JPH01217562A - System for generating computing grid - Google Patents

Abstract

PURPOSE:To generate a grid to have desired distribution without executing a trial and error by having a grid data storing means to store a spline interpolating computed result and a grid distribution control computed result. CONSTITUTION:When data to be needed for the computation of a boundary condition, etc., and the data of a grid distributing method are inputted from a data input means 1, these data are stored in an input storing means 2 and a grid distributing method storing means 3. For the data to be inputted to the input data storing means 2, grid data is generated in a grid generating means 4 and interpolating data is prepared in a spline interpolation computing means 5. After that, a grid point is distributed on a constant curve and the desired grid data is generated. In functions P and Q computing means 6, the values of the P and Q are computed. The grid data and the values of the P and Q are stored in a grid data storing means 7 and the computed result is confirmed.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a method for generating a computational grid for solving partial differential equations, for example, by a finite difference method.

[Conventional technology]

When solving initial value/boundary value problems of partial differential equations using the finite difference method, it is necessary to generate a grid for calculation in the analysis domain. For analysis regions of arbitrary shapes, a boundary fitting method is known as a computational grid generation method using elliptic partial differential equations. In the boundary fitting method, a grid is generated using the following Poisson equation.

The boundary conditions are, for example, in a physical coordinate system as shown in Figure 4(a), where (x, y) represent the coordinates of the physical coordinate system, and ξ, η
) represents coordinates in a curvilinear coordinate system along the grid. A computational grid can be generated by tracing the line where ξ = constant and η = constant. That is, the coordinates (x(ξ, η)) corresponding to discretized ξ=1...n, η=1...m.

If y(ξ, η)) (nXm pieces) are found, it means that the lattice has been generated.

In practice, calculations are performed by mapping a physical coordinate system as shown in FIG. 4(a) onto a regular grid along (ξ, η) as shown in FIG. 4(b). In other words, a computational grid is generated by solving the following quasi-linear partial differential equation in which the dependent variables and independent variables in equations (1) and (2) are swapped using the difference method.

here It is. For example, the boundary condition in FIG. 4(b) is as follows.

Further, P (ξ, η) and Q (ξ, η) are functions for controlling the distribution of the lattice.

In the conventional technology, a grid was generated using the processing flow shown in FIG.

Step ■: Input boundary conditions, etc.

Step ■: Input functions P and Q.

Step ■: Solve equation (4) based on the boundary conditions and leap numbers P and Q to generate a grid.

Step ■: Outputting the results.

Step ■: If the grid distribution is as desired, proceed to step ■. If not, change the functions P and Q and go to step ■.

Step ■: Output grid data.

Regarding the above conventional techniques, see Joe F., Lampson et al. [Numerical grid generation - Basics and applications - J (1985
Year, North Holland) (English name: Joe F, Tho
mpsonet, al, rNumerical Gu
rid Generation-Foundation
sand Applications-J (1985
, North-Holland).

[Problem to be solved by the invention]

However, with conventional technology, it is impossible to know what kind of distribution the lattice will have depending on the values of the functions P and Q without looking at the calculation results, so it is extremely difficult to obtain the desired lattice distribution with a single calculation. there were.

Therefore, the values of the functions P and Q had to be determined by trial and error to generate the grid, and the selection of the values of the functions P and Q required intuition and experience.

An object of the present invention is to provide a computational grid generation method for generating grids with a desired distribution without trial and error.

[Means to solve the problem]

The computational grid generation method of the present invention includes a data input means for inputting data such as boundary conditions necessary for calculation and data of a grid distribution method, and an input data storage means for storing input data such as boundary conditions. , a lattice distribution method storage means for storing input lattice distribution method data, a lattice generation means for generating lattice data based on the data in the input data storage means, and a lattice distribution method storage means based on the lattice data. spline interpolation calculation means for changing the lattice distribution by spline interpolation according to the data; lattice distribution control function calculation means for calculating the value of the lattice distribution control function based on the output of the spline interpolation calculation means; and calculation of the spline interpolation calculation means. and lattice data storage means for storing the results and calculation results of the lattice distribution control function calculation means.

〔Example〕

FIG. 1 is a block diagram of an embodiment of the computational grid generation method of the present invention.

The calculation grid generation method of this embodiment includes a data input means 1 for inputting data such as boundary conditions necessary for calculation and data of a grid distribution method, and an input data storage for storing input data such as boundary conditions. means 2, a lattice distribution method storage means 3 for storing data of the input lattice distribution method, a lattice generation means 4 for generating lattice data based on the data in the input data storage means 2; a spline interpolation calculation means 5 for changing the lattice distribution by spline interpolation according to the data in the lattice distribution method storage means 3; and functions P and Q for calculating the values of the functions P and Q based on the output results of the spline interpolation calculation means 5. It has calculation means 6 and grid data storage means 7 for storing the calculation results of the spline interpolation calculation means 5 and the calculation results of the function P and Q calculation means 5.

