Simulation device, simulation method, and simulation program

Abstract

To provide a simulation device that can highly accurately perform an analysis of a flowing field including areas mutually separated by a wall, using a particle method.SOLUTION: A simulation condition is input to an input unit. A processing unit is configured to: represent a fluid body by a plurality of calculation particles on the basis of the simulation condition; numerically solve a dominant equation about each of the plurality of calculation particles; and subject a position and physical quantity of the plurality of calculation particles to a time evolution. Upon solving the dominant equation, other calculation particle arranged apart from a wall surface is excluded with respect to the calculation particle of interest. Information indicative of the shortest distance vector is calculated, which is defined by a length and direction of the shortest route to respective positions of the plurality of calculation particles from the wall surface. Using respective position vectors of two calculation particles, and the shortest distance vector with respect to each of the two calculation particles, a determination is made as to whether the two calculation particles are arranged mutually apart from the wall surface.SELECTED DRAWING: Figure 4

Description

[Technical field]

[0001] The present invention relates to a simulation device, a simulation method, and a program. [Background technology]

[0002] As a fluid analysis technique, a particle method is known that discretizes a continuous field using a set of virtual particles (hereinafter referred to as computational particles) and solves the governing equations to analyze the time evolution of a flow field. When analyzing a flow around a given object, a wall boundary condition is imposed as an analysis condition. For example, Patent Documents 1 and 2 describe a method of imposing a wall boundary condition on an object of any shape. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] JP 2010-243293 A [Patent Document 2] Patent Publication No. 2022-80643 Summary of the Invention [Problem to be solved by the invention]

[0004] When solving governing equations using the particle method, other computational particles in the vicinity of the computational particle of interest are referenced, and the physical quantities assigned to the other computational particles are used to update the physical quantities assigned to the computational particle of interest. If a flow exists within the reference range set for each computational particle and in a region separated by a thin wall, the reference range of the computational particle of interest extends to the computational particles in the region separated by the wall.

[0005] Generally, there is almost no interaction between fluids flowing through a region separated by a wall. However, when analyzing a flow field using a conventional particle method, an exchange of physical quantities occurs between two computational particles separated by a wall. As a result, the accuracy of the analysis decreases.

[0006] An object of the present invention is to provide a simulation device, a simulation method, and a program that are capable of analyzing a flow field including regions separated from each other by walls with high accuracy using a particle method. [Means for solving the problem]

[0007] According to one aspect of the present invention, A simulation device that uses a particle method to analyze a fluid flow in a space having a wall, comprising: an input unit for inputting information defining a fluid to be analyzed, initial and boundary conditions for the analysis, and information defining the shape of a wall surface to be placed in the analysis space; a processing unit that represents the fluid as a plurality of computational particles based on information input to the input unit, numerically solves a governing equation for each of the plurality of computational particles, and evolves positions and physical quantities of the plurality of computational particles over time; Equipped with The processing unit includes: a function of solving the governing equation by excluding other computational particles disposed across the wall surface from a computational particle of interest when solving the governing equation; a function of calculating information indicating a shortest distance vector defined by the length and direction of a shortest path from the wall surface to each position of the plurality of computational particles; a function of determining whether or not the two computational particles are arranged across the wall surface by using the position vectors of the two computational particles and the shortest distance vectors for the two computational particles; A simulation device is provided having:

[0008] According to another aspect of the invention, A simulation method for analyzing a fluid flow in a space having a wall surface by using a particle method, comprising the steps of: A computer given simulation conditions performs the following based on the given simulation conditions: expressing the fluid as a plurality of computational particles, numerically solving a governing equation for each of the plurality of computational particles, and evolving positions and physical quantities of the plurality of computational particles over time; When solving the governing equation, the governing equation is solved while excluding other computational particles disposed across the wall surface with respect to the computational particle of interest; calculating information indicating a shortest distance vector defined by the length and direction of a shortest path from the wall surface to each position of the plurality of computational particles; A simulation method is provided for determining whether or not two computational particles are located across the wall surface from each other using respective position vectors of the two computational particles and the shortest distance vector for each of the two computational particles.

