Rotation turbulence prediction method applying bstmq turbulence model
The BSTMQ model addresses inaccuracies in existing turbulent flow models by correcting for rotational curvature and eddy viscosity decay, resulting in improved predictions of rotating turbulent flows in fluid machinery.
Patent Information
- Application Number
- JP2024095794
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Priority Date
- 2024-01-17
- Filing Date
- 2024-06-13
- Publication Date
- 2025-07-30
- Estimated Expiration
- 2044-06-13
AI Technical Summary
Existing turbulent flow models, such as the STRUCT model, struggle to accurately predict rotating turbulent flows due to issues with eddy viscosity decay near walls and inadequate representation of rotation and curvature effects, leading to inaccurate predictions in fluid machinery.
The BSTMQ turbulent flow model corrects the STRUCT model by incorporating rotational curvature effects through a branching method, using a Spalart-Shur tensor to unify rotation and curvature, and constructing a new eddy viscosity decay function to enhance prediction accuracy.
The BSTMQ model improves the simulation of rotating turbulent flows, providing more accurate predictions of fluid machinery internal flow fields and enhancing analytical capabilities near walls.
Smart Images
Figure 2025111360000001_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to turbulent flow simulation in engineering fluid dynamics, and specifically to a method for predicting rotating turbulent flow using the BSTMQ turbulent model.
Background Art
[0002] In recent years, a hybrid turbulent model that takes into account both the accuracy of calculation and the calculation cost has promising future applications. In addition to various hybrid turbulent models based on the grid spatial scale, the STRUCT model proposed by Professor Emilion based on the time scale can achieve monotonic convergence of the grid and has excellent calculation accuracy and robustness.
[0003] However, in fluid machinery, since the impeller rotates at high speed, the blades are twisted, and the wall surface is complex, the internal flow field is subject to strong rotation effects and curvature effects. The existing STRUCT model cannot be directly applied and has the following problems: (1) Since the eddy viscosity decay of the STRUCT model is close to 1 in the region near the wall, the model reverts to the conventional Reynolds-averaged Navier-Stokes (RANS) model and is not suitable for analyzing the region near the wall of rotating machinery. (2) In the existing STRUCT model, the analysis time scale calculated based on the conventional eddy detection criterion does not reflect the rotation effect and curvature effect. Due to the above defects, the model may not be able to accurately predict the development process of rotating turbulent flow.
Summary of the Invention
Problems to be Solved by the Invention
[0004] Objective of the invention: In view of the above problems, the present invention provides a method for predicting rotating turbulent flow using the BSTMQ turbulent model, which can improve the prediction effect of the internal flow field of fluid machinery.
Means for Solving the Problems
[0005] Technical solution: To solve the above problems, the present invention is a rotational turbulent flow prediction method using the BSTMQ turbulent flow model, comprising: Performing solid modeling on the object to be predicted of rotational turbulent flow by 3D modeling software to obtain a simulation model in step (1); Meshing the simulation model in step (2); Performing rotational curvature correction on the existing STRUCT turbulent flow model based on the branching method to construct the BSTMQ turbulent flow model, where the 、B STMQ turbulent flow model Equation is as follows:
Equation
Equation
Equation
Equation
Equation
[0006] Furthermore, in step (3) above, the step of constructing the BSTMQ turbulence model specifically includes: Step (31): Introduce the strain rate tensor and the rotation rate tensor in the rotating coordinate system. Step (32): Spalart - Use the Shur tensor to unify the rotation effect and the curvature effect to obtain a corrected rotation rate tensor. Step (33): Create a velocity gradient invariant from the strain rate tensor introduced in step (31) and the corrected rotation rate tensor obtained in step (32). Step (34): Determine a corrected analysis time scale from the velocity gradient invariant obtained in step (33). Step (35): Determine the modeling time scale of the rotational turbulence from the specific dissipation rate. Step (36): According to steps (34) and (35), construct a turbulent viscosity decay function D that reflects the rotation effect and the curvature effect. f-b
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[0007] Furthermore, in the inertial coordinate system, the calculation formulas of the strain rate tensor S ij and the rotation speed tensor Ω ij are as follows:
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[0008] Furthermore, Spalart-When the rotation effect and the curvature effect are unified based on the Shur tensor, the following corrected rotation speed tensor Ω mod ij has the following calculation formula obtained:
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[0009] Furthermore, the determination of the correction variable W A ij is in the case of two-dimensional flow, W A ij = Ω SS ij and TIFF2025111360000127.tif11170
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[0010] Furthermore,
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[0011] Furthermore, the corrected analysis time scale is as follows:
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[0012] Furthermore, a vortex viscosity decay function D f reflecting the rotation effect and the curvature effect is constructed based on the conventional vortex viscosity decay function D f-b and the conventional vortex viscosity decay function D f is
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[0013] The present invention also adopts a computer device including a memory, a processor, and a computer program stored in the memory and operable on the processor, wherein when the processor executes the computer program, the steps of the above method are realized.
