JP2010026579A - Computational grid forming device, computational grid forming method and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a computational grid forming device, a computational grid forming method and a program, for forming a high-quality computational grid by suppressing crush or deformation occurring when moving the computational grid. <P>SOLUTION: When moving a grid, a movement vector computing part 210 determines a movement vector ΔPc wherein a grid point as a movement target satisfies the following request. That is, the movement vector ΔPc is computed such that grid lines are orthogonalized as thoroughly as possible (orthogonalization), that grid points are smoothly distributed on the grid line based on a prescribed rule (smoothing), that a shape of the computational grid in an initial state is maintained (reproducibility of the initial grid), that a grid point interval becomes a prescribed minimum interval or above (to secure minimum interval), and that the grid point interval becomes a maximum interval or below (to secure maximum interval), and the grid is moved according to the computed movement vector ΔPc. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a calculation grid forming apparatus, a calculation grid forming method, and a program, and more particularly to a calculation grid forming apparatus, a calculation grid forming method, and a program for forming a calculation grid used for fluid analysis, structural analysis, and the like. .

  In recent years, various methods for numerical analysis of physical phenomena using computers and the like have been researched and developed. For example, an ALE (Arbitrary Lagrangian Eulerian formulations) method is known as one of fluid analysis methods around a moving object. In the ALE method, a physical space to be analyzed is discretized by a large number of grid points, and the physical space is mapped to a calculation space composed of a mesh-like calculation grid (hereinafter referred to as a grid). Then, the flow around the moving object is analyzed by moving and deforming the lattice over time. The quality of the lattice formed here greatly contributes to the accuracy and stability of the fluid analysis.

  The initial lattice (hereinafter referred to as the initial lattice) can be formed by (1) Geometrical Method, (2) Algebraic lattice formation (Transfinite method), (3) Lattice formation method using elliptic partial differential equations for coordinates, etc. The method is known. In addition, as a lattice moving method for moving the lattice from the initial state, (4) lattice moving method by spring analogy, (5) lattice moving method by elastodynamic approach, (6) smoothing by partial differential equation of velocity field, Such a method is known.

In addition, when creating a lattice when the shape is partially changed for a complex object using the elastodynamic method of (5), the lattice is regarded as an elastic body, and the outline of the existing lattice is A technique for simplifying the creation of a lattice by obtaining a moving vector of an internal lattice by performing structural analysis instead is disclosed (Patent Document 1).
In addition, for structural analysis, a method is disclosed that corrects the degree of deformation based on a geometrical relationship with respect to each coordinate direction so that the deformation of the object does not become excessive when large deformation is involved. (Patent Document 2).
In addition, a method of algebraically moving the lattice so that the lattice spacing of locations with large physical quantity changes in the orthogonal coordinate system is disclosed (Patent Document 3).

JP-A-9-128436 JP-A-7-302354 Japanese Patent Laid-Open No. 7-063643

  However, since the method of Patent Document 1 described above takes a balance equation with respect to the immediately preceding lattice, the initial lattice information is not reflected and it is difficult to control the spatial resolution. That is, once the grid is crushed, there is a problem that the grid does not return to the original size even if the boundary position returns to the original position. In addition, since the orthogonalization and concentration of the lattice are adjusted by one stiffness parameter, there is a problem that this parameter must be adjusted by trial and error depending on the object and motion in a complicated shape.

  Further, the technique of Patent Document 2 has a problem that two-dimensional or three-dimensional distortion cannot be suppressed because correction is independently obtained so that the lattice is not excessively deformed in each lattice line direction. Moreover, since the method of Patent Document 3 obtains correction independently for each lattice line direction, it cannot suppress two-dimensional or three-dimensional distortion. Furthermore, since a rectangular coordinate system is assumed, there is a problem that it cannot cope with complicated shapes.

FIGS. 13A and 13B are output examples of the flow analysis result when the prismatic object 60 is rotated using the conventional method. FIG. 13A is an overall view of the initial state, and FIG. 13B is the upper left of the object 60 in FIG. The figure which expanded the calculation space containing a corner part, (c) is a whole figure at the time of the maximum displacement, (d) is the figure which expanded the calculation space of the upper corner part of the prismatic object 60 of (c).

Here, the lattice is moved using a method of extending the above-described spring analogy to a structured lattice. The rotation angle of the prism is a maximum of 45 degrees.
In the conventional method shown in FIG. 13, the lattice is crushed particularly at the corners near the wall.

  The present invention has been made in view of the above-described problems, and an object of the present invention is to provide a calculation grid forming apparatus and a calculation grid forming apparatus that can suppress crushing and distortion generated when moving the calculation grid and form a high-quality calculation grid. A method and program are provided.

