JP2006171867A - Numerical value calculation method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To solve the following problems in a numerical value calculation of a fluid-structure coupled problem; that a numerical value fluctuation occurs when a dynamic interaction between a fluid and a structure is calculated; that a high-frequency component causes a local transformation to a structure to deteriorate accuracy in a solution; and that it is difficult to design a filter necessary for executing a desired filtering operation required for preventing the deterioration of accuracy in a solution. <P>SOLUTION: A desired filter is automatically provided in response to a change in characteristics of an objective structure, and filtering is made to a high-frequency component generated in a pressure field of a fluid to restrain the occurrence of a local transformation in the structure. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a numerical calculation of a fluid-structure interaction problem, and mitigates the occurrence of local deformation in a structure caused by a high-frequency component of a numerical vibration of a fluid pressure field caused by a numerical discretization error. The present invention relates to a filtering technique for a fluid pressure field.

2. Description of the Related Art In recent years, there has been a demand for a numerical simulation method that takes into account the interaction between a fluid and a structure in the design of automobile tires and the coupled vibration analysis of fluid machines such as gas turbines and pump turbines. When performing such a numerical simulation, the simulation for fluid or structure is performed independently and the boundary condition is determined by using the calculation result of the other. Element Computation of Incompressible Flows with Emphasis on Flows Involving Oscillating Cylinders "(S. Mittal, A. Ratner, D. Hastreiter and TE Tezduyar, International Video Journal of Engineering Research, 1991, 83-96) is known. By introducing additional mass and additional attenuation required for handling such a coupled problem, numerical accuracy is improved and calculation is stabilized (see, for example, [Patent Document 1]). In addition, a finite element method is used for structural analysis and an individual element method is used for fluid analysis, and a coupled analysis method using different discretization techniques for structural analysis and fluid analysis is shown (for example, [Patent Document 2] reference). In these conventional technologies, due to the fact that the fluid analysis and the structural analysis are performed independently, the solution to the system equation including both the fluid and the structure is solved, and the solution to the system equation different from the case where the solution is solved. And technology to correct it has been introduced. However, in the analysis software using the conventional technology, the high-frequency component of the numerical vibration generated when calculating the mechanical interaction between the fluid and the structure causes local deformation in the structure and the accuracy of the solution deteriorates. No solution is shown.
JP-A-8-249314 JP 2001-305022 A

  In the numerical calculation of fluid-structure interaction problems, it is known that the numerical vibration generated when calculating the mechanical interaction between the fluid and the structure is known. In addition, the high-frequency component causes local deformation in the structure and deteriorates the accuracy of the solution. In order to prevent the solution accuracy from deteriorating, it is necessary to perform a desired filtering operation, but the design of the filter is difficult. As a problem related to the present invention, a desired filter is automatically provided in response to a change in the characteristics of a target structure, and a high frequency component generated in a fluid pressure field is filtered to locally apply the structure. This is to prevent the occurrence of various deformations.

  According to the present invention, the specific frequency component of the numerical vibration generated when calculating the dynamic interaction between the fluid and the structure in the numerical calculation method for numerically simulating the dynamic coupling problem between the fluid and the structure is obtained. A numerical calculation method characterized by filtering using a stiffness matrix of a structure is provided.

  The numerical value generated when calculating the dynamic interaction between fluid and structure in the numerical calculation method that numerically simulates the dynamic coupling problem between fluid and structure by the filtering method for the fluid pressure field of the present invention. When filtering a specific frequency component of vibration, appropriate filtering can be performed for any system.