When the computational grid generation method with the above configuration is implemented on a computer, the data input means 1 is, for example, an editor on a terminal, and the storage means 2. 3. 7 is, for example, a magnetic disk device or a memory device.

Next, the operation of this embodiment will be explained with reference to the flowchart shown in FIG.

Data necessary for calculation of boundary conditions etc. and data of grid distribution method are inputted from data input means 1 (step
(2) These data are stored in the input data storage means 2 and the lattice distribution method storage means 3.

For example, when the data shown in FIG. 3(a) is input to the input data storage means 2, the grid generation means 4 stores (
3) Grid data as shown in FIG. 3(b) is generated by setting the functions P and Q of the equation to zero and solving the equation.

Equation (6) is discretely approximated by the finite difference method and converted into simultaneous-order equations to be solved; however, since Equation (6) is a quasi-linear equation, repeated calculations are required. Let k be the number of iterations for the calculation. Step 0: Calculate the initial grid by algebraic interpolation based on the input data and obtain the result (x, y). , is stored as =1.

Step @: 11th data (x+3') k
The coefficient α is calculated by equation (4) based on −+.

Calculate β and γ and calculate the simultaneous -order equations. Create a coefficient matrix.

Step (2): Solve simultaneous-order equations using the coefficient matrix and boundary conditions as input data to generate grid data (x, y)i+.

Step @: (x, y) * and (X+ y)
*−r, and if the difference satisfies the convergence condition, the iteration ends. Otherwise, set = to +l and return to Stellap ■.

It is done like this.

In the lattice data calculated in this way as shown in Figure 3(b), the lattice distribution is defined as ``the lattice points are 2 along the line with η = constant.''
Concentrate inside so that it has a power distribution. ” and express this in the formula, S (η) = L ・((77
-1) / (m-1) ) ”(η=1...m)
(7) becomes. Here, L is η=length of a constant curve.

S is a function representing the distance from η=1.

In the spline interpolation calculation means 5, after creating interpolation data to express a curve with η=constant based on the grid data of FIG. Grid points are distributed to generate desired grid data (step 0).

The results are shown in FIG. 3(C).

The function P, Q calculation means 6 calculates the values of P and Q using (3) 2 based on the calculation result data of the spline interpolation calculation means 5 (step [phase]).

The lattice data and function P recalculated by the spline interpolation calculation means 5, and the values of P and Q calculated by the Q calculation means 6 are stored in the lattice data storage means 7, and these calculation results are
For example, it can be confirmed by outputting a graphic display or a printer (step 0).

〔Effect of the invention〕

As explained above, when the computational grid generation method of the present invention is used to generate a computational grid, a computational grid having a desired grid distribution can be generated extremely easily without trial and error.

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing the computational grid generation method of the present invention, FIG. 2 is a flowchart for explaining the operation of the computational grid generation method of FIG. 1, and FIG. 3 is a block diagram showing the computational grid generation method of FIG. FIG. 3(a) is a diagram for explaining the operation of the generation method.
Figure 3(b) shows an example of input data, Figure 3(b) shows an example of grid data generated using equation (6), and Figure 3(C) shows an example of changing the grid distribution using spline interpolation. FIG. 4 is a diagram showing the mapping relationship between the (x, y) coordinate system and the (ξ, η) coordinate system, and FIG. 5 is a diagram showing a flowchart of the computational grid generation method according to the prior art. l... Data input means 2... Input data storage means 3... Lattice distribution method storage means 4... Lattice generation means 5... Spline interpolation calculation means 6... Function P, Q calculation means 7 ...Grid data storage means Fig. 1 Fig. 2 Fig. 4

Claims (1)

[Claims] (1) Data input means for inputting data such as boundary conditions and grid distribution method data required for calculation, input data storage means for storing input data such as boundary conditions, and input grid distribution. lattice distribution method storage means for storing method data; lattice generation means for generating lattice data based on the data in the input data storage means; Spline interpolation calculation means for changing the lattice distribution; Lattice distribution control function calculation means for calculating the value of the lattice distribution control function based on the output of the spline interpolation calculation means; Calculation results of the spline interpolation calculation means and the lattice distribution control function. A computational grid generation method comprising grid data storage means for storing calculation results of the calculation means.