  In order to achieve the above-described object, the first invention is a calculation grid forming apparatus that forms a calculation grid composed of a plurality of grid points in a calculation space and moves each grid point over time, and is a moving object. Movement vector calculation means for calculating a movement vector of a lattice point; and lattice movement means for sequentially calculating a position after movement of the lattice point according to the movement vector calculated by the movement vector calculation means; The means includes an orthogonalization request for defining the movement vector so that a crossing angle of grid lines of the calculation grid is vertical or substantially vertical, and the grid points are smoothly distributed in the calculation space based on a predetermined rule. The smoothing request to define the movement vector and the movement vector so that the lattice distribution of the calculation grid after movement approaches the lattice distribution of the corresponding calculation grid in the initial state An initial grid reproduction request to be defined, a minimum interval ensuring request for defining the movement vector such that an interval between the grid point to be moved and an adjacent grid point is equal to or greater than a predetermined minimum interval, and the movement target A calculation lattice forming apparatus, wherein the movement vector is calculated based on a request for securing a maximum interval that defines the movement vector so that an interval between the lattice point and an adjacent lattice point is equal to or less than a predetermined maximum interval. It is.

  Further, in the smoothing request, the initial lattice reproduction request, the minimum interval ensuring request, and the maximum interval ensuring request, the position information of the calculation lattice in the initial state and the position information of each lattice in the previous lattice moving step are included. Based on each, a movement vector is defined.

  The movement vector calculating means may satisfy the orthogonalization request, the smoothing request, the initial lattice reproduction request, the minimum interval ensuring request, and the maximum interval ensuring request, in order to satisfy each of the relative lattice points. Each movement vector is calculated from the positional relationship using a predetermined relational expression, a linear sum obtained by superimposing the calculated movement vectors using a predetermined weight is calculated, and the lattice moving means calculates the calculated linear sum To move the position of each grid point.

  Further, an initial value extrapolating unit for extrapolating an initial value to the movement vector calculating unit based on position information of the grid point at the previous time may be further provided.

  A second invention is a calculation grid forming method in which a calculation grid including a plurality of grid points is formed in a calculation space, and each grid point is moved with time, and a movement vector of a grid point to be moved is calculated. A movement vector calculation step; and a lattice movement step for sequentially calculating a position after movement of the lattice point according to the movement vector calculated by the movement vector calculation step, and the movement vector calculation step includes a lattice of the calculation lattice An orthogonalization request for defining the movement vector so that the intersection angle of the lines is vertical or substantially vertical, and a smoothing for defining the movement vector so that the grid points are smoothly distributed in the calculation space based on a predetermined rule. And an initial case that defines the movement vector so that the lattice distribution of the calculation lattice after the movement approaches the lattice distribution of the corresponding calculation lattice in the initial state. A reproduction request, a minimum interval securing request for defining the movement vector so that an interval between the lattice point to be moved and an adjacent lattice point is equal to or greater than a predetermined minimum interval, and an adjacent to the lattice point to be moved In the calculation grid forming method, the movement vector is calculated on the basis of a request for securing a maximum interval that defines the movement vector so that an interval between the grid point to be equal to or less than a predetermined maximum interval.

  The third invention is a program for causing a computer to function as the calculation grid forming apparatus of the first invention.

  According to the present invention, it is possible to provide a calculation grid forming apparatus, a calculation grid forming method, and a program that can suppress the collapse and distortion generated when moving the calculation grid and form a high-quality calculation grid.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

FIG. 1 is a diagram for explaining a calculation grid formed by the calculation grid forming apparatus 1 of the present embodiment.
FIG. 2 is a hardware configuration diagram of a computer that realizes the calculation grid forming apparatus 1 according to the present embodiment.

  In order to map the physical space to be analyzed to the calculation space 50, the calculation grid forming apparatus 1 discretizes the calculation space 50 with a plurality of grid points to form a calculation grid (hereinafter referred to as a grid). The calculation space 50 shown in FIG. 1 is represented by a plurality of grid lines that intersect in the vertical and horizontal directions. The point where the grid lines intersect is the grid point.

FIG. 1 shows a state in which a prismatic object 60 placed in the center of the calculation space 50 is viewed from above. The calculation grid of FIG. 1 is formed so that the grid line spacing is narrow on the extension lines of the sides of the object 60.

In FIG. 1, a two-dimensional calculation space 50 is illustrated for simplification of the following description, but may be three-dimensional. The shape of the lattice is not limited to a quadrangle, and may be a hexahedron. In the calculation space 50, the coordinates are represented by (ξ, η) in the case of two dimensions, and (ξ, η, ζ) in the case of three dimensions.
The lattice vector represents a vector determined from the position of each lattice point, and the movement vector represents a vector that defines the direction and length of the lattice point to be moved.

