JPH02226186A - Simulation method - Google Patents

Abstract

PURPOSE:To enable numerically stable and fast simulation by calculating a corrector from variables after integration operation and derivatives as to some of the variables among the variables of an ordinary differential equation system, and correcting respective variable values by using the corrector. CONSTITUTION:The corrector is calculated from the variables after the integration operation and the derivatives as to some of the variables, namely, particularly those variables that tend to be unstable, among a group of variables of the ordinary differential equation system, and the corrector is used to correct the values of the respective variables. Therefore, even if a large time step DELTAt is used, a stable calculation result is obtained without any numeric divergence and the calculation for the corrector is simple to eliminate a large increase in calculation time. Consequently, the numerically stable and fast simulation is enabled.

Description

DETAILED DESCRIPTION OF THE INVENTION [Object of the Invention] (Industrial Application Field) The present invention relates to a simulation method for simulating transient phenomena using a computer.

(Prior Art) Generally, a simulation device calculates moment-to-moment changes by numerically integrating a differential equation that describes the dynamic characteristics of an object to be simulated, such as a differential equation that describes the dynamic characteristics of a nuclear reactor. to display it.

FIG. 2 shows an example of a conventional simulation method in such a simulation apparatus.

That is, in the conventional simulation method, first, the initial state Yio(t-to) of the simulation target is calculated (1).

This is usually the value of various physical quantities Yl (+-1, 2, 3,...) such as pressure, temperature, position, plate, etc., but these are saved in a file (2) and also displayed. Displayed by the device (3).

Next, the differential coefficient Yio- of each variable is determined from an ordinary differential equation that describes the time change of these physical quantities Y1 (4).

After that, the above-mentioned differential coefficient Yj o - is time-integrated at a constant time step Δt by Euler's method based on the following formula, for example, to find the value of each variable Y11 (4)
.

Yl ,←Y]o+Y1o-・Δt・・・・・・・・・
・■Then, advance the time so that t1←to+Δt, and save the time t1 and the value Y1 of various variables in a file.

Repeat the above steps, from time to to tl, t2...
. . . t, the time progresses sequentially, the moment-by-moment state is calculated, and the simulation is performed by displaying the saved files to the user on a screen or the like.

(Problem to be Solved by the Invention) In the conventional simulation method described above, the simulation speed is controlled by the time required for - calculations, but if the performance of the computer is constant, the time step Δ
By increasing t, time progresses faster and, for example, it is possible to simulate a phenomenon at the same speed as in real time.

However, in the conventional simulation method described above, if the time step Δt is made too large, it becomes numerically unstable, and there is a risk that the calculation results will diverge and become meaningless. Therefore, for example, it is not possible to perform high-speed simulations, such as simulating phenomena at the same speed as real time, for things that require time to calculate - times or that include variables that are likely to become numerically unstable. There was a problem.

The present invention has been made in response to such conventional circumstances,
The objective is to provide a simulation method that is numerically stable and capable of performing high-speed simulations.

[Structure of the Invention (Means for Solving the Problem) That is, the present invention performs an integral operation at a predetermined time interval on a system of simultaneous ordinary differential equations consisting of a plurality of variable groups representing temporal changes in a simulated object, In the simulation method, in which the values of the variable group are determined and the integral operation is sequentially repeated using the values of the variable group to simulate changes in the simulated object, some of the variable groups of the ordinary differential equation system are Regarding the variables, a modifier is calculated using the variable after the integral operation and a differential coefficient, and each variable value is modified using this modifier.

(Function) In the simulation method of the present invention having the above configuration, for some of the variables of the variable group of the ordinary differential equation system, that is, for variables that are particularly likely to become unstable, the variables after the integral operation and the differential A modifier is calculated using the coefficient, and the value of each variable is modified using this modifier to stabilize numerically.

Therefore, even when a large time step Δt is used, there is no numerical divergence, stable calculation results are obtained, and the calculation to calculate the above modifier is extremely simple. Since there is no significant increase in time, it is possible to stably simulate objects that cannot be simulated in real time conventionally.

(Example) Hereinafter, the simulation method of the present invention will be explained with reference to the drawings.

FIG. 1 shows a simulation method according to an embodiment of the present invention. In this embodiment method, like the conventional method shown in FIG. 2, first the initial state Y1g(t-
A) and save these values to a file (
B), and display (C). Next, these differential coefficients Y
lo −determined (D), which is determined at a constant time step Δ
Time integration is performed by t, and the value of each variable Yi l is determined by Euler's method based on the above-mentioned equation 0 (E).

Then, among the above Y11, group j of stable variables (
For Yj), its value is updated as before (E).

On the other hand, for some unstable variable group k (Yk), a new modifier Yk+ is calculated (F), and from the value Yko before Euler integration, Yk ,←Yk o
+Yk + * ・・・・・・・・・■ Perform correction (G).

This correction ff1Yk+ is based on, for example, the concept of the rational Rungekut integral method (^, Wambecq Ration
al Runge-Kutta Methods
for Solving 5ystea+so
f'0rdlnary Dif'f'erent
ial Equatrons, Coalput
ing, 20°333-342.1978. ).

That is, according to the rational Runge-Kutta integral method, for the ordinary differential equation system y−f(y), g+−f (y)
・・・・・・・・・■g2-f
(y0c・Δt−g1)・・・・・・・・・■ Find out and use this, g 1 ll g 1 y←y+ ・Δt・・・・・・
...-■ If the value at the next time is determined as b, g+ +b2 g2, it will always be stable regardless of the value of Δt. Here, y is the variable y
It is a vector of l, and the operation of the 0 expression is performed on the vector. C1b1. b2 is a constant.

Now, by using the above method, it is possible to create a variable correction method that can also be used in conjunction with the conventional Euler method. That is,
Since gl in the formula (■) is the same as Yl'', g, -yi-...■ Also, in the formula (■), by specifically setting C-1, g
2 can be obtained as g2-yk -...■ by using the variable Yk after Euler integration and performing the differential coefficient calculation (D) again based on this value. Determined in this way■,
According to gl and g2 in ■, the modified RYk is g 1
° gl Yk ゝ-Δt ・・・・・・■b, g+
+b2 g2 can be easily determined, and correction calculations can be performed using formula (2).

The time required to calculate these vectors is extremely short, and the calculation time does not increase.

Note that formula (2) is performed only for a part of Yk of all variables Yi, and for other variables Yj, all << is the same as the conventional calculation. Furthermore, the calculation of the correction amount in equation (2) can be performed for each variable vector by further dividing the variable group Yk into several subgroups. When performing subgrouping in this way, calculation errors can be reduced by grouping variables with similar time constants.

[Effects of the Invention] As explained above, according to the simulation method of the present invention, numerically extremely stable simulations can be performed, and even for high-speed simulations that require real-time performance, accuracy can be improved. A good simulation is possible.

[Brief explanation of the drawing]

FIG. 1 is a diagram for explaining a simulation method according to an embodiment of the present invention, and FIG. 2 is a diagram for explaining a conventional simulation method. Applicant Japan Atomic Energy Corporation Applicant
Toshiba Corporation Representative Patent Attorney Sasa Suyama - Figure 2

Claims (1)

[Claims] (1) Integrate a system of simultaneous ordinary differential equations consisting of multiple variable groups representing temporal changes in the simulated object at predetermined time intervals, obtain the values of the variable groups, and use the values of this variable group. In the simulation method of simulating changes in the simulated object by sequentially repeating the integral operation, for some of the variables of the variable group of the ordinary differential equation system, the variables after the integral operation and the differential coefficient A simulation method characterized by calculating a modifier using , and modifying each variable value using this modifier.