[0009] According to yet another aspect of the present invention, A program for enabling a computer to perform a function of analyzing a fluid flow in a space having a wall surface using a particle method, comprising: Based on the given simulation conditions, a function of expressing the fluid as a plurality of computational particles, numerically solving a governing equation for each of the plurality of computational particles, and evolving positions and physical quantities of the plurality of computational particles over time; a function of solving the governing equation by excluding other computational particles disposed across the wall surface from a computational particle of interest when solving the governing equation; a function of calculating information indicating a shortest distance vector defined by the length and direction of a shortest path from the wall surface to each position of the plurality of computational particles; a function of determining whether or not the two computational particles are arranged across the wall surface by using the position vectors of the two computational particles and the shortest distance vectors for the two computational particles; A program to achieve this is provided. Effect of the Invention

[0010] When solving the governing equations, a highly accurate analysis can be performed by solving the governing equations while excluding other computational particles arranged across a wall surface from the computational particle of interest. [Brief description of the drawings]

[0011] [Figure 1] FIG. 1 is a cross-sectional view of an object placed in an analysis space. [Diagram 2] Figure 2A is a schematic diagram of a case where a computational particle of interest and other computational particles within the reference range are arranged separated by a thin wall, and Figure 2B is a schematic diagram of a case where a computational particle of interest and other computational particles within the reference range are on the same side of the thin wall. [Diagram 3] FIG. 3 is a block diagram of the simulation device according to the first embodiment. [Figure 4] FIG. 4 is a flowchart showing the procedure of the simulation method according to the first embodiment. [Diagram 5] FIG. 5 is a schematic diagram showing the positional relationship between two computational particles and a wall surface, for explaining a simulation method according to a modified example of the first embodiment. [Figure 6] FIG. 6 is a schematic diagram showing an example of the shape of a wall surface to be analyzed by the simulation apparatus according to the second embodiment. [Figure 7] FIG. 7 is a schematic diagram for explaining the minimum distance vector used in the simulation method according to the second embodiment. [Figure 8] FIG. 8 is a schematic diagram of two computational particles arranged near the outer wall surface and separated by a thin wall. [Figure 9] FIG. 9 is a flowchart showing the procedure of the simulation method according to the second embodiment. [Figure 10] 10A to 10D are diagrams showing other computational particles to be referred to for a computational particle of interest. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0012] [Overview of particle method] Before describing an embodiment of the present invention, a general SPH (Smoothed Particle Hydrodynamics) method will be briefly described. The SPH method is a Lagrangian type numerical calculation method that discretizes a continuum using a set of multiple calculation particles and calculates the time evolution of a flow field. The SPH method uses a continuous and differentiable kernel function as the mass distribution of a single particle, and also uses a discretization model in which the superposition of the differential coefficients of the kernel function is the spatial derivative.

[0013] In the SPH method, the mass m of a computational particle is distributed around it by a kernel function W, which is continuously distributed, and the density field is given as a superposition of the mass m and the density field of the i-th computational particle. i Density ρ i is expressed by the following formula:

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[0014] For example, the following function can be used as the kernel function W. The following function is called the C2Wendland kernel.

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[0015] h is the smoothing length, also called the kernel width. The kernel width h is equal to the diameter of an equivalent sphere obtained by replacing each of the multiple calculation particles with a sphere having the same mass and physical density. In this specification, the kernel width h may be referred to as the diameter of the calculation particle.

[0016] Any position x iThe value of any scalar quantity A and vector quantity A in can be expressed by the following equation by superposition of kernel functions.

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[0017] The gradient of any scalar quantity A is expressed by the following equation by superposing the derivatives of the kernel function:

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[0018] Here, ∇W(x ij ,h) is the derivative of the kernel function, and when the C2Wendland kernel is used as the kernel function, it is expressed by the following equation.

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[0019] The divergence for any vector quantity A can be expressed by the following equation, similar to equation (4).

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[0020] The second derivative with respect to any scalar quantity A can be calculated, for example, using the following formula:

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[0021] [Governing equations of incompressible flows] The continuity equation and Navier-Stokes equations for incompressible flow are expressed as follows:

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[0022] [Discretization of governing equations using the SPH method] If the governing equations of the flow shown in equations (9) and (10) are discretized using the SPH method, they can be expressed, for example, as follows.

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[0023] [First Example] Next, a simulation device according to a first embodiment will be described. In the first embodiment, an object of an arbitrary shape is placed in an analysis space, and the flow around this object is analyzed. The shape of the object is given by, for example, CAD data. In order to provide boundary conditions on the object surface (hereinafter sometimes referred to as a wall surface), it is necessary to calculate the distance from each position of a plurality of computational particles to the object surface.