  As shown in FIG. 2, the calculation grid forming apparatus 1 includes a control unit 3, a storage unit 5, a media input / output unit 7, a communication control unit 9, an input unit 11, a display unit 13, a peripheral device I / F unit 15, and the like. Are connected to the bus 17.

  The control unit 3 includes a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), and the like.

The CPU calls and executes a program stored in the storage unit 5, ROM, recording medium, or the like to a work memory area on the RAM, drives and controls each device connected via the bus 17, and calculates the grid 1. The processing described later (see FIGS. 9, 11, and 12) is realized.
The ROM is a non-volatile memory and permanently holds a computer boot program, a program such as BIOS, data, and the like.
The RAM is a volatile memory, and temporarily stores programs, data, and the like loaded from the storage unit 5, ROM, recording medium, and the like, and includes a work area used by the control unit 3 for performing various processes.

The storage unit 5 is an HDD (hard disk drive), and stores a program executed by the control unit 3, data necessary for program execution, an OS (operating system), and the like. As for the program, a control program corresponding to an OS (operating system) and an application program are stored.
Each of these program codes is read by the control unit 3 as necessary, transferred to the RAM, read by the CPU, and executed as various means.

  The media input / output unit 7 (drive device) inputs / outputs data, for example, floppy (registered trademark) disk drive, PD drive, CD drive (-ROM, -R, RW, etc.), DVD drive (-ROM, -R, -RW, etc.) and a media input / output device such as an MO drive.

  The communication control unit 9 includes a communication control device, a communication port, and the like, and is a communication interface that mediates communication between the computer and the network 19, and performs communication control between other computers via the network 19.

  The input unit 11 is, for example, a keyboard, a pointing device such as a mouse, or an input device such as a numeric keypad, and inputs data.

  The display unit 13 includes a display device such as a liquid crystal panel and a CRT monitor, and a logic circuit or the like (video adapter or the like) for realizing a video function of the computer in cooperation with the display device.

  The peripheral device I / F (interface) unit 15 is a port for connecting a peripheral device to the computer, and the computer transmits and receives data to and from the peripheral device via the peripheral device I / F unit 15. The peripheral device I / F unit 15 is configured by USB, IEEE 1394, RS-232C, or the like, and usually has a plurality of peripheral devices I / F. The connection form with the peripheral device may be wired or wireless.

  The bus 17 is a path that mediates transmission / reception of control signals, data signals, and the like between the devices.

Next, the functional configuration of the calculation grid forming apparatus 1 will be described with reference to FIG.
FIG. 3A is a functional schematic configuration diagram of the entire calculation grid forming apparatus 1, and FIG. 3B is a block diagram of the grid movement calculation unit 200.

As shown in FIG. 3, the calculation grid forming apparatus 1 includes an initial grid forming unit 100, a grid movement calculation unit 200, a fluid analysis unit 300, and a result output unit 400.
The initial lattice forming unit 100 forms an initial state lattice (hereinafter referred to as an initial lattice). Any method may be used for forming the initial lattice. For example, a known method such as Geometrical Method, a lattice formation method using an algebraic expression (Transfinite method), a lattice formation method using an elliptic partial differential equation with respect to coordinates may be used. Alternatively, data related to the initial lattice may be stored in advance in the storage unit 5 and read from the storage unit 5 by the initial lattice forming unit 100 during analysis. The initial lattice forming unit 100 outputs the formed initial lattice to the lattice movement calculation unit 200.

  The lattice movement calculation unit 200 includes an initial lattice input from the initial lattice forming unit 100, flow field information to be analyzed, lattice information d10, and the like input from the input unit 11 or read from the storage unit 5. , To perform a calculation for moving the grid. The movement of the lattice is to change the position of each lattice point in the calculation space 50 for each time step, and is sequentially calculated by the lattice movement calculation unit 200. The processing performed by the lattice movement calculation unit 200 will be described later.

  The fluid analysis unit 300 calculates a Jacobian determinant, a metric relational equation, and the like for the moved lattice input from the lattice movement calculation unit 200 and performs fluid calculation. For example, the flow field, calculation of various statistics, analysis of changes with time of the grid, etc. are performed. Then, the analysis result is output to the result output unit 400. After the calculation by the fluid analysis unit 300, the process returns to the lattice movement calculation unit 200 again, the lattice position at the next time is obtained, and the fluid calculation is performed. The result output unit 400 displays the analysis result input from the fluid analysis unit 300 on the display unit 13 as a numerical value, a graph, or a graphic display.

Next, the lattice movement calculation unit 200 will be described with reference to FIGS. 3B, 4, 5, 6, 7, and 8.
As shown in FIG. 3B, the lattice movement calculation unit 200 includes an orthogonalization unit 211, a smoothing unit 212, an initial lattice reproduction unit 213, a minimum interval ensuring unit 214, a maximum interval ensuring unit 215, and a linear sum calculation unit. The movement vector calculation unit 210 having 216 and the lattice movement unit 220 are configured.