[0014] The present invention also provides a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, it realizes the steps of the above method, and a computer-readable storage medium is adopted.
Advantages of the Invention
[0015] The beneficial effects are as follows. Compared with the prior art, an important advantage of the present invention is that the BSTMQ model can simulate rotating turbulent flow more appropriately, improve the prediction effect of the internal flow field of fluid machinery, and provide a new idea for efficiently and accurately calculating rotating turbulent flow. The STRUCT model with corrected rotational curvature based on the branching method uses the BSkO model as the base model and improves the analytical ability of the region near the wall. Spalart By unifying the rotation effect and the curvature effect using the Shur tensor and constructing a new analytical time scale, the constructed BSTMQ model can simulate rotating turbulent flow more appropriately.
Brief Description of the Drawings
[0016]
Figure 1
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Figure 9
Mode for Carrying Out the Invention
[0017] As shown in FIG. 1, in this embodiment, the rotating turbulent flow simulation method using the BSTMQ model includes the following steps (1) to (4).
[0018] Step (1): Perform solid modeling on the prediction targets of rotating turbulent flow (classical basic instances such as rotating channel flow and rotating flow sudden expansion pipes, and rotating machinery such as centrifugal pumps and axial flow pumps) using three-dimensional modeling software to obtain a simulation model.
[0019] Step (2): Mesh the simulation model using (Registered trademark) proprietary software or third-party software.
[0020] Step (3): Perform rotational curvature correction on the existing STRUCT turbulence model based on the branching method to construct a BSTMQ turbulence model.
[0021] Step (4): Based on the program of the rotational turbulent flow numerical simulation method using the BSTMQ turbulence model on the OpenFOAM (Registered trademark) platform, perform numerical simulation calculations, and finally, use (Registered trademark) proprietary or third-party software to perform post-processing to obtain more accurate prediction results of the rotational turbulent flow of the prediction target.
[0022] The BSTMQ turbulence model is a STRUCT model corrected based on the rotational curvature of the branching method, and the steps are specifically as follows.
[0023] Step (31): Introduce the strain rate tensor and the rotation rate tensor in the rotating coordinate system.
[0024] In this step, for the inertial coordinate system, the strain rate tensor S ij and the rotation rate tensor Ω ij are obtained from the following equations.
Equation
[0025] Here, i and j are two free indices in the tensor representation, each taking the values 1, 2, 3, indicating that all values of the indices need to be traversed. U i and U j are velocity vectors, and the velocity components in three directions are U1 = U, U2 = V, U3 = W, and x i and x j are coordinate axes, which may be represented as x1 = x, x2 = y, x3 = y,
Equation
[0026] For a coordinate system rotating with the angular velocity vector Ω F k the rotation rate tensor is defined as follows.
Equation
[0027] TIFF2025111360000142.tif7170
[0028] Step (32): Spalart - Unify the rotation effect and the curvature effect using the Shur tensor.
[0029] In this step, the Spalart - Shur tensor (Ω SS ij ) is obtained by the following formula.
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[0030] Here,
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[0031] When the rotation effect and the curvature effect are unified, a corrected rotation rate tensor is obtained.
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[0032] Here, C r is a model constant, and W A ij is Spalart a correction variable based on the - Shur tensor, In the case of two - dimensional flow,
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Mathematics
Mathematics
[0033] Tensor X ij is an intermediate variable, where δ ij is the Kronecker symbol tensor, and S ik and S kj physically also represent the strain rate tensor, and the indices have been changed to represent tensor operations. S ik S kj has two free indices and one summation index, so it is necessary to sum first and then traverse all components.
[0034] II S and III S are obtained by the following equations respectively.