<Embodiment 1>
The object of the present invention is that an external force condition on a structure 6601 having an originally smooth distribution such as 6002 in FIG. 6 contains a high frequency component as 50002 in FIG. 5 due to a numerical discretization error. In this case, it is intended to suppress the local deformation of the structure by converting the pressure field having a smooth distribution by a desired filtering operation. The situation where the discretization error occurs here means that, for example, the pressure field of the fluid has an unrealistic distribution in which a grid with relatively high pressure and a grid with low pressure are alternately arranged as shown in FIG. ing. Such a phenomenon is introduced as a checkerboard-like distribution in, for example, “Computational Fluid Dynamics” (Seiichi Koshizuka, Baifukan, 1997). When such a numerical discretization error occurs, it is considered necessary to perform desired filtering. For example, a method of removing high frequency components by using an FFT can be considered. In such a case, it is easily understood that an appropriate filter needs to be redesigned according to the specific situation of the structure every time the target structure is changed. Designing a filter according to the analysis target places a heavy burden on the analyst, and it is strongly required to reduce the load. In the present invention, the filter is designed by using a stiffness matrix generally used in structural analysis. Here, the stiffness matrix is an equilibrium equation for a structure that has been discretized based on the finite element method, as shown in, for example, “Introduction to the Finite Element Method” (by Toshiro Miyoshi, Baifukan, published in 1994) It is a matrix which shows the relationship between the displacement vector and external force vector which reflected the characteristic of the system. As described above, by using the stiffness matrix reflecting the characteristics unique to the structure, an appropriate filter can be provided for any target. Therefore, the use of the present invention can reduce the burden on the analyst and improve the accuracy of the solution.

  The following algorithm is stored in the hard disk in the computer shown in FIGS. In this embodiment, the case where the present invention is performed on a computer according to the flowchart shown in FIG. 1 will be described. As shown in FIGS. 8 and 9, the computer here is an arithmetic processing unit including a CPU (116) and a memory (118), a storage device unit including a hard disk (117) and a floppy (registered trademark) disk 110, a keyboard. In this system, an input unit including 115 and a mouse 114 and an output display unit including a display 112 are included. Each calculation unit and the like are accommodated in the main body 111.

  The computer loads a program designed and coded according to the flowchart shown in FIG. 1 onto the memory, secures the necessary calculation area, and performs predetermined arithmetic processing based on images and parameters input in an appropriate manner. And the value of the physical quantity in the area obtained as a result is written and stored in a hard disk or the like. It is also displayed on the display.

  In the present invention, as shown in the flowchart of FIG. 1, after setting the external force condition necessary for the structural analysis using the calculation result of the fluid analysis, the external force condition is corrected by a filtering operation using the stiffness matrix of the structure. Features. Hereinafter, a method of filtering high-frequency components of numerical vibration generated in the fluid pressure field using the structure stiffness matrix will be described with reference to the flowchart of FIG. Here, the high frequency component refers to a frequency component having a frequency larger than a desired frequency determined from a material constant or the like among a plurality of natural frequencies derived from the balance equation of the structure. Further, it is assumed that the state quantities of the fluid and the structure in the previous step are known from the initial conditions or the calculation results up to the previous step.

  In the first step, a fluid region and a velocity boundary condition are set as preparation for fluid analysis. At this time, the interface between the structure and the fluid is set by a desired operation from the state quantity of the structure. Further, the boundary conditions of other regions are given as data.

  In the second step, the state quantity of the fluid is updated. At this time, it is necessary to update the pressure field, but it is not always necessary to update the velocity field. In addition, if a method that involves multiple steps, such as the fractional step method, is selected as the method for updating the velocity field, use an arbitrary velocity update method, such as performing only the first step or only the initial few steps. Is possible. In such a case, it is necessary to correct the velocity field in consideration of the velocity update method in the seventh step described later. When the update method using only the first step of the fractional step method is selected, it is necessary to consider the influence after the second step of the fractional step method in the seventh step. The fractional step method is one of the time integration methods used in numerical fluid analysis, as introduced in “Fine element analysis of flow” (Takahiko Tanahashi, Asakura Shoten, 1997).

  In the third step, an external force condition for the structure is set as preparation for structural analysis. An external force vector applied to the structure by the fluid is calculated by integrating the pressure calculated in the second step on the boundary between the structure and the fluid by a desired method. Terminology in structural analysis such as external force vector is defined in “Introduction to Finite Element Method” (written by Toshiro Miyoshi, Baifukan, published in 1994), and so on.

  In the fourth step, the stiffness matrix of the structure is calculated as a preparation for filtering the high-frequency component of the external force applied to the structure by the fluid. In the structural analysis, it is essential to calculate the stiffness matrix, and by using the program, the stiffness matrix can be calculated without developing a new program.