The movement vector calculation unit 210 calculates a movement vector of each lattice point for each step. The movement vector is defined by its direction and length.
Furthermore, in the calculation grid generation device 1 of the present invention, the movement vector is in accordance with the respective requests of the orthogonalization unit 211, the smoothing unit 212, the initial grid reproduction unit 213, the minimum interval ensuring unit 214, and the maximum interval ensuring unit 215. It is determined.
In other words, the orthogonalizing unit 211 intersects the lattice lines as orthogonally as possible (orthogonal or substantially orthogonal) to suppress distortion and twisting of the lattice. In addition, the smoothing unit 212 smoothly distributes the lattice points on the lattice lines, thereby reducing abrupt changes in lattice spacing and position. In addition, the initial lattice reproduction unit 213 keeps the initial lattice distribution as much as possible. Also, the minimum interval securing unit 214 prevents the lattice interval from becoming too narrow. Further, the maximum interval ensuring unit 215 prevents the lattice interval from becoming too wide.

  As described above, by directly inputting a request for orthogonalization or the like when calculating the movement vector, an effect that the lattice is not easily broken is obtained. Further, since the request regarding the position of the grid point is directly given when calculating the movement vector, the user can easily control the weight of each request intuitively.

In addition, the movement vector calculation unit 210, for each request other than orthogonalization (smoothing unit 212, initial lattice reproduction unit 213, minimum interval securing unit 214, maximum interval securing unit 215), The moving vector is calculated by reflecting the lattice position information reconstructed by the immediately preceding lattice moving step.
Further, in calculating the movement vector corresponding to each request, as will be described below, a predetermined geometric relational expression (formula (1) to formula (to be described later) is obtained from the relative positional relation with the surrounding grid points. (9)).

FIG. 4 is a diagram for explaining the movement vector ΔPc ^ortho determined by the orthogonalizing unit 211, FIG. 5 is a diagram for explaining the movement vector ΔPc ^smo determined by the smoothing unit 212, and FIG. FIG. 7 is a diagram illustrating the movement vector ΔPc ⁱⁿⁱ determined by the initial lattice reproduction unit 213, FIG. 7 is a diagram illustrating the movement vector ΔPc ^min determined by the minimum interval securing unit 214, and FIG. it is a diagram illustrating a movement vector Delta] Pc ^max determined by the secured portion 215.
4 to 8, Pnw, Pn, Pne, Pe, Pse, Ps, Psw, Pw, and Pc each represent a lattice point. Of these lattice points, a line connecting adjacent lattice points is a lattice line.
4 to 8, an arrow (→) is added as a symbol representing a vector, but no arrow is added in the specification. Instead, for example, in order to distinguish the point P from the vector P, the term “vector P” is used when referring to a vector.

As shown in FIG. 4, the orthogonalizing unit 211 calculates a movement vector of a lattice point (central lattice point Pc) to be moved so that the intersection angle of each lattice line intersects perpendicularly or substantially perpendicularly. Specifically, the lattice point Pc is first calculated from the points Pw, Pe, Psw, and Pse passing through the perpendicular line from the point Ps in order to satisfy the orthogonality from the point Ps side (for example, passing through the point Ps). It is desirable to move to a line perpendicular to the vector b. This movement vector is set as ΔPc ^(s) .
The movement vector ΔPorth for improving the orthogonality to be finally ^obtained is obtained by superimposing the movement vectors in the four surrounding directions in the two-dimensional case and the ^six surrounding directions in the three-dimensional case as in the following equation (1). can get.

Here, w _w , w _e , w _s , w _n , w _h , and w _l are weights in the w direction, e direction, s direction, n direction, h direction, and l direction, respectively. Calculate so that
In addition, w _w , w _e , w _s , w _n , w _h , and w _l change the balance of the weights in consideration of the length of the grid in each direction (lattice point interval) and the deviation angle from the right angle. Shall.

The smoothing unit 212 defines the movement vector ΔPc so that the lattice points Pc are smoothly distributed on the lattice lines according to a predetermined rule. Here, “smoothness” and “smoothness” mean that the lattice points are distributed according to a predetermined rule without concentrating on a part of the lattice points and without varying the lattice spacing ratio. For example, the case where the intervals and the interval ratio are equal, or the case where the intervals are distributed according to the geometric series.
Specifically, when a lattice arrangement as shown in FIG. 5 is considered, a movement vector ΔPc ^(η) that improves the smoothness in the η direction is given as follows.

In equation (2), the superscript “0” means the initial lattice position. Expression (2) indicates that the target lattice point Pc moves on a straight line connecting the adjacent lattices Ps and Pn and moves to a position that maintains the initial lattice spacing ratio.
The three-dimensional smoothed lattice movement vector ΔPc ^smo is calculated as shown in the following equation (3) by superimposing movement vectors in each direction of ξ, η, and ζ.