[0024] To calculate the distance from a wall to an arbitrary position in the analytical space, for example, a signed distance function can be used. If an arbitrary position in the analytical space is denoted as x and the value of the signed distance function at position x is denoted as f(x), f(x) is defined as follows:

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[0025] [Issues when thin walls exist in analytical space] Next, a problem that occurs when a thin wall exists in the analytical space will be described with reference to FIG. 1 is a cross-sectional view of an object 10 placed in an analysis space. The object 10 includes an outer wall 10A surrounding a flow path in which a fluid is contained, and a thin wall 10B placed within the flow path. A plurality of computational particles 20 are placed within the flow path. A plurality of computational particles 20 are also placed on both sides of the thin wall 10B.

[0026] The computational particle 20 for which the governing equation is to be solved is referred to as the computational particle 20i of interest. In Fig. 1, the computational particle 20i of interest is hatched with relatively thicker lines slanting downward to the right. The reference range 23i when solving the governing equation for the computational particle 20i is, for example, a sphere centered on the position of the computational particle 20i of interest, and the radius of the reference range 23i is, for example, about 3 to 10 times the diameter of the computational particle 20. In Fig. 1, the outer periphery of the reference range 23i is indicated by a dashed line.

[0027] When a computational particle 20i of interest is located near the thin wall 10B, the reference range 23i extends to the space on the opposite side of the computational particle 20i of interest, separated by the thin wall 10B. In Fig. 1, among the computational particles 20 existing within the reference range 23i, the computational particle 20a existing on the same side as the computational particle 20i of interest, with the thin wall 10B as the boundary, is indicated by relatively light hatching slanting upward to the right, and the computational particle 20b existing on the opposite side is indicated by gray.

[0028] The fluids flowing through the spaces on both sides separated by the thin wall 10B do not affect each other. For this reason, it is preferable to exclude the computational particle 20b when solving the governing equation for the computational particle 20i of interest. However, in an analysis using the conventional SPH method, both the computational particle 20a and the computational particle 20b are referenced when solving the governing equation for the computational particle 20i of interest. In a first embodiment described below, the computational particle 20b is excluded and the governing equation for the computational particle 20i of interest is solved.

[0029] Next, a method for determining whether two computational particles are arranged with a thin wall 10B between them will be described with reference to Figures 2A and 2B. Figure 2A is a schematic diagram of a case where a computational particle of interest 20i and another computational particle 20j (reference lattice point) in a reference range 23i (Figure 1) are arranged with a thin wall 10B between them, and Figure 2B is a schematic diagram of a case where a computational particle of interest 20i and another computational particle 20j in a reference range 23i (Figure 1) are present on the same side of the thin wall 10B. If the position vector of the computational particle of interest 20i is x i The position vector of the other particle 20j is denoted as x j It is marked as such.

[0030] In Fig. 2A, one wall surface 10F of the thin wall 10B faces the computational particle 20i of interest, and the other wall surface 10F faces the computational particle 20j of interest. In Fig. 2B, one wall surface 10F of the thin wall 10B faces the computational particle 20i of interest and the other computational particles 20j of interest.

[0031] A plurality of grid points of an orthogonal equally spaced grid are defined in the analysis space, and at each position of the plurality of grid points, a signed distance function for a given object 10 (Figure 1) is calculated, and the value is associated with the grid point and stored.

[0032] First, for each of the computational particle 20i of interest and the other computational particles 20j, the shortest distance vector d i , d j The shortest distance vector is a vector having the length and direction of the shortest path from the wall surface 10F to the positions of the computational particles 20i and 20j. For example, the shortest distance vector d is calculated by performing linear interpolation based on the values ​​of the signed distance function stored in association with each of the multiple lattice points in the vicinity of the computational particle 20i and its gradient vector. i The shortest distance vector d j can be calculated in a similar manner.

[0033] Position vector x of wall surface 10F for calculation particles 20i and 20j wi , x wj is calculated according to the following formula:

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[0034] When either of the following two formulas is satisfied, it can be determined that the computational particle 20i and the computational particle 20j are disposed across the wall surface 10F.

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[0035] Next, the physical meaning of formulas (25) and (26) will be explained. The left side of equation (25) is the vector x i -x wj and the shortest distance vector d j The angle θ ji The left side of equation (26) represents the vector x j -x wi and the shortest distance vector d i The angle θ ij If γ is set to zero, the angle θ ji , θ ij When at least one of these is greater than 90°, at least one of the formula (25) and the formula (26) is satisfied.