Mathematics
[0035] Here, S 11 , S 22 and S 33 are the three components on the diagonal of the strain rate tensor.
[0036] Step (33): Create dimensionless velocity gradient invariants from the strain rate tensor introduced in step (31) and the corrected rotational velocity tensor in step (32), thereby ensuring that the subsequent model equations have Galilean invariance and can reflect the effects of rotation and curvature.
[0037] In this step, the velocity gradient invariant is given by:
number
[0038] where k is the turbulent kinetic energy, ε is the dissipation rate, S is the mode of the strain rate tensor, and Ω mod are the modes of the corrected rotation rate tensor,
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[0039] Step (34): From the velocity gradient invariant of Step (33), we obtain the analytical time scale t r Determine.
[0040] The Q vortex detection criterion, which takes into account the rotation and curvature effects, is given by the following equation:
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[0041] where k is the turbulent kinetic energy, ε is the dissipation rate, S and Ω mod are the modes of the strain rate tensor and the corrected rotation rate tensor, respectively.
[0042] The corrected analysis time scale is:
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[0043] Step (35): Determine the modeling time scale t of the rotational turbulent flow from the specific dissipation rate. m The modeling time scale t m is obtained by the following equation.
Equation
[0044] Here, α is the empirical constant of the modeling time scale, ω is the specific dissipation rate,
Equation
[0045] Step (36): Construct the eddy viscosity attenuation function D that reflects the rotational effect and the curvature effect according to Steps (34) and (35). f-b Build it.
[0046] The conventional eddy viscosity attenuation function D f is as follows.
Equation
[0047] Finally, construct the eddy viscosity attenuation function D that reflects the rotational effect and the curvature effect. f-b Build it.
Equation
[0048] Step (37): Construct the BSTMQ turbulence model according to the eddy viscosity attenuation function in Step (36).
[0049] Taking the BSkO model as the base model, correct the turbulent viscosity. The equation of the eddy viscosity coefficient constructed using the invariants of the velocity gradient tensor is as follows.
Equation
[0050] There are two basic constraint conditions that the equation for the eddy viscosity coefficient must satisfy. (1) The linear constitutive relation needs to be maintained. (2) In the case of a uniform shear flow in an inertial reference system, the model simplifies to the original form that is a constant.
[0051] By adjusting the model constants in the equation through the bifurcation diagram, the following can be obtained.
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[0052] Finally, the equation of the BSTMQ turbulence model with BSkO as the base model is as follows.
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[0053] OpenFOAM (Registered trademark) The calculation program based on it is specifically as follows. OpenFOAM (Registered trademark) is an open-source CFD computing platform that discretizes equations using the finite volume method and discretizes the computational domain using an unstructured grid. The current OpenFOAM (Registered trademark) already has relatively complete solvers, turbulence models, boundary conditions, and post-processing procedures, and can calculate most complex flows. OpenFOAM (Registered trademark) is divided into steady calculations and unsteady calculations. Steady calculations do not include time discretization, and the time discretization of unsteady calculations is divided into a series of time steps according to the user's instructions. A specific time step is usually estimated based on the Courant number (CFL: Courant - Friedrichs - Lewy). The spatial discretization of the computational domain is meshing, and OpenFOAM (Registered trademark)It can be split using a separate meshing tool or the computational domain grid can be imported from third-party software. The discrete equations obtained by meshing can be calculated using the three pressure correction methods provided by OpenFOAM (Registered trademark) : SIMPLE (Semi-Implicit Method for Pressure Linked Equations), PISO (Pressure Implicit with Splitting of Operator), and PIMPLE (Pressure Implicit Method for Pressure Linked Equations). The SIMPLE algorithm is used for steady calculations, and for unsteady calculations of incompressible turbulent flows, the PISO or PIMPLE algorithms are usually selected. When solving algebraic equations, the pressure equation is generally an anti-symmetric matrix, while the velocity, turbulent kinetic energy, etc. are symmetric matrices. Since the anti-symmetric matrix is not a diagonally dominant matrix and is prone to divergence during calculation, a multigrid preconditioner is used during calculation to convert it into a diagonally dominant matrix, then a diagonal incomplete Gauss-Seidel smoother is used, and finally, a conjugate gradient solver with conditions is selected to calculate the pressure equation. When calculating symmetric matrices such as velocity, a smoother is used to calculate the velocity equation.