Here, w _ξ , w _η , and w _ζ are weights in the directions of ξ, η, and ζ, respectively, and are calculated to be 1 when all are added.
The weights w _ξ , w _η , and w _ζ are defined so as to change according to the initial length of the lattice in each direction.

The initial lattice reproduction unit 213 defines the movement vector so that the lattice distribution after the movement approaches the lattice distribution in the initial state. Here, the lattice distribution means a distribution of lattice points existing on each lattice line. “Making the lattice distribution closer to the initial lattice distribution” means that even when the entire lattice line expands or contracts, the lattice points move accordingly, and the relative positional relationship (distribution) of the lattice points does not change.
Specifically, when the lattice arrangement as shown in FIG. 6 is considered with respect to the η direction, the movement vector ΔPc ^(s) relating to the reproducibility of the initial lattice from the point Ps side with respect to the lattice point Pc is given by the following equation. .

Equation (4) indicates that the point Pc is moved in the direction of the vector PsPn connecting both adjacent lattices Ps and Pn so that the lattice interval between the points Pc and Ps is equal to the initial lattice interval between the same points. Represents. The movement vector ΔPc ⁱⁿⁱ for the reproducibility of the final initial lattice is obtained by superimposing the movement vectors in the six surrounding directions as in the following equation (5) in three dimensions.

Here, w _w , w _e , w _s , w _n , w _h , and w _l are weights in the w direction, e direction, s direction, n direction, h direction, and l direction, respectively. Calculate so that
The weights w _w , w _e , w _s , w _n , w _h , and w _l are defined so as to change according to the initial length of the lattice.

The minimum interval ensuring unit 214 defines the movement vector so as to ensure the minimum interval between the lattice points. Specifically, considering the lattice arrangement as shown in FIG. 7 with respect to the η direction, the movement vector ΔPc ^(s) for securing the minimum lattice spacing on the Ps side is given by the following equation (6).

Equation (6), when the distance between the grid point Pc and the lattice point Ps becomes less than the allowable minimum grid spacing delta _min, so the point Pc is equal to the allowable minimum grid spacing of points Ps side, grid on both sides The movement in the direction of the vector PsPn connecting the points Ps and Pn is shown.

Here, a fixed value may be used for the allowable minimum grid interval, or a different value may be used for each grid.
When the lattice spacing on the opposite side (Pn side) is equal to or smaller than the allowable minimum lattice spacing, the movement vector in the η direction is obtained by superimposing the movement vectors of both on the basis of the weight related to the lattice length.
Finally, the movement vector ΔPc ^min for securing the minimum lattice spacing is obtained by the following equation (7) by superimposing the movement vectors in the ξ, η, and ζ directions.

The maximum interval ensuring unit 215 defines a movement vector so as to ensure the maximum interval between lattice points. Specifically, considering the lattice arrangement as shown in FIG. 8 with respect to the η direction, the movement vector ΔPc ^(s) for securing the maximum lattice spacing on the Ps side is given by the following equation (8).

If the distance between the formula (8) is the point Pc and the point Ps is equal to or greater than the allowable maximum grid spacing delta _max, so the point Pc is equal to the allowable maximum grid spacing of points Ps side, grid on both sides Ps and Pn Represents movement in the direction of a vector PsPn connecting the two.
Here, a constant value may be used for the maximum allowable lattice spacing, or a different value may be used for each lattice. When the lattice spacing on the opposite side (Pn side) is equal to or greater than the allowable maximum lattice spacing, the movement vectors in the η direction are obtained by superimposing the movement vectors of both on the basis of the weight related to the lattice length.
Finally, the movement vector ΔPc ^max related to securing the maximum lattice spacing is obtained by the following formula (9) by superimposing the contributions in the ξ, η, and ζ directions.

  The linear sum calculation unit 216 is configured to calculate the movement vector of each lattice point calculated by the orthogonalization unit 211, the smoothing unit 212, the initial lattice reproduction unit 213, the minimum interval ensuring unit 214, and the maximum interval ensuring unit 215 of the movement vector calculating unit 210. Is calculated as a lattice movement vector ΔPc at the next time. The linear sum is expressed by the following equation (10).

Here, C _ortho , C _smo , C _ini , C _min , and C _max are respective weights relating to orthogonality, smoothness, initial lattice reproducibility, ensuring the minimum lattice spacing, and securing the maximum lattice spacing.
Further, dt _sub is a pseudo time step of a sub-step (see FIG. 9) used for sequential calculation described later.

  The lattice movement unit 220 sequentially calculates the position of the lattice point after the movement according to the linear sum ΔPc of the movement vectors calculated by the linear sum calculation unit 216.

