculated as the adaptation end point Pa.
Thereafter, the flow returns to step 230 again to check whether or not the line segment PnPa intersects with the obstacle boundary position data Lm in the analysis area stored in the obstacle boundary data storage unit 70.
If there is an obstacle boundary that intersects with the line segment PnPa, the process proceeds to step 240;
Proceed to. In step 250, the adaptive ending point Pa is set as the trajectory segment end point Pn + 1, and the next trajectory calculation end determination step 5 is performed.
Go to 0. Hereinafter, the creation of the trajectory is continued in step 50.
Consider the case where it is determined. Step the next trajectory line segment
Perform from 20. First, the trajectory of Pn + 1 in the previous trajectory line segment
Set to the end point of the line segment. The vector value storage unit 60 has
Limited number of vector value data V (x) and vector value calculation
Point data x is stored. These V (x) are
From physical quantities continuously distributed in the physical space, experiments and numbers
By value analysis, at a finite number of points x set in the space
The data obtained. From the processing in step 240, Pn + 1
Is set closer to the obstacle boundary than Pn. Vector value
Calculate V (Pn + 1) from data stored in storage unit 60
However, for this reason, V (Pn + 1) is more faulty than V (Pn).
V (Pn + 1) is calculated as a value reflecting the influence of the object boundary.
By using this, an appropriate trajectory is calculated.

As described above, in the trajectory calculation method according to the first aspect of the present invention, when calculating the trajectory in the analysis space from the vector values at each point in the physical space , the calculation is performed near the obstacle boundary.
By setting a small step width,
The closer the vector value calculation point, the greater the effect of obstacles
Using the vector values that appear frequently , an appropriate trajectory can be calculated without crossing an obstacle.

Next , a second embodiment of the invention according to claim 1 is described.
As an example, specify the nature of the obstacle when setting the obstacle, and
Vector value data on the boundary between the
The trajectory calculation method when the trajectory can be output will be described in detail with reference to the drawings.

Referring to FIG. 3, a trajectory calculation method according to one embodiment of the present invention includes a trajectory calculation start point setting step 10 for setting a trajectory calculation start point, and a vector value storage unit 6.
Trajectory line end point calculation step 2 for calculating the end point of the trajectory line by referring to the vector value and the vector value calculation point from 0
0 and whether or not the trajectory line segment calculated in the trajectory line segment end point calculating step 20 with reference to the boundary position between the obstacle and the obstacle in the analysis space from the obstacle boundary data storage unit 70 intersects with the obstacle boundary. Obstacle passing judgment step 30
And not to cross the obstacle boundary
Obstacle boundary processing step 40 in which a trajectory line segment is generated again using vector value data on the field , and trajectory calculation end in which the trajectory point sequence calculated by determining the end of trajectory calculation is stored in the trajectory point sequence storage unit 80 It consists of a decision step 50. The trajectory calculation start point setting step 10, the trajectory line segment end point calculation step 20, and the trajectory calculation end determination step 50
Performs the same processing as that of the first invention of the present application .

Referring to FIG. 4, step 410 corresponds to trajectory line segment end point calculating step 20, and step 420
Corresponds to the obstacle passage determination step 30 and the step 43
0, step 440, and step 450 correspond to the obstacle boundary processing step 40. First, in step 410, after the trajectory line segment end point Pn + 1 is calculated, step 420
, The line segment PnPn + 1 and the obstacle boundary data storage unit 70
Boundary position data L in the analysis area stored in
It is checked whether there is an intersection with m, and if there is an obstacle boundary that intersects with the line segment PnPn + 1, the flow proceeds to step 430;
Proceed to.

In step 430, an intersection Pc between the line segment PnPn + 1 and the obstacle boundary position data Lm is calculated, and a vector value V (Pc) on the boundary is set according to the type of the obstacle surface corresponding to the position. . Step 44
In the case of 0, the intersection calculation step width tc is obtained by dividing a value obtained by subtracting the trajectory segment tip point Pn from the intersection Pc by the vector value V (Pn). Then, in step 450,
The vector V (Pc) multiplied by the calculation step width (t−tc) is added to the intersection position Pc, and the trajectory line segment end point Pn
Recalculate +1. Thus, a trajectory is generated that does not intersect with the obstacle boundary and takes into account the properties on the obstacle boundary.