[0036] As shown in FIG. 2A, the angle θ ji , θ ij If both of the angles θ are greater than 90°, it is determined that the computational particle 20i and the computational particle 20j are disposed across the wall surface 10F. ji , θ ij If both of these angles are smaller than 90°, it is determined that the computational particle 20i and the computational particle 20j are not separated from each other by the wall surface 10F.

[0037] 3 is a block diagram of the simulation device according to the first embodiment. The simulation device according to the first embodiment includes an input unit 30, a processing unit 31, an output unit 32, and a storage unit 33. Simulation conditions and the like are input from the input unit 30 to the processing unit 31. Furthermore, various instructions (commands) and the like are input from a user to the input unit 30. The input unit 30 is composed of, for example, a communication device, a removable media reader, a keyboard, a pointing device, and the like.

[0038] The processing unit 31 executes a simulation using the particle method based on the input simulation conditions and commands. Furthermore, it outputs the simulation results to the output unit 32. The simulation results include information representing the state of particles in the particle system that is the simulation target, and the change over time in the physical quantity of the particle system. The processing unit 31 includes, for example, a central processing unit (CPU) of a computer. A program for causing the computer to execute the simulation using the particle method is stored in the storage unit 33. The output unit 32 includes a communication device, a removable media writing device, a display, and the like.

[0039] Fig. 4 is a flowchart showing the procedure of the simulation method according to Example 1. The function of each step of the flowchart shown in Fig. 4 is realized by the processing unit 31 executing a program stored in the storage unit 33.

[0040] First, the processing unit 31 acquires the simulation conditions inputted by the operator to the input unit 30 (step S1). The simulation conditions include information defining the fluid to be simulated, initial conditions, boundary conditions, etc. The information defining the fluid includes physical property values ​​such as the density and viscosity of the fluid. The initial conditions include information for arranging a plurality of computational particles in the analysis space, a method for specifying the initial physical property values ​​of the computational particles, etc. The boundary conditions include information specifying the shape and size of the object to be arranged in the analysis space, etc.

[0041] The processing unit 31 calculates the value of the signed distance function at each position of the lattice points of the orthogonal equally spaced lattice for a given object shape (step S2).

[0042] Next, the processing unit 31 places a plurality of computational particles 20 in the analysis space based on the input simulation conditions and the value of the signed distance function (step S3). Specifically, the processing unit 31 places a plurality of computational particles 20 in a region where the value of the signed distance function is positive. After that, for each of the plurality of computational particles 20 (a computational particle of interest 20i), a neighboring particle list is created that lists the computational particles 20j within the reference range 23i (step S4).

[0043] Next, it is determined whether the computational particle 20i focused on when creating the neighbor particle list and each of the other computational particles 20j included in the neighbor particle list are arranged across a wall, and the other computational particles 20j that are arranged across a wall from the computational particle 20i of interest are excluded from the neighbor particle list (step S5). To determine whether the computational particle 20i of interest and each of the other computational particles 20j included in the neighbor particle list are arranged across a wall, equations (25) and (26) are used.

[0044] For each of the plurality of computational particles, the governing equations shown in Equations (11) to (14) are numerically solved, and the physical quantities and positions of each of the computational particles 20 are updated (step S6). When solving the governing equation for the computational particle 20i of interest, the plurality of computational particles 20j included in the neighbor particle list after the process of excluding some of the computational particles 20j in step S5 is performed is referenced. In other words, the governing equation is solved by excluding other computational particles arranged across a wall from the computational particle 20 of interest.

[0045] Next, it is determined whether or not to update the neighbor particle list (step S7). For example, it is determined whether or not the movement amount from the position at the time when the current neighbor particle list was created for each of the multiple computational particles 20 exceeds the judgment upper limit value. If the movement amount of at least one computational particle 20 exceeds the judgment upper limit value, it is determined to update the neighbor particle list, and otherwise it is determined not to update the neighbor particle list.

[0046] If it is determined that the neighbor particle list should be updated, the neighbor particle list is updated (step S8). The neighbor particle list is updated in the same procedure as that for creating the neighbor particle list in step S4. Furthermore, for the neighbor particle list after updating, other computational particles that are arranged across a wall surface from the computational particle 20i of interest are excluded from the neighbor particle list (step S9). This procedure is the same as that in step S5.

[0047] Steps S6 to S9 are repeated until a calculation end condition is satisfied (step S10). When the calculation end condition is satisfied, the calculation result is output to the output unit 32 (FIG. 3) (step S11).