  Next, with reference to FIGS. 9 and 10, the operation in the calculation grid forming apparatus 1 will be described.

FIG. 9 is a flowchart showing a processing procedure of the calculation grid forming apparatus 1.
FIG. 10 is a diagram illustrating a result example obtained by the calculation grid forming apparatus 1 of the present embodiment.

The calculation grid forming apparatus 1 forms and moves a grid according to the procedure of the flowchart of FIG. 9 and executes fluid analysis calculation.
In FIG. 9, the left side is a portion related to normal fluid calculation, and the right side is a portion related to grid movement processing executed by the calculation grid forming apparatus 1 of the present embodiment. The grid movement process is incorporated as part of the time progression of the fluid calculation.

  First, the initial lattice forming unit 100 reads information about the initial lattice from the storage unit 5 (step S101) and passes the information to the lattice movement calculation unit 200. The lattice movement calculation unit 200 calculates initial lattice information (lattice vector, lattice interval) necessary for moving the lattice (step S102) and stores it in the RAM. Next, the initial lattice forming unit 100 reads a file having information on the flow field and the lattice from the storage unit 5 (step S103) and passes the file to the lattice movement calculation unit 200.

  The lattice movement calculation unit 200 performs a process of moving the lattice based on the read information about the initial lattice, the flow field, and the lattice. In the subsequent processing, the movement vector of each lattice is calculated for each pseudo time step (hereinafter referred to as time step) of the fluid calculation. At that time, a sub-step is provided in each time step, and the movement vector is sequentially calculated in an explicit manner.

  First, in step S104, the boundary with the object 60 is moved to a position at the next time. Here, the initial value of the substep is set. As the initial value, the lattice information at the previous time is used. Alternatively, the initial value may be extrapolated from lattice information at a time before the previous time. For example, the lattice information at the last two times is given as the initial value. (Step S105). However, for the first time step, step S105 is skipped and the process proceeds to step S106. When the initial values are extrapolated, it is expected that the convergence of the solution is accelerated and the lattice quality near the wall is improved.

  In step S106, the movement vector calculation unit 210 calculates a lattice vector and a lattice interval from the current lattice point position information. In step S107, the movement vector calculation unit 210 calculates the movement vector of each lattice.

As described above, the movement vector is first moved so that each request by the orthogonalizing unit 211, the smoothing unit 212, the initial lattice reproducing unit 213, the minimum interval securing unit 214, and the maximum interval securing unit 215 is satisfied. Vectors ΔPc ^ortho , ΔPc ^smo , ΔPc ⁱⁿⁱ , ΔPc ^min , and ΔPc ^max are calculated. Then, the linear sum calculation unit 220 calculates the linear sum ΔPc of the movement vectors ΔPc ^ortho , ΔPc ^smo , ΔPc ⁱⁿⁱ , ΔPc ^min , and ΔPc ^max according to the calculated request of each unit. That is, the movement vector ΔPc that satisfies all the requirements for orthogonalization, smoothing, reproducibility of the initial lattice, ensuring the minimum lattice spacing, and securing the maximum lattice spacing is determined. The lattice moving unit 220 moves the position of the lattice according to the determined movement vector ΔPc (step S108).

The movement vector calculation unit 210 repeats the processing from step S106 to step S108 K times. When the upper limit number (Kmax) is reached (step S109; Yes), the lattice position of the next step is finally determined by the movement vector at that time. .
Thereafter, a lattice moving speed is calculated from each lattice position in the current step and the previous step (step S110), and the flow proceeds to the fluid calculation unit 300.

  The fluid analysis unit 300 uses the lattice position information after the movement to calculate a Jacobian (Jacobi determinant) and a metric relational expression in the same manner as a known fluid calculation process (step S111), and performs fluid calculation at the time step. Execute (Step S112). The fluid analysis unit 300 repeats the processing from step S104 to step S112 for N time steps. When the upper limit number (Nmax) is reached (step S113; Yes), the final flow field state and various statistics are updated. An analysis result including the time history, the grid position at that time, and the like is passed to the result output unit 400. The result output unit 400 outputs the fluid analysis result as a numerical value, a graph, or a graphic display (step S114).

FIGS. 10A and 10B are output examples of the result of the rotation problem of the prismatic object 60 obtained by the calculation grid forming apparatus 1 of the present embodiment. FIG. 10A is an overall view in an initial state, and FIG. The figure which expanded the calculation space containing the upper left corner part of the object 60, (c) is the whole figure at the time of maximum displacement, (d) is the figure which expanded the calculation space containing the upper corner part of the prismatic object 60 of (c). It is.
It is assumed that the motion of the prismatic object 60 is given by the following equation (11).

In Expression (11), θ represents a rotation angle.
The maximum rotation angle θ _max is 45 degrees.

