JPH08263470A - Numerical fluid analytic method using two kinds of time integration methods - Google Patents

Abstract

PURPOSE: To stably and efficiently advance analysis employing a finite difference method of differential equation controlling a flow. CONSTITUTION: When analyzing the different equation controlling the flow using a finite difference method, a processor PE(0) of an analysis calculation part 2 finds the physical quantity of the next step using an implicit solution method which divides the entire analysis region by a time segmenting value Δt. In parallel with this processing, other processors PE(1) to PE(L) find the physical quantities of the next step using an explicit solution method with a time segmenting value Δt/m for partial regions with violent change of flow change. For the partial regions to which the explicit solution method is applied the value found by the implicit solution method and the value found by the explicit solution method are averaged with weight.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a numerical fluid analysis method for analyzing a differential equation governing a flow by a finite difference method, and particularly stably and efficiently using two types of time integration methods, an implicit method and an explicit method. The present invention relates to a computational fluid dynamics analysis method.

[0002]

2. Description of the Related Art In the field of numerical fluid analysis, the finite difference method is often used for analysis. That is, a grid is set up in the analysis space, and the basic equation that governs the flow is differentiated with respect to this grid for analysis. In particular, there are an explicit method and an implicit method for time integration. In the case of the explicit method, if the grid width is small, the time step width must be small. That is, there is a maximum value in every time step ("Difference method", Ryoichi Takahashi, Yoshihiro Tanamachi)
Co-authored Baifukan). On the other hand, in the case of the implicit method, there is no maximum value for the step value, and the step value can be made large, but in the case of an analysis with a rapidly changing flow, the solution may diverge (see "Some of incompressible viscous fluids"). Difference analysis method ”, Nobumasa Takemitsu, Proceedings of the Japan Society of Mechanical Engineers (B), Vol. 52, No. 478, No. 85-0291A, June 1986). In the conventional computational fluid analysis method, the analysis is performed using either the implicit method or the explicit method.

[0003]

As described above, with respect to the time integral of the basic equation governing the flow, if the explicit method is used, the time step value is limited (the maximum value exists), and the implicit method is used. If the step value is set to a large value, the solution may diverge when a complicated flow is analyzed, and there is a problem in that it is difficult to proceed efficiently and stably in both cases.

The present invention solves such a conventional problem, and an object thereof is to enable the analysis of the differential equation governing the flow by the finite difference method to proceed stably and efficiently. To do.

[0005]

As described above, there are the implicit method and the explicit method as the time integration method of the basic equation governing the fluid. The present invention does not use either one of them,
Basically, the whole analysis area is analyzed by the implicit method, and in the part where the flow changes drastically, the explicit method is also analyzed and averaged with the result of the implicit method. Therefore, in the present invention, n
Physical quantity (speed, etc.) at step (n = 0, 1, ...)
When k is known, the physical quantity of (n + 1) steps is first obtained by the implicit method in the entire analysis area. The time step value Δt at this time can be taken relatively large as compared with the case of solving by the explicit method, since there are no limiting conditions caused by the analysis method.
This time step value Δt is given as an input. Then, in parallel with the calculation of the time integration by the implicit method in the whole area, the partial area designated by the user as an input where the flow is expected to change drastically is also analyzed by the explicit method. In this explicit calculation, n
Using the physical quantity of the step as an initial value, the time step value Δt ′ is set to m so that Δt ′ = Δt / m does not exceed the limit caused by the explicit method, and the time step value Δt ′ is used to calculate m by the explicit method. Repeated times, the value of the mth time is set as the physical quantity of the (n + 1) step of the partial area. Then, for the partial region to which the explicit method is applied, the value obtained by the implicit method and the value obtained by the explicit method are weighted and averaged. The weighting value for this averaging is given at the input. The calculation by the implicit method in all the above areas and the calculation by the explicit method in the partial area specified by the input are performed in parallel by the processors of the parallel computer.

[0006]

Embodiments of the present invention will now be described in detail with reference to the drawings.

Referring to FIG. 1, an example of a numerical fluid analysis system to which the present invention is applied comprises an analysis condition input section 1, an analysis calculation section 2, an analysis result display section 3, a display device 4 and an input device 5. ing. Here, the analysis condition input unit 1 includes a grid generation unit 11 and an analysis condition setting unit 12, and the analysis calculation unit 2 includes L + 1 processors P that form a parallel computer.
E (0) to PE (L) and local memory LM (0) to L
And M (L). A and B are files.