[0048] Next, the excellent effects of the first embodiment will be described. In the first embodiment, even if a thin wall 10B (FIG. 1) is placed in the analysis space and a fluid flows on both sides of the wall, in steps S5 and S9 (FIG. 4), other computational particles that are placed across the wall from the computational particle 20i of interest are excluded from the neighboring particle list, so that analysis can be performed without a decrease in analysis accuracy.

[0049] 2A and 2B, in the first embodiment, whether or not two computational particles 20i and 20j are arranged across a wall is determined based only on the value of the signed distance function, so there is no need to perform a process of searching for the wall by referring to information that defines the shape and position of the wall arranged in the analysis space.

[0050] Next, a modification of the first embodiment will be described with reference to FIG. 5 is a schematic diagram showing the positional relationship between the computational particles 20i and 20j and the wall surface 10F for explaining the simulation method according to the modified example of the first embodiment. In the example shown in FIG. 2A and FIG. 2B, the shortest distance vectors d i , d jis perpendicular to the wall surface 10F. In contrast, in the example shown in FIG. 5, the computational particles 20i and 20j are arranged near the edge of the wall surface 10F. The shortest distance vector d i is perpendicular to the wall surface 10F, but the shortest distance vector d j The starting point of is located at the edge of the wall 10F, and the shortest distance vector d j is not perpendicular to wall 10F.

[0051] In the example shown in FIG. 5, as in the example shown in FIG. 2A, the angle θ ij and angle θ ji are both greater than 90°. Therefore, when zero is used as the parameter γ in equations (25) and (26), the computational particle 20j is excluded from the computation target when solving the governing equation for the computational particle 20i of interest.

[0052] 5, the fluid flow at the position of the computational particle 20i and the fluid flow at the position of the computational particle 20j are considered to affect each other, so it is preferable to refer to the computational particle 20j when solving the governing equation for the computational particle 20i of interest.

[0053] When the parameter γ in equations (25) and (26) is set to a value greater than -1 and less than or equal to 0, the angle θ ij and θ ji is greater than 90°, it is also determined that the computational particle 20i and the computational particle 20j are not separated from each other by the wall surface 10F. As a result, the computational particle 20j is referred to when solving the governing equation for the computational particle 20i of interest. By adjusting the value of the parameter γ, the angle θ ij , θ ji The conditions change.

[0054] It is preferable that the value of the parameter γ is appropriately set based on the shape of the wall surface 10F disposed in the analysis space, the characteristics of the fluid, and the like.

[0055] In the first embodiment, a neighbor particle list is created in step S4 (FIG. 4), and updated in step S8 (FIG. 4). The neighbor particle list is not updated for each time step in which the governing equation is solved, but is updated only when the conditions for updating the neighbor particle list are met. When updating the neighbor particle list, a calculation is performed to remove other computational particles arranged across a wall from the neighbor particle list for each computational particle. This makes it possible to suppress an increase in the calculation load compared to a case in which a calculation is performed to remove other computational particles arranged across a wall from the neighbor particle list for each computational particle for each time step.

[0056] [Second Example] Next, a simulation device and a simulation method according to a second embodiment will be described with reference to Fig. 6 to Fig. 10D. Below, a description of the configuration common to the simulation device and the simulation method according to the first embodiment described with reference to Fig. 1 to Fig. 4 will be omitted.

[0057] Fig. 6 is a schematic diagram showing an example of the shape of a wall surface 10F to be analyzed by the simulation device according to Example 2. It has been found that when solving a governing equation for a computational particle 20i of interest under conditions in which the wall surface 10F of an object 10 arranged in the analysis space includes a corner portion as shown in Fig. 6, for example, a computational particle 20j that should be excluded from reference may not be excluded.

[0058] As shown in Figure 6, the object 10 includes an outer wall 10A that defines a flow path, and a thin wall 10B that protrudes from the outer wall 10A into the flow path. Fluid flows on both sides of the thin wall 10B. The connection between the outer wall 10A and the thin wall 10B forms a corner of a wall surface 10F.