  As shown in FIG. 10 (d), the grid formed by the calculation grid forming apparatus 1 of the present embodiment is less crushed and distorted even at the maximum displacement. Especially in the vicinity of the wall (object), the result appears remarkably.

As described above, when the lattice movement calculation unit 200 moves the lattice, the calculation lattice generation apparatus 1 according to the present embodiment calculates the movement vector of the lattice point to be moved by the movement vector calculation unit 210. . The movement vector calculated at that time is defined so as to satisfy the respective requirements of orthogonality, smoothness, initial lattice reproducibility, securing the minimum lattice spacing, and securing the maximum lattice spacing. As a result, it is possible to form a high-quality lattice with less crushing and distortion, and the accuracy of fluid analysis can be improved.
In addition, since the movement vector is calculated with reference to the initial grid and the previous grid position information, a grid that reflects the grid distribution (spatial resolution) of the initial grid and that has less distortion as time progresses is configured. it can.

  In the flowchart of FIG. 9 described above, the processing operation in the case where the movement of the boundary is known is shown. However, for example, it may be coupled with another analysis method such as structural analysis or mechanism analysis. In that case, processing based on the flowchart of FIG. 11 or 12 is performed instead of the flowchart of FIG. In the functional block diagram of FIG. 3A, the “fluid analysis unit 300” is provided with a “structure analysis or mechanism analysis coupled analysis unit”.

  FIG. 11 and FIG. 12 show a processing procedure for coupling with structural analysis or mechanism analysis when a lattice is formed using the movement vector calculation method of the present embodiment, and FIG. 11 shows a case of weak coupling. FIG. 12 is a flowchart showing the case of strong coupling.

  In the weakly coupled example of FIG. 11, Steps S201 to S212 form and move a lattice in the same manner as Steps S101 to S112 of FIG. 9, and execute fluid calculation. In step S213, a structure calculation or a mechanism calculation process is added after the fluid calculation. Thereafter, the processing from step S204 to step S213 is repeated until the upper limit number (Nmax) is reached (step S214), and then the result is output (step S215), and the processing is terminated.

Also in the strongly coupled example of FIG. 12, steps S301 to S312 form and move a lattice in the same manner as steps S101 to S112 of FIG. 9, and perform fluid calculation. In step S313, a structure calculation or mechanism calculation process is added after the fluid calculation (step S313). In the case of strong coupling, force and displacement values are exchanged between fluid calculation and structural calculation (or mechanism calculation) to balance the two. Therefore, a sub-step M is provided in the time step N. While repeating the sub-step until the upper limit number (Mmax) is reached (step S314), the time step corresponding to the real time progression in the unsteady calculation is repeated until the upper limit number (Nmax) is reached (step S315).
Thereafter, the result is output (step S316), and the process is terminated.

Note that the calculation grid moving method of the present embodiment is not only applied to the above-described fluid analysis (FIG. 9) or the coupling between the fluid analysis and the structural analysis (FIGS. 11 and 12), but also applied to the structural analysis. It is also possible to do.
In the case of application to structural analysis, the “fluid calculation” process in step S112 is replaced with a “structural calculation” process in the flowchart of FIG.
In the functional block diagram of FIG. 3A, the fluid analysis unit 300 is replaced with a structural analysis unit.

  Note that the programs for performing the processes shown in FIGS. 9, 11, and 12 may be distributed on a recording medium such as a CD-ROM, or may be transmitted / received via a communication line.

  The preferred embodiments of the calculation grid forming apparatus and the like according to the present invention have been described above with reference to the accompanying drawings, but the present invention is not limited to such examples. It will be apparent to those skilled in the art that various changes or modifications can be conceived within the scope of the technical idea disclosed in the present application, and these naturally belong to the technical scope of the present invention. Understood.

The figure explaining the calculation grid formed with the calculation grid formation apparatus 1 Hardware configuration diagram of a computer realizing the calculation grid forming apparatus 1 (A) Functional schematic block diagram of the entire calculation grid forming apparatus 1 (b) Block diagram of the grid moving unit 200 The figure explaining the movement vector determined by the orthogonalization part 211 The figure explaining the movement vector determined by the smoothing part 212 The figure explaining the movement vector determined by the initial lattice reproduction part 213 The figure explaining the movement vector determined by the minimum space ensuring part 214 The figure explaining the movement vector determined by the maximum space | interval ensuring part 215 The flowchart which shows the process sequence of the calculation grid | lattice formation apparatus 1. The figure which shows the example of a result output obtained by the calculation grid formation apparatus 1 Flow chart showing the processing procedure when weakly coupled with structural analysis or mechanism analysis Flow chart showing the processing procedure for strong coupling with structural analysis or mechanism analysis Result output example of rotation problem of prismatic object 60 using conventional method