The analysis condition input unit 1 is a unit for generating grid points and setting analysis conditions according to data input by the user through the input device 5, and the grid generation means 11 sets x, y in the analysis region. , Z coordinate axes are defined,
The coordinate of the calculation point (this is called a grid point) is obtained using the coordinate axis, and the result is output to the file A. The analysis condition setting means 12 also outputs data such as boundary conditions, initial conditions and various parameters necessary for analysis to the file A.

The analysis / calculation unit 2 is a unit for calculating a physical quantity such as velocity, pressure, temperature, etc. at a designated time by differentiating the basic equation governing the flow and performing time integration. Two methods, an explicit method and an implicit method, are used for the time integration. First, using one processor PE (0) that constitutes a parallel computer,
For all areas of the analysis area, the physical quantity at the new time tnew is obtained by the implicit method, and the result calculated here is output to the local memory LM (0) attached to the processor PE (0). In parallel with this, I of the analysis area specified by the user
A processor PE (J) having a number of J = MOD (L, I) (L + 1 = number of processors) of a parallel computer is assigned to the th partial area, and a physical quantity at time tnew is obtained by using the explicit method for each partial area. . The results calculated here are the processors PE (1) to PE
Local memories LM (1) to LM associated with (L)
It is output to (L). Then, when the calculation of all the processors is completed, the value obtained by the implicit method in the local memory LM (0) and the local memories LM (1) to LM
The weighted average is taken with the value obtained by the explicit method in (L). That is the physical quantity at the final time tnew,
Local memory LM (0) to all areas and partial areas
It is stored again in LM (L). In addition, when the calculation result is the input data at the output specified time, the local memory L
The physical quantity of M (0) is output to the file B.

The analysis result display unit 3 reads the physical quantity data in the file B calculated by the analysis calculation unit 2,
This is a portion displayed on the display device 4 in the form of a graph or a table.

FIG. 2 is a flow chart showing the flow of processing of the embodiment shown in FIG. 1. The operation of this embodiment will be described below with reference to the drawings.

First, the user activates the grid generating means 11 of the analysis condition input section 1 from the input device 5 to give necessary data, and sets x, y, and z axes on the analysis area, and meshes on the analysis area. Form a grid. Each grid point becomes a calculation point,
The grid generating means 11 outputs the coordinate value of each grid point to the file A. Next, the user activates the analysis condition setting means 12 of the analysis condition input unit 1 from the input device 5 to give input data necessary for performing the calculation, and outputs it to the file A through the analysis condition setting means 12.

FIG. 3 shows an example of the contents of file A. In the figure, 1 is a part for designating an analysis method, and 1-1
Then, the analysis start time, the analysis end time, and the time step value (Δt) for the implicit method are applied in 1-2, the grid data is applied in 1-3, the obstacle data is applied in 1-4, and the explicit method is applied. The weights (α) for taking the average value of the result of the implicit method and the result of the explicit method are designated in 1-5 for the power subregions. In this example, there are two partial areas to which the explicit method should be applied. That is, the grid point "1" where X = 1, Y = 3, Z = 1
31 ”and the grid point“ 24 ”where X = 2, Y = 4, Z = 2
A rectangular parallelepiped region having "2" as an apexes and a rectangular parallelepiped region having lattice points "211" and a lattice point "342" as opposite apexes are partial regions. The part 2 designates the physical property data, and the density is specified in 2-1 and 2-2.
Specifies the viscosity, 2-3 specifies the specific heat, and 2-4 specifies the thermal conductivity. Further, portions 3 and 4 are portions for designating boundary conditions and initial conditions, for example, velocity boundary conditions and initial conditions are designated. Further, the portion 5 is designation data relating to display, and in this example, it is designated that the speed should be displayed at intervals of 0.1 from time 0.0 to time 0.4. The grid data portion 1-2 is a portion generated by the lattice generating means 11, and the remaining portion is a portion set by the analysis condition setting means 12.

When the file A as described above is prepared,
The analysis calculation unit 2 starts operation and executes the following processing.

S1: In the processor PE (0), the coordinate data of the grid points created in the file A by the analysis condition input unit 1, the initial conditions and boundary conditions of the physical properties of the fluid and physical quantities (velocity, pressure, temperature). , Data such as the time step value Δt for the implicit method is read and stored in the local memory LM (0). Regarding the input condition for the I-th partial area, the processor PE with the number J = MOD (L, I) is used.
(J) is transferred to the local memory LM (J).

S2: The coefficient required for time integration by the difference method is obtained for each of the whole area and the partial area. The coefficients for all areas are calculated by the processor PE (0) and stored in the local memory LM (0). The coefficient for the I-th partial area is the processor P with the number J = MOD (L, I).
It is calculated by E (J) and stored in the local memory LM (J).