[0059] The computational particle 20i and the computational particle 20j are arranged to be separated from each other by a thin wall 10B. Note that the position vector x wi , x wjThe position defined by is located on the wall surface 10F of the outer wall 10A, not on the wall surface 10F of the thin wall 10B. The two calculation particles 20i and 20j are arranged on the same side as viewed from the wall surface 10F of the outer wall 10A. Therefore, the angle θ ij , θ ji are both less than 90°. In the method described with reference to Fig. 2A and Fig. 2B, the computational particle 20i and the computational particle 20j are determined to be not separated from each other by the wall surface 10F. In the second embodiment described below, the determination process is further optimized so that the computational particle 20i and the computational particle 20j are determined to be disposed with the wall surface 10F in between.

[0060] FIG. 7 shows the minimum distance vector d 2i A schematic diagram for explaining the above. A plurality of lattice points of an orthogonal equally spaced lattice are defined in the analysis space. The position vector of the lattice point 15i of interest is expressed as x i The position vectors of the plurality of lattice points 15j within the reference range 23i of the lattice point of interest are denoted as x j The reference range 23i is a circle with a radius R and centered on the position of the lattice point 15i. The radius R can be set to, for example, about 10 times the lattice interval.

[0061] The shortest distance vector d between lattice points 15i and 15j i , d j can be obtained from the signed distance function. In FIG. 7, the shortest distance vector d i The starting point of is located on the first area A1 of the wall surface 10F, and the shortest distance vector d j In this example, the starting point of the first region A1 is located on the second region A2 of the wall surface 10F. For example, the first region A1 and the second region A2 are perpendicular to each other.

[0062] First, for the grid point 15j, the following vector d ij Define.

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[0063] The following evaluation score D ij Calculate.

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[0064] Based on the calculation results, the largest evaluation value D ij Vector d at lattice point 15j gives ij The minimum distance vector d from the wall surface 15F to the grid point 15i of interest 2i The shortest distance vector d i corresponds to the direction of the shortest distance and the shortest path to the first area A1 of the wall surface 15F that is closest to the lattice point 15i. 2i can be considered to represent a length equal to the minimum value of the length of the path from the lattice point 15i to the second closest second region A2 on the wall surface 15F, and the direction of that path.

[0065] Next, the meaning of equation (28) will be explained. The value of the first expression in the braces of (28) is the vector d i and vector d j The value of the expression in the second braces in equation (28) is the vector d ij and vector d i The value of the expression in parentheses in (28) is the vector d ij and vector d j The maximum value is reached when and are parallel to each other.

[0066] Therefore, the evaluation value D ij Searching for the lattice point 15j where is the maximum of vector d i and vector d j The angle between vector d and is close to 90°. ij and vector d i The angle with vector d is also close to 90°. ij and vector d j The angle between vector d and is close to 0°. ij It can be thought of as searching for a lattice point 15j that shortens the length of

[0067] Vector d i and d j The vector d is close to 90° from the condition that the angle between i and vector d j The lattice point 15j for which the vector d is parallel to the wall surface 15F is excluded from the search target. In other words, the lattice point 15j for which the first region A1 of the wall surface 15F is the nearest wall surface is excluded from the search target. ij and d i The angle between the vector and the vector d must be close to 90°. ij and d j The condition that the angle between is close to 0° is satisfied when the shortest distance vector d passes through the lattice point 15i of interest. i Therefore, the vector d for the lattice point 15j that satisfies these conditions is searched for. ij The minimum distance vector d of the lattice point 15i of interest 2i It can be regarded as:

[0068] By performing the above operation on each of the lattice points in the analysis space as the lattice points 15i of interest, the shortest distance vector d i and the minimum distance vector d 2i can be sought.

[0069] Next, a method for determining whether two computational particles are arranged with a thin wall between them will be described with reference to Fig. 8. Fig. 8 is a schematic diagram of a case where two computational particles 20i and 20j are arranged near a wall surface 15F of an outer wall 15A with a thin wall 10B between them. The wall surface 15F of the outer wall 15A is referred to as a first wall surface area A1, and the wall surface 15F of the thin wall 15B is referred to as a second wall surface area A2.

[0070] First, the shortest distance vector d i , d j , and the minimal distance vector d 2i , d 2j These vectors can be calculated by performing linear interpolation based on the shortest distance vectors and the minimum distance vectors calculated for a plurality of lattice points in the vicinity of the calculation particles 20i and 20j.

[0071] Next, the wall position vector x for the calculation particle 20i wi , x w2i is calculated using the following formula: Position vector x wi and x w2i The points represented by are located on the first area A1 and the second area A2, respectively.

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[0072] If any of the four equations below, that is, the equations (25) and (26) and the two equations (31) and (32), is satisfied, it is determined that the computational particle 20i and the computational particle 20j are arranged separated by a wall surface.