[0054] As shown in Figure 2, in the compilation of the turbulence model, all turbulence models in OpenFOAM (Registered trademark) share the basic class turbulenceModel, and three different subclasses of Laminar, RASModel, and LESModel are defined. These three subclasses represent the laminar model, the RANS model, and the LES model respectively. Since the BSTMQ model only corrects the turbulent viscosity of the RANS model, the new model program is compiled under the RASModel subclass.
[0055] As shown in Figure 2, the central dotted box represents the implementation processes of steps (31) and (32), the right side represents the implementation processes of steps (33) to (36), and the right side represents the implementation process of the BSkO base model in step (37).
[0056] Spalart - When using the Shur tensor to unify the rotation effect and the curvature effect and construct the invariant of the velocity gradient tensor, specifically, first, define a symmetric tensor field where the data is stored at the center of the body, that is, the strain rate tensor. Next, calculate based on the equations for constructing II S =S ij S ji and III S =S ij S jk S ki and calculate based on the constructed equations. The intermediate variable X ij is a very complex symmetric tensor. First, create an empty symmetric tensor field according to the dimension of X ij , and then it is necessary to calculate the results of each component of this tensor individually and replace the empty symmetric tensor field. W ij is also defined in this way to obtain the corrected rotation velocity tensor Ω mod , and recalculate it to obtain the corrected rotation velocity tensor invariant
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[0057] When constructing the BSkO base model considering the rotation effect and the curvature effect based on the invariant of the velocity gradient tensor constructed in step (33), specifically, it is as follows. First, the private member function: tmp <volscalarfield>Declare `f()const`, which is declared as a template class of scalar field, and `f()` returns the result of calculating the eddy viscosity coefficient formula. This private function variable can only be called by member functions.
[0058] To improve the eddy viscosity decay function of the existing STRUCT model, the following specific BSTMQ model is proposed. As mentioned above, the private member function: tmp <volscalarfield>Declare Df()const. This function is declared as a template class of the scalar field, and Df() is to return the calculation result of the eddy viscosity decay function formula. Next, multiply the calculation results of the returned eddy viscosity coefficient formula f() and the eddy viscosity decay function formula Df() by the original eddy viscosity formula. Use this eddy viscosity to recalculate the turbulent kinetic energy equation and the specific dissipation rate equation, and re-update the private functions f() and Df() based on the results obtained at each step.
[0059] After building the model, OpenFOAM (Registered trademark) combines the eddy viscosity coefficient and the kinematic viscosity coefficient into the effective viscosity coefficient, then calculates the turbulent stress, and uses the turbulence→divDevReff(U) statement by the solver to call the results of the turbulence model.
[0060] OpenFOAM (Registered trademark) Based on the unique functions and the turbulencce model compiled independently, a program for the rotational turbulence numerical simulation using the BSTMQ model can be implemented.
[0061] To better show the advantages of the embodiments of the present invention, compare the SSTk-ω model generally used in the current rotational turbulence calculation in fluid engineering and the conventional STRUCT model (STSST). As shown in FIGS. 3 and 4, taking the rotational channel flow and the rotational sudden expansion pipe as examples respectively, use the finite volume method to discretize the control equations, and use high-quality hexahedral grids to spatially discretize the calculation domain. The total number of grids in the instance of the rotational channel flow is about 390,000, and the total number of meshes in the instance of the rotational sudden expansion pipe is about 1,660,000. After introducing BSTMQ in the embodiments of the present invention, perform transient calculations to ensure that the maximum Courant number is less than 1 at each time step. To quantitatively compare the advantages of the BSTMQ model, FIGS. 5 to 9 attached are the results of different variables in two instances.