S3: In the processor PE (0), S
From the initial value of the physical quantity read in 1 and the coefficient obtained in S2, the physical quantity of the first step in the entire area, that is, the speed (speed at analysis time t = Δt) is obtained by the implicit method.

S4: Each processor PE in parallel with S3
In (J) (J = 1, L), the maximum value of the time step due to the explicit method is obtained for each partial region. This is dt (I)
(I is the area number).

S5: Further, each processor PE (J) (J
= 1, L), m (I) = [0.5 + Δt / dt (I)] ([]] using the initial value of the physical quantity stored in S1 for each partial area and the coefficient of the explicit method obtained in S2. Is a Gaussian symbol), and time integration is performed by the explicit method only once to obtain the velocity at one step (analysis time t = Δt). Here, I is the number of the partial area.

S6: When the calculation of the explicit method in all the partial areas is completed, the local memory LM (J) (J = 1 to 1)
The value of the velocity in L) is stored in the local memory LM (0). At this time, it is stored as follows. U1 (I, J, K) = (I, J, K) is the coordinate of a certain partial area, the speed newly obtained in that area. If (I, J, K) does not belong to any subregion,
0. In addition, (I, J, K) moves the coordinate value of the entire area.

S7: When the processor PE (0) uses the velocity of the entire region obtained by the implicit method as U, the velocity at the final step (analysis time t = Δt) is U (I, J, K). ) = Α × U (I, J, K) + (1-α)
× U1 (I, J, K) (I, J, K) moves in the coordinates of the entire area. Ask in. Here, α is a weighting parameter specified by the input.

S8: The newly obtained speed U of all areas is stored in the local memory LM (0). Further, the speed in the I-th partial area is the local memory LM (J) (J = M
It is also transferred to and stored in OD (L, I).

S9: If the analysis time this time is the graph output time specified by the input data, the local memory LM
The speed value at (0) is output to file B.

S10: Returning to S3, the initial value of the speed is changed to the speed of the next step (1 step), and the speed of the new step (2 steps) is calculated in the same manner. That is, S
The processing of 3 to S9 is repeated to sequentially obtain the speed of n steps from the speed of n-1 steps (analysis time t = n × Δ).
t, n = 2, 3, ...).

S11: When the analysis time reaches the analysis end time specified by the input data, the control is transferred to the analysis result display section 3.

The analysis result display section 3 creates a graph or table based on the physical quantity (speed) data output to the file B and displays it on the display device 4. For example, the stream line, the trajectory line, and the stream line at the time specified by the input data are calculated, and the stream line diagram, the stream line diagram, and the stream line diagram are displayed.

[0027]

As described above, according to the present invention, the entire analysis area is analyzed by the implicit method, and the partial area in which the change in the flow designated in advance is drastically analyzed by the explicit method and the result of the implicit method is averaged. As a result, the solution is less likely to diverge as compared to the case where the implicit method alone is used, and the flow can be stably analyzed.

Further, the implicit method can take a large time step value, the explicit method is applied only to a part of the area, and the implicit method and the explicit method are processed in parallel.
Furthermore, since the explicit calculation is also processed in parallel for each sub-region, efficient analysis is possible.

[Brief description of drawings]

FIG. 1 is a block diagram showing an example of a numerical fluid analysis system to which the present invention is applied.

FIG. 2 is a flowchart illustrating a processing example of an analysis calculation unit.

FIG. 3 is a diagram showing an example of input data.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 ... Analysis condition input part 11 ... Lattice generation means 12 ... Analysis condition setting means 2 ... Analysis calculation part PE (0) -PE (L) ... Processor LM (0) -LM (L) ... Local memory 3 ... Analysis result display Part 4 ... Display device 5 ... Input device A, B ... File

Claims (3)

[Claims] 1. In a computational fluid dynamics analysis method for analyzing a differential equation governing a flow by a finite difference method, a physical quantity of the next step is obtained by an implicit method over the entire analysis region with a time step value Δt, and is specified in parallel with it. The physical quantity of the next step is calculated by the explicit method with the time step value Δt / m only for the selected partial area, and for the partial area to which the explicit method is applied, the value obtained by the implicit method and the value obtained by the explicit method are weighted and averaged. A numerical fluid analysis method using two kinds of time integration methods characterized by: 2. The method according to claim 1, wherein when there are a plurality of partial regions to which the explicit method is applied, the calculation by the explicit method for each partial region is performed in parallel by using different processors. Computational fluid dynamics using various kinds of time integration methods. 3. The numerical fluid analysis method using two types of time integration methods according to claim 2, wherein the calculated result is output in the form of a graph or a table.