In the fifth step, the external force condition of the structure set in the third step is corrected. The external force condition is corrected by (Equation 1). Here, (Equation 2) is an equilibrium equation of the structure, K is a stiffness matrix, U is a displacement vector, and F is an external force vector. When (Equation 2) is separately displayed for the displacement component U ₁ and the other component U ₂ corresponding to the region where the fluid force acts, it can be transformed as (Equation 3). Here, it is assumed that (Equation 3) right sides F ₁ , F ₂ , and F _flu satisfy ( _Equation 4). F _flu is an external force condition given from the fluid state quantity, and F ₁ and F ₂ are obtained by separating other external force components into an external force component corresponding to a region where the fluid force acts and other components. In this way, from the fluid corrected by performing the operation of ( _Equation 1) for the external force condition F _flu from the fluid using K ₁₁ defined using (Equation 2) to (Equation 4). The external force condition F ′ is calculated. Note that α in (Equation 1) is a parameter determined to satisfy (Equation 5) or an approximate value thereof, and for example, (Equation 6) can be used. In (Equation 1), another matrix such as a tangential stiffness matrix can be used as an approximate value of the stiffness matrix K.

このように外力条件に対するフィルタリングを行うことにより、第３のステップで図5中50002のような滑らかでない分布を持つ外力条件が設定された場合でも、図6中60002のような滑らかな分布を持つ外力条件に修正することができる。図５、６中において、構造物50001,60001周辺部50003, 60003は流体領域を表している。

By performing filtering on the external force condition in this way, even if an external force condition having a non-smooth distribution such as 50002 in FIG. 5 is set in the third step, it has a smooth distribution such as 6002 in FIG. It can be corrected to external force conditions. In FIGS. 5 and 6, peripheral portions 50003 and 60003 of the structures 50001 and 6001 represent fluid regions.

  In the sixth step, the state quantity of the structure is updated using the corrected external force condition obtained in the fifth step.

  In the seventh step, the fluid state quantity is corrected. Here, it is necessary to correct the state quantity by a desired operation in view of the adopted pressure calculation method, speed update technique and the update of the fluid state quantity performed in the second step.

  In the eighth step, convergence determination is performed. If the equilibrium condition between the fluid and the structure is not satisfied when the seventh step is completed, the process returns to the third step and the loop is repeated until the equilibrium condition is satisfied. When the equilibrium condition is satisfied or when the maximum number of loops specified in advance is reached, the loop is terminated.

  The reason why the stiffness matrix of the structure is used for filtering in the fourth step is that the stiffness matrix has a feature of converting a local load into an overall deformation. For example, considering the deformation when a local external force condition as shown in 20002 in FIG. 2 occurs in the structure, the local region as shown in area 30003 in FIG. A smooth displacement distribution in which the entire structure is deformed, such as 40001 in 4, occurs. By using such a characteristic of the structure stiffness matrix, a filtering operation is applied to the external force condition for the structure including a high frequency component as indicated by 50002 in FIG. 5 calculated in the third step. It becomes possible to correct to an external force condition having a smooth distribution as shown in 60002. In this way, the specific frequency component of the numerical vibration that occurs when calculating the mechanical interaction between the fluid and the structure without developing a new program is taken into consideration, taking into account the characteristics of the structure's stiffness matrix. The point of filtering using the object stiffness matrix is the greatest feature of this embodiment.

<Embodiment 2>
Hereinafter, other embodiments of the method for filtering the numerical vibration of the mechanical interaction according to the present invention will be described in detail. Henceforth, description is abbreviate | omitted about the same point as a 1st Example. The flowchart in the second embodiment is the same as that in the first embodiment. The difference is the filtering method in the fourth step. In the first embodiment, filtering is performed using (Equation 1), but in the second embodiment, filtering is performed using (Equation 7). Note that? In (Equation 7) is a parameter determined to satisfy (Equation 8) or an approximate value thereof. For example, the value of (Equation 9) can be used.