[0062] Figure 5 shows the average velocity distribution along the normal direction of the rotating flow path calculated by various models. The average velocity calculated by the BSTMQ model is closest to the result of direct numerical simulation (DNS) and can predict the velocity distribution of the asymmetric distribution. The results of the conventional SSTk-ω model and the STSST model are significantly different from the DNS results. Figure 6 shows the root mean square distribution of the average pulsating velocity along the flow direction of the rotating flow path flow calculated by various models. Near the negative pressure surface (y / h = 2) where the rotation effect is more prominent, the calculation results of the BSTMQ model are much better than those of the SSTk-ω model and the STSST model. Figure 7 is the ratio of the turbulent viscosity nut to the molecular viscosity nu of the rotating flow path flow calculated by various models and can be used to show the degree of analysis of the flow field by the model. In the conventional SSTk-ω model, the value of nut / nu exceeds 10 in most regions of the flow path, and the degree of analysis is close to that of the RANS model. Near the negative pressure surface of the STSST model, the values of nut / nu all exceed 10, and the degree of analysis is close to that of the RANS model. At other positions, the value of nut / nu is less than 10, and the degree of analysis is close to that of large eddy simulation. In the BSTMQ model, the value of Nut / nu of the flow path flow is less than 1, and the degree of analysis is close to DNS. Figure 8 is a diagram comparing the axial average velocity at the position of Z / D = 0.25 of the instance of the rotating flow sudden expansion pipe. Figure 9 is a diagram comparing the root mean square of the circumferential average velocity pulsation at the position of Z / D = 4 of the instance of the rotating flow sudden expansion pipe. It was also found that in the case of the rotating flow sudden expansion pipe, the calculation results of the BSTMQ model are better than those of the SSTk-ω model and the STSST model.< / volscalarfield> < / volscalarfield>
Claims
1. A method for predicting rotating turbulent flow using the BSTMQ turbulent flow model, comprising: Step (1) of performing solid modeling on the object to be predicted of rotating turbulent flow by means of 3D modeling software to obtain a simulation model; Step (2) of meshing the simulation model; A step of constructing a BSTMQ turbulent flow model by performing rotational curvature correction on an existing STRUC turbulent flow model based on the branching method, wherein the equation of the BSTMQ turbulent flow model is as follows: 【Number 51】 Here, k is the turbulent kinetic energy, and ω is the specific dissipation rate. 【Number 52】 is the partial derivative of the turbulent kinetic energy with respect to time. 【Number 53】 is the partial derivative of the turbulent kinetic energy in the coordinate direction. 【Number 54】 is the partial derivative of the specific dissipation rate with respect to time. 【Number 55】 is the partial derivative of the specific dissipation rate in the coordinate direction, and u ｊ is the velocity, and C ＊ μ is the formula for the eddy viscosity coefficient, and C μ is the eddy viscosity coefficient, S is the mode of the strain rate tensor, v is the kinematic viscosity coefficient, and v Ｔ is the eddy viscosity coefficient, and P ｋ is the turbulent kinetic energy generation term, and D ｆ－ｂ is the eddy viscosity decay function, and б ｋ , б ω , α, β, F １ , б ω２ is a constant coefficient, step (3), and Step (4) of obtaining the prediction result of the rotating turbulent flow of the object to be predicted by performing numerical simulation calculations on the rotating turbulent flow using the BSTMQ turbulent flow model by means of a calculation program based on OpenFoam. A method for predicting rotating turbulent flow, characterized by including the above steps.
2. In step (3), the step of constructing the BSTMQ turbulent flow model specifically includes: Step (31): Introducing the strain rate tensor and the rotation rate tensor in the rotating coordinate system; Step (32): Using the Spalart-Shur tensor to unify the rotation effect and the curvature effect to obtain a corrected rotation rate tensor; Step (33): Creating a velocity gradient invariant from the strain rate tensor introduced in step (31) and the corrected rotation rate tensor obtained in step (32); Step (34): Determining a corrected analytical time scale from the velocity gradient invariant obtained in step (33); Step (35): Determining a modeling time scale of the rotating turbulent flow from the specific dissipation rate. Here, Step (36): Construct a turbulent viscosity attenuation function D that reflects the rotation effect and the curvature effect according to steps (34) and (35). ｆ－ｂ and 【Number 56】 where 【Number 57】 and 【Number 58】 is the dimensionless velocity gradient invariant III, 【Number 59】 is the dimensionless velocity gradient invariant I constructed based on the strain rate tensor, 【Number 60】 is the dimensionless velocity gradient invariant II constructed based on the corrected rotation rate tensor, and α is an empirical constant of the modeling time scale. Step (37): Using the BSkO model as the base model, correct the turbulent viscosity and construct a STRUC turbulent model corrected based on the rotation curvature of the branching method according to the eddy viscosity decay function D, that is, the BSTMQ turbulent model. ｆ－ｂ The rotational turbulent flow prediction method according to claim 1, characterized in that a STRUC turbulent model corrected based on the rotation curvature of the branching method according to the eddy viscosity decay function D, that is, a BSTMQ turbulent model, is constructed using the BSkO model as the base model.