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[0073] Equation (31) is the vector x i -x w2j and vector d 2j The angle θ 2ji is equal to or larger than a given angle, and equation (32) expresses the vector x j -x w2i and vector d 2i The angle θ 2ij is equal to or larger than a predetermined angle. The value of the parameter γ should be set to the same value as the parameter γ in the equations (25) and (26).

[0074] 8, in the judgment using only formulas (25) and (26), the thin wall 15B is not detected, and it is judged that the two computational particles 20i and 20j are not separated by a wall surface. In contrast, in the second embodiment, formulas (31) and (32) are satisfied, and it is judged that the two computational particles 20i and 20j are arranged with the wall 15B between them.

[0075] Fig. 9 is a flowchart showing the procedure of the simulation method according to the second embodiment. Below, steps different from those in the flowchart shown in Fig. 4 are explained. In step S2 shown in Fig. 4, a signed distance function is calculated, but in step S2a shown in Fig. 8, a signed distance function is calculated, and further, the shortest distance vector d for each of the multiple lattice points is calculated by the method explained with reference to Fig. 7. i and the minimum distance vector d 2i Calculate.

[0076] In steps S5 and S9 shown in Fig. 4, when excluding other calculation particles arranged across a wall from the calculation particle of interest from the neighbor particle list, formulas (25) and (26) are used. In contrast, in steps S5a and S9a shown in Fig. 8, formulas (31) and (32) are used in addition to formulas (25) and (26).

[0077] Next, the advantageous effects of the second embodiment will be described. In the second embodiment, even when a corner portion exists on the wall surface 15F as shown in FIG. 8, it is possible to correctly determine whether or not two computational particles are arranged across a wall surface.

[0078] Next, with reference to Fig. 10A to Fig. 10D, the results of an actual determination performed by the method used in the second embodiment for determining whether two computational particles are arranged across a wall surface will be described. Fig. 10A to Fig. 10D are diagrams showing another computational particle 20j to be referred to for a computational particle 20i of interest. Two spaces 11A and 11B in which fluids are contained are separated from each other by a thin wall 15B.

[0079] 10A and 10B show the determination results when focusing on the computational particle 20i in one space 11A, and 10C and 10D show the determination results when focusing on the computational particle 20i in the other space 11B. Also, 10A and 10C show the determination results when the computational particle 20i of interest is located near the center of the thin wall 15B, and 10B and 10D show the determination results when the computational particle 20i of interest is located near the corner.

[0080] The relatively light gray calculation particles 20j indicate other calculation particles 20j to be referenced that have not been excluded from the neighboring particle list. The radius R of the reference range 23i was set to 10 times the diameter of the calculation particle. It was confirmed that the calculation particles (shown in a relatively dark color) within the reference range 23i that are arranged across a thin wall 15B from the calculation particle 20i of interest were excluded from the neighboring particle list.

[0081] Next, a modification of the second embodiment will be described. In the second embodiment (FIGS. 7 and 8), the analysis space is a two-dimensional plane, and one shortest distance vector d i and one minimal distance vector d 2i When the analysis space is three-dimensional, a corner may be formed in the area of ​​three planes of the wall, for example, near the vertex of a rectangular parallelepiped. In this case, the shortest distance vector d i and the minimum distance vector d 2i In addition to the above, the third shortest distance vector d 3i may be defined.

[0082] When expanding the analytical space to three dimensions, in addition to equation (28), D2 is calculated using the following equation. ij Calculate.

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[0083] The largest evaluation value D2 ij Vector d at lattice point 15j gives ij The third shortest distance vector d from the wall surface 15F to the grid point 15i of interest 3i It can be regarded as:

[0084] In addition to equations (29) and (30), the position vector x is calculated using the following equation: w3i Calculate.

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[0085] When any of the six equations, including the following two equations (35) and (36), in addition to equations (25), (26), (31), and (32), is satisfied, it is determined that the computational particle 20i and the computational particle 20j are arranged separated by a wall surface.

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[0086] By using the above-mentioned determination method, it becomes possible to analyze a three-dimensional flow field with high accuracy.