(数７)においてaは任意の正の数であり、指定可能なパラメータである。aが大きな値を持つ場合には(数１０)が成立することからフィルタリングが行われない。ここで、(数１０)右辺Iは単位行列とする。反対に、aに小さな値を用いた場合には大きなフィルタリングの効果が得られることとなる。このようにパラメータaを与えることによりフィルタリングの効果を調整可能である点が第二の実施例の最大の特徴である。

In (Expression 7), a is an arbitrary positive number and is a parameter that can be specified. When a has a large value, (Equation 10) is satisfied, and thus filtering is not performed. Here, the right side I of (Equation 10) is a unit matrix. Conversely, when a small value is used for a, a large filtering effect is obtained. The point that the effect of filtering can be adjusted by giving the parameter a in this way is the greatest feature of the second embodiment.

<Embodiment 3>
Hereinafter, other embodiments of the method for filtering the numerical vibration of the mechanical interaction according to the present invention will be described in detail. Henceforth, description is abbreviate | omitted about the same point as a 1st Example. The flowchart in the third embodiment is the same as that in the first embodiment. The difference is the filtering method in the fourth step. In the first embodiment, filtering is performed using (Equation 1), but in the third embodiment, filtering is performed using (Equation 11). Here, b is an arbitrary positive integer. K- ¹ on the right side of equation (1) is replaced by its Taylor expansion. Note that the method for determining the parameter? In (Equation 11) is the same as in the first embodiment. Further, the D (Equation 11) in a matrix with only the diagonal elements of K ₁₁ matrix defined in equation (3), A is a matrix with only off-diagonal elements.

ここでbを零とすればF'はFと厳密に一致し、フィルタリングの効果が除外される。一方、bの値を大きくすればK^-1に漸近し、(数1)とほぼ同様のフィルタリング効果を得ることが可能となる。第三の実施例においては、剛性行列の逆行列の計算は必要としない。逆行列の計算が必要なのはD行列に対してのみである。D行列は対角行列であるため、逆行列は高速に計算可能である。このようにフィルタリングの効果の強弱を調整可能であり、かつ高速に計算可能である点が第三の実施例の特徴である。

Here, if b is zero, F ′ matches F exactly and the filtering effect is excluded. On the other hand, if the value of b is increased, it becomes asymptotic to K ⁻¹ , and it is possible to obtain a filtering effect almost the same as in (Equation 1). In the third embodiment, calculation of the inverse matrix of the stiffness matrix is not required. The inverse matrix needs to be calculated only for the D matrix. Since the D matrix is a diagonal matrix, the inverse matrix can be calculated at high speed. Thus, the feature of the third embodiment is that the strength of the filtering effect can be adjusted and the calculation can be performed at high speed.

  In this way, by using the stiffness matrix that is essential in structural analysis based on the finite element method, an appropriate filtering operation is realized without depending on the characteristics of the target structure, and a new program for filtering The feature of the present invention is that no development is required. The filtering method according to the present invention is considered to be applicable to objects based on other physical laws when the matrix in the equilibrium equation has a positive definite property like the stiffness matrix of the structure. Further, it is considered that the present invention can also be applied when other discretization methods such as other finite difference methods are used.

5 is a flowchart of a specific frequency component filtering method for numerical vibration according to the present invention. Local external force acting on the structure. Unrealistic deformation of structures due to local external forces. Realistic deformation of structures due to local external forces. An external force acting on the structure from the fluid calculated without filtering. An external force acting on the structure from the filtered fluid. Fluid pressure field distribution. Explanatory drawing 1 of the apparatus which mounts the crack connection method of this invention. Explanatory drawing 2 of the apparatus carrying the crack connection method of this invention.

Explanation of symbols

20001 Structure 20002 Local external force acting on the structure 30001 Structure 30002 Local external force acting on the structure 30003 Local deformation region 40001 Structure 40002 Local external force acting on the structure 50001 Structure Article 50002 External force condition applied to structure from fluid (before filtering)
50003 Fluid region 60001 Structure 60002 External force condition applied to structure from fluid (after filtering)
60003 Fluid region 70001 Relatively high pressure grid 70002 Relatively low pressure grid 110 Floppy disk 111 Computer body 112 Display 113 Floppy disk drive 114 Mouse 115 Keyboard 116 CPU
117 hard disk 118 memory

Claims (1)

  Stiffness matrix of the structure is a specific frequency component of the numerical vibration generated when calculating the dynamic interaction between the fluid and the structure in the numerical calculation method that numerically simulates the dynamic coupling problem between the fluid and the structure A numerical calculation method characterized by filtering using a filter.

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