Simulation program, simulation method, and simulation apparatus

Abstract

This invention provides a simulation program, a simulation method, and a simulation apparatus that improve the calculation accuracy of simulations. [Solution] For each particle representing the fluid pressurized by the wall surface, the first acceleration of the particle is calculated using the SPH method. Based on the physical properties of the fluid and the amount of pressurization, a calculated amount of pressurization to be used in the calculation is calculated. Based on the calculated amount of pressurization and the first acceleration, the second acceleration of the particle and the third acceleration of the wall surface particle representing the wall surface are calculated. Based on the second and third accelerations, the computer is made to perform a process to update the position and velocity of the particle and the wall surface particle.

Description

[Technical Field]

[0001] This invention relates to a simulation program, a simulation method, and a simulation apparatus. [Background technology]

[0002] In the casting process, molten metal is poured into a mold and cooled to produce metal products. In this casting process, solidification shrinkage defects can occur due to the shrinkage of the molten metal during solidification. Solidification shrinkage defects refer to relatively large cavities inside the casting and occur during the solidification shrinkage when the molten metal turns into a solid. Solidification shrinkage defects are particularly likely to occur in high-pressure casting. Therefore, to reduce solidification shrinkage defects, pressure is applied to the product during the solidification of the molten metal in the casting process.

[0003] To predict solidification shrinkage defects in such pressurized conditions, the use of simulation technology is expected. In this case, since the simulation includes moving boundaries such as pressurized areas, the application of particle methods such as SPH (Smoothed Particle Hydrodynamics) is being considered.

[0004] Furthermore, the following techniques exist for fluid analysis. For example, a technique has been proposed in which the provisional velocity and position of particles are calculated, the pressure term is calculated based on the Poisson equation using a pre-prepared particle number density, an auxiliary pressure is calculated using an equation with particle number density and added to the pressure term, and then the provisional velocity and position are corrected. In addition, a technique has been proposed in which a flow field with an inlet / outlet interface is connected to the inlet / outlet interface of the analysis domain via a boundary region, an analysis model is defined that allows particle movement between the heat bath and the boundary region and between the boundary region and the analysis domain, and the pressure within the boundary region is controlled to stay within a target value. [Prior art documents] [Patent Documents]

[0005] [Patent Document 1] Japanese Patent Publication No. 2009-129193 [Patent Document 2] Japanese Patent Publication No. 2020-101387 [Overview of the Initiative] [Problems that the invention aims to solve]

[0006] However, conventional SPH method calculations are designed for casting simulations that do not involve pressurization. Therefore, when applied to casting simulations that do involve pressurization, the simulated liquid may be compressed more than it actually is due to the pressurization. When the simulated liquid is compressed to such an extent, accurate calculations become difficult, and the accuracy of the simulation may deteriorate.

[0007] Furthermore, techniques that correct the pressure term calculated based on the Poisson equation using particle number density with an auxiliary pressure, and techniques that use analytical models that allow particle movement between the heat bath and the boundary region, and between the boundary region and the analysis region, do not take into account the behavior under pressurization. Therefore, even with these techniques, it is difficult to avoid a decrease in calculation accuracy in simulations of the casting process under pressurization.

[0008] The disclosed technology was developed in view of the above, and aims to provide a simulation program, a simulation method, and a simulation apparatus that improve the calculation accuracy of simulations. [Means for solving the problem]

[0009] In one aspect of the simulation program, simulation method, and simulation apparatus disclosed in the present application, for each particle representing a fluid pressurized by a wall surface, a first acceleration of the particle is calculated by the SPH method, a calculated pressure amount for use in calculation is calculated based on the physical property value and the pressure amount of the fluid, and a second acceleration of the particle and a third acceleration of a wall surface particle representing the wall surface are calculated based on the calculated pressure amount and the first acceleration. The computer is caused to execute a process of updating the positions and velocities of the particle and the wall surface particle based on the second acceleration and the third acceleration.

Advantages of the Invention

[0010] On one side, the present invention can improve the calculation accuracy of the simulation.

Brief Description of the Drawings

[0011] [Figure 1] FIG. 1 is a block diagram of a simulation apparatus. [Figure 2] FIG. 2 is a diagram showing an example of a casting process of a metal product. [Figure 3] FIG. 3 is a diagram showing parameters used in calculation in an embodiment. [Figure 4] FIG. 4 is a diagram showing the influence range of particles. [Figure 5] FIG. 5 is a diagram showing information for representing particles. [Figure 6] FIG. 6 is a schematic diagram showing particles of molten metal and wall surface particles. [Figure 7] FIG. 7 is a diagram for explaining the calculation of the acceleration of a wall surface. [Figure 8] FIG. 8 is a flowchart of a simulation process by a simulation apparatus according to an embodiment. [Figure 9] FIG. 9 is a hardware configuration diagram of a simulation apparatus.