Explanation of symbols

1 ... Calculation grid forming device 50 ......... Calculation grid 60 ......... Object (Pollar object)
DESCRIPTION OF SYMBOLS 100 ......... Initial lattice formation part 200 ......... Grid movement calculating part 210 ......... Movement vector calculation part 211 ......... Orthogonalization part 212 ......... Smoothing part 213 ......... Initial lattice reproduction part 214 ......... Minimum interval securing unit 215 ......... Maximum interval securing unit 216 ......... Linear sum calculation unit 220 ......... Lattice moving unit 300 ......... Fluid analysis unit 400 ......... Result output unit

Claims (9)

A calculation grid forming device that forms a calculation grid consisting of a plurality of grid points in a calculation space and moves each grid point over time,
A movement vector calculation means for calculating a movement vector of a lattice point to be moved;
Grid movement means for sequentially calculating the position after movement of the grid point according to the movement vector calculated by the movement vector calculation means,
The movement vector calculation means includes
An orthogonalization request for defining the movement vector so that an intersection angle of grid lines of the calculation grid is vertical or substantially vertical;
A smoothing request for defining the movement vector so that the grid points are smoothly distributed in the calculation space based on a predetermined rule;
An initial lattice reproduction request for defining the movement vector so that the lattice distribution of the calculation lattice after the movement approaches the lattice distribution of the corresponding calculation lattice in the initial state,
A minimum interval ensuring request that defines the movement vector such that an interval between the lattice point to be moved and an adjacent lattice point is equal to or greater than a predetermined minimum interval;
A maximum interval ensuring request that defines the movement vector so that an interval between the lattice point to be moved and an adjacent lattice point is equal to or less than a predetermined maximum interval;
The calculation lattice forming apparatus, wherein the movement vector is calculated based on   In the smoothing request, the initial lattice reproduction request, the minimum interval ensuring request, and the maximum interval ensuring request, based on the position information of the calculation lattice in the initial state and the position information of each lattice in the previous lattice moving step, The calculation grid forming apparatus according to claim 1, wherein each vector defines a movement vector. The movement vector calculating means may satisfy the orthogonalization request, the smoothing request, the initial lattice reproduction request, the minimum interval ensuring request, and the maximum interval ensuring request, in order to satisfy each of the relative lattice points. Calculate each movement vector using a predetermined relational expression from the positional relationship, calculate a linear sum obtained by superimposing each calculated movement vector using a predetermined weight,
The calculation grid forming apparatus according to claim 1, wherein the grid moving unit moves the position of each grid point according to the calculated linear sum.   2. The calculation grid forming apparatus according to claim 1, further comprising initial value extrapolation means for extrapolating an initial value to the movement vector calculation means based on position information of grid points at a previous time. A calculation grid forming method of forming a calculation grid consisting of a plurality of grid points in a calculation space and moving each grid point over time,
A movement vector calculation step for calculating a movement vector of a lattice point to be moved;
A lattice movement step of sequentially calculating the position after movement of the lattice point according to the movement vector calculated by the movement vector calculation step,
The movement vector calculation step includes:
An orthogonalization request for defining the movement vector so that a crossing angle of grid lines of the calculation grid is vertical or substantially vertical;
A smoothing request for defining the movement vector so that the grid points are smoothly distributed in the calculation space based on a predetermined rule;
An initial lattice reproduction request for defining the movement vector so that the lattice distribution of the calculation lattice after the movement approaches the lattice distribution of the corresponding calculation lattice in the initial state,
A minimum interval ensuring request that defines the movement vector such that an interval between the lattice point to be moved and an adjacent lattice point is equal to or greater than a predetermined minimum interval;
A maximum interval ensuring request that defines the movement vector so that an interval between the lattice point to be moved and an adjacent lattice point is equal to or less than a predetermined maximum interval;
And calculating the movement vector based on the calculation grid.   In the smoothing request, the initial lattice reproduction request, the minimum interval ensuring request, and the maximum interval ensuring request, based on the position information of the calculation lattice in the initial state and the position information of each lattice in the previous lattice moving step, 6. The calculation grid forming method according to claim 5, wherein each of the movement vectors is defined. The movement vector calculating step may be performed in order to satisfy the orthogonalization request, the smoothing request, the initial lattice reproduction request, the minimum interval ensuring request, and the maximum interval ensuring request, respectively. Calculate each movement vector using a predetermined relational expression from the positional relationship, calculate a linear sum obtained by superimposing each calculated movement vector using a predetermined weight,
6. The calculation grid forming method according to claim 5, wherein the grid moving step moves the position of each grid point according to the calculated linear sum.   6. The calculation grid forming method according to claim 5, further comprising an initial value extrapolation step of extrapolating an initial value to the movement vector calculation step based on position information of grid points at a previous time.   A program for causing a computer to function as the calculation grid forming apparatus according to claim 1.

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