[0087] The above-mentioned embodiments are merely examples, and it goes without saying that partial replacement or combination of the configurations shown in different embodiments is possible. Similar effects due to similar configurations of multiple embodiments are not mentioned in each embodiment. Furthermore, the present invention is not limited to the above-mentioned embodiments. For example, it will be obvious to those skilled in the art that various modifications, improvements, combinations, etc. are possible. [Explanation of symbols]

[0088] 10 objects 10A Outer Wall 10B Thin Wall 10F wall 11A, 11B A space separated by a thin wall 15i Lattice point of interest 15j Lattice points within the reference range of the target lattice point 20 computational particles 20a A computational particle placed at a position not separated by a wall from the computational particle of interest 20b A computational particle arranged across a wall from the computational particle of interest 20i Focused computational particles 20j Other computational particles 23i Reference range for the computational particle of interest 30 Input section 31 Processing section 32 Storage section 33 Output section

Claims

1. A simulation device that uses a particle method to analyze a fluid flow in a space having a wall, comprising: an input unit for inputting information defining a fluid to be analyzed, initial and boundary conditions for the analysis, and information defining the shape of a wall surface to be placed in the analysis space; a processing unit that represents the fluid as a plurality of computational particles based on information input to the input unit, numerically solves a governing equation for each of the plurality of computational particles, and evolves positions and physical quantities of the plurality of computational particles over time; Equipped with The processing unit includes: a function of solving the governing equation by excluding other computational particles disposed across the wall surface from a computational particle of interest when solving the governing equation; a function of calculating information indicating a shortest distance vector defined by the length and direction of a shortest path from the wall surface to each position of the plurality of computational particles; a function of determining whether or not the two computational particles are arranged across the wall surface by using the position vectors of the two computational particles and the shortest distance vector for each of the two computational particles; A simulation device having the above configuration.

2. The processing unit includes: a function of calculating information indicating a minimum distance vector defined by a minimum value of a path length and a path direction from a region of the wall surface other than the region that gives the shortest distance vector to each position of the plurality of calculation particles, The simulation device according to claim 1, wherein when determining whether two computational particles are arranged across the wall surface, the device determines whether the two computational particles are arranged across the wall surface using the minimal distance vector for each of the two computational particles in addition to the position vectors of the two computational particles and the shortest distance vector for each of the two computational particles.

3. a storage unit in which information indicating the shortest distance vector from the wall surface to each of a plurality of lattice points of a lattice laid out in the analysis space is stored, 3. The simulation device according to claim 2, wherein the processing unit further has a function of calculating the shortest distance vector at each position of the plurality of computational particles by interpolating information indicating the shortest distance vector corresponding to each position of the plurality of lattice points at each position of the plurality of computational particles.

4. 4. The simulation device according to claim 2 or 3, wherein the processing unit further has a function of calculating, at each position of the plurality of lattice points, information indicating the minimum distance vector for a lattice point of interest, using the shortest distance vector for the lattice point of interest, a position vector of the lattice point of interest, a difference between the position vector of the lattice point of interest and each of position vectors of reference lattice points which are other lattice points present within a predetermined distance from the lattice point of interest, and the minimum distance vector for each of the plurality of reference lattice points.

5. A simulation method for analyzing a fluid flow in a space having a wall surface by using a particle method, comprising the steps of: A computer given simulation conditions performs the following based on the given simulation conditions: expressing the fluid as a plurality of computational particles, numerically solving a governing equation for each of the plurality of computational particles, and evolving positions and physical quantities of the plurality of computational particles over time; When solving the governing equation, the governing equation is solved while excluding other computational particles disposed across the wall surface with respect to the computational particle of interest; calculating information indicating a shortest distance vector defined by the length and direction of a shortest path from the wall surface to each position of the plurality of computational particles; A simulation method for determining whether or not two computational particles are arranged across the wall surface from each other, using the position vectors of each of the two computational particles and the shortest distance vector for each of the two computational particles.

6. A program for enabling a computer to perform a function of analyzing a fluid flow in a space having a wall surface using a particle method, comprising: Based on the given simulation conditions, a function of expressing the fluid as a plurality of computational particles, numerically solving a governing equation for each of the plurality of computational particles, and evolving positions and physical quantities of the plurality of computational particles over time; a function of solving the governing equation by excluding other computational particles disposed across the wall surface from a computational particle of interest when solving the governing equation; a function of calculating information indicating a shortest distance vector defined by the length and direction of a shortest path from the wall surface to each position of the plurality of computational particles; a function of determining whether or not the two computational particles are arranged across the wall surface by using the position vectors of the two computational particles and the shortest distance vector for each of the two computational particles; A program to achieve this.

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