Referring to FIG. 5, in the two-dimensional analysis region, vector value calculation points 510, which are the results of numerical analysis, are located on each grid point in space, and the trajectory line segment tip point Pn520
An intersection Pc 550 between the uncorrected trajectory line segment 530, which is a line segment from the trajectory segment end point 540 to the uncorrected trajectory line segment, and the obstacle boundary position data Lm580 is shown. Here, a state of “slip” with no friction on the obstacle surface is shown, and the corrected trajectory segment end point 560 is positioned at a position that has slipped rightward from the intersection Pc550.

As described above, according to the first aspect of the present invention,
In the trajectory calculation method in the second embodiment ,
When calculating the trajectory in the analysis space from the vector value at each point, it is possible to calculate an appropriate trajectory reflecting the properties of the obstacle surface.

[0030]

As described above, according to the trajectory calculation method of the present invention, when calculating the trajectory in the analysis space from the vector value at each point in the physical space , the trajectory does not intersect with the obstacle boundary, and There is an effect that an appropriate trajectory reflecting the property of the obstacle surface can be calculated.

[Brief description of the drawings]

FIG. 1 is a configuration diagram of an embodiment of a trajectory calculation method according to the first invention of the present application.

FIG. 2 is a flowchart of one embodiment of a trajectory calculation method according to the first invention of the present application.

FIG. 3 is a configuration diagram of an embodiment of a trajectory calculation method according to the second invention of the present application.

FIG. 4 is a flowchart of an embodiment of a trajectory calculation method according to the second invention of the present application.

FIG. 5 is an example of a trajectory calculation in the second invention of the present application.

FIG. 6 is a configuration diagram of a conventional trajectory calculation method.

FIG. 7 is a representation example of an obstacle in the analysis space.

FIG. 8 is an example of trajectory calculation in a conventional trajectory calculation method.

[Explanation of symbols]

Reference Signs List 10 trajectory calculation start point setting step 20 trajectory line segment end point calculation step 30 obstacle passing determination step 40 obstacle boundary processing step 50 trajectory calculation end determination step 60 vector value storage unit 70 obstacle boundary data storage unit 80 trajectory point column storage Part 510 vector value calculation point 520 trajectory line tip point Pn 530 trajectory line segment before correction 540 trajectory line end point before correction 550 intersection Pc 560 trajectory line segment end point after correction 570 trajectory line segment 580 after correction Obstacle boundary position data Lm 710 Obstacle area 720 Analysis area 810 Vector value calculation point 820 Trail point end point Pn 830 Vector value at trace end point V (P
n) 840 Trail segment end point Pn + 1 850 Obstacle area

 ────────────────────────────────────────────────── ─── Continuation of front page (56) References JP-A 1-263769 (JP, A) JP-A 4-168337 (JP, A) JP-A 4-312178 (JP, A) Toshio Nakanishi, "Computer Simulation ”, Kindai Kagaku-sha (Showa 52-10-10)

Claims (3)

(57) [Claims] 1. From a vector value at each point in a physical space,
A trajectory calculation method for calculating a trajectory line segment at an arbitrary point; a trajectory calculation start point setting step of setting a calculation start point of the trajectory segment and storing the calculated start point in a trajectory point sequence storage unit; A trajectory line end point calculating step of calculating the trajectory line end point by referring to the vector value at each point of the trajectory line segment to obtain the trajectory line segment; and a boundary with the obstacle in the analysis space from the obstacle boundary data storage unit. An obstacle passage determining step of determining whether or not the trajectory line segment calculated in the trajectory line segment end point calculating step with reference to a position intersects with an obstacle boundary ; Judged
Again generates a trajectory line that does not intersect with the obstacle boundary
And a trajectory calculation end determining step of determining the end of trajectory calculation and storing the calculated trajectory line segment in the trajectory point sequence storage unit if the trajectory calculation is to be ended and ending as a result. Method. 2. A trajectory line segment at an arbitrary point is calculated from a flow velocity vector value of a gas at each point in a physical space.
The trajectory calculation method described in 1. 3. A trajectory segment at an arbitrary point is calculated from a flow velocity vector value of the liquid at each point in the physical space.
The trajectory calculation method described in 1.