3. In the inertial coordinate system, the strain rate tensor S ｉｊ and the rotation rate tensor Ω ｉｊ are calculated as follows: 【Number 61】 Here, i and j are two free indices in the tensor representation, both taking the values 1, 2, and 3, which means that it is necessary to traverse all the values of the indices, and U ｉ and U ｊ are velocity vectors, and the three-direction velocity components in the inertial coordinate system are U １ = U, U ２ = V, U ３ = W, and x ｉ and x ｊ are the coordinate axes in the inertial coordinate system, and x １ = x, x ２ = y, x ３ = z, represented as 【Number 62】 is the partial derivative of the three velocity components in three directions. Angular velocity vector Ω Ｆ ｋ In a coordinate system rotating with Ａ ｉｊ the rotation speed tensor Ω is calculated as follows: 【Number 63】 Here, ・ ｉｊｋ is a cyclic permutation operator, and Ω Ｆ ｉｊ is a rotation tensor of the coordinate system. The rotational turbulent flow prediction method according to claim 2, characterized in that.
4. When the rotation effect and the curvature effect are unified based on the Spalart-Allmaras tensor, the following calculation formula for the corrected rotation speed tensor Ω ｍｏｄ ｉｊ is obtained, 【Number 64】 Here, C ｒ is a model constant, and W Ａ ｉｊ is a correction variable based on the Spalart-Allmaras tensor, and the rotational turbulent flow prediction method according to claim 3, characterized in that.
5. Correction variable W Ａ ｉｊ is determined by In the case of two-dimensional flow, W Ａ ｉｊ = Ω ＳＳ ｉｊ shall be made to, and In the case of three-dimensional flow, W Ａ ｉｊ = Ω Ｆ ｉｊ - ・ ｉｊｋ w ｉ including making it Here, Ω ＳＳ ｉｊ is the Spalart-Allmaras tensor, and w ｉ is an intermediate variable, 【Number 65】 Here, Ω Ｆ ｐｑ is the rotation tensor of a coordinate system with a different index from Ω Ｆ ｉｊ and Ω ＳＳ ｒｓ is the Spalart-Allmaras tensor with a different index from Ω ＳＳ ｉｊ and ・ ｐｑｊ and ・ ｒｓｊ are ・ ｉｊｋ the cyclic permutation operators with different indices from ｉｊ where X is an intermediate variable 【Number 66】 Here, δ ｉｊ is the Kronecker symbol tensor, S ｉｋ , and S ｋｊ are strain rate tensors with indices different from those of S ｉｊ and 【Number 67】 The method for predicting rotating turbulent flow according to claim 4, characterized in that
6. 【No. 68】 The calculation formula of is as follows: 【Number 69】 Here, k is the turbulent kinetic energy, ε is the dissipation rate, S is the mode of the strain rate tensor, and Ω ｍｏｄ is the mode of the corrected rotation rate tensor, and the rotational turbulent flow prediction method according to claim 2, characterized in that.
7. The corrected analytical time scale is as follows: 【Number 70】 Here, 【Number 71】 where Modeling time scale t of rotational turbulent flow from specific dissipation rate ｍ to determine 【Number 72】 Here, α is an empirical constant of the modeling time scale, ω is the specific dissipation rate, 【Number 73】 The rotational turbulent flow prediction method according to claim 6, characterized in that [[ ]] performs a geometric mean operation in the flow region of interest. **Claim 8** Conventional eddy viscosity decay function D ｆ Based on this, an eddy viscosity decay function D ｆ－ｂ that reflects the rotation effect and the curvature effect is constructed. The conventional eddy viscosity decay function D ｆ is 【Number 74】 The rotational turbulent flow prediction method according to claim 7, characterized in that it is [[ ]]. **Claim 9** A computer device including a memory, a processor, and a computer program stored in the memory and operable by the processor, When the processor executes the computer program, the steps of the method according to any one of claims 1 to 8 are realized. A computer device characterized by this. **Claim 10** A computer-readable storage medium storing a computer program, When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 8 are realized. A computer-readable storage medium characterized by this.