Modes for Carrying Out the Invention

[0012] Hereinafter, embodiments of the simulation program, simulation method, and simulation apparatus disclosed in the present application will be described in detail based on the drawings. Note that the simulation program, simulation method, and simulation apparatus disclosed in the present application are not limited by the following embodiments.

Embodiment

[0013] FIG. 1 is a block diagram of a simulation apparatus. The simulation apparatus 1 simulates, for example, the casting process of metal products. More specifically, the simulation apparatus 1 executes a simulation using the SPH method for casting metal products.

[0014] FIG. 2 is a diagram showing an example of the casting process of a metal product. Here, the x-direction, y-direction, and z-direction described in FIG. 2 will be used for explanation.

[0015] For example, in the casting of a metal product, molten metal 10 obtained by melting the metal that is the material of the metal product is poured into a mold 21. The mold 21 has openings in the opposite directions in the x-direction where a pressure wall 22 fits. In the state where the molten metal 10 is poured into the mold 21, a gravitational acceleration G in the opposite direction in the z-direction is applied. And in order to reduce shrinkage defects, during the casting process, a pressure Pe is applied toward the inside of the mold 21 with respect to the pressure wall 22 during the solidification of the molten metal 10. That is, the pressure Pe applies a force to the molten metal 10 in the x-direction. The molten metal 10 is pressurized in the x-direction by the pressure Pe. The molten metal 10 solidifies in the state pressurized by the pressure Pe, and a metal product is generated. The simulation apparatus 1 simulates, for example, the movement of the molten metal 10 in the mold 21 in the casting process of the metal product shown in FIG. 2.

[0016] Returning to FIG. 1 and continuing the explanation. As shown in FIG. 1, the simulation apparatus 1 includes a calculation condition acquisition unit 11, a pseudo acceleration calculation unit 12, a calculation pressurization amount calculation unit 13, an output unit 14, a position velocity update unit 15, and an acceleration calculation unit 16.

[0017] The calculation condition acquisition unit 11 receives calculation conditions to be used for the simulation, which are entered by the user, from the user terminal device 2. The calculation conditions include initial conditions for a simulation of metal product casting using the SPH method.

[0018] The calculation condition acquisition unit 11 acquires, for example, the height of the molten metal 10, the physical properties of the molten metal 10, the gravitational acceleration G, the amount of pressure, and the position and velocity of each particle contained in the molten metal 10 as calculation conditions for casting a metal product. The height of the molten metal 10 is the width of the molten metal 10 in the direction in which the gravitational acceleration G acts. The physical properties of the molten metal 10 include the density of the particles contained in the molten metal 10 and the speed of sound of the molten metal 10. The amount of pressure is the magnitude of the pressure Pe, and may be 0 in the initial conditions. The velocity of the particles in the initial conditions may be 0, or it may have a predetermined velocity given by the gravitational acceleration G. The calculation condition acquisition unit 11 outputs the acquired calculation conditions to the provisional acceleration calculation unit 12 and the calculated pressure amount calculation unit 13.

[0019] Here, the molten metal 10 is an example of a "fluid." That is, the calculation condition acquisition unit 11 acquires calculation condition information including the height and physical properties of the fluid, gravity, pressurization amount, and the position and velocity of each particle contained in the fluid.

[0020] The provisional acceleration calculation unit 12 receives the calculation conditions from the calculation condition acquisition unit 11. The provisional acceleration calculation unit 12 then calculates the provisional acceleration as the acceleration under conditions where each particle in the molten metal 10 is subjected to pressure due to gravity acceleration G, but no pressure Pe is applied, using the SPH method.

[0021] Here, the speed of sound used in the SPH method calculation is set as follows: the height of the molten metal 10 is h (m), and the acceleration due to gravity G is g (m / s²). 2 If the speed of sound is Cs_c, then Cs_c = 10 × (2gh) 1 / 2 This can be determined. This calculation is an example of a "predetermined calculation". For example, if the height of the molten metal 10 is h=1(m) and the acceleration due to gravity G is g=9.8(m / s²), then this can be determined. 2In this case, Cs_c = 45 (m / s).

[0022] The actual speed of sound as a physical property is, for example, 1470 m / s for water, 2500 m / s for molten aluminum, and 4650 m / s for copper. However, in simulations of the casting process of metal products, the speed of sound used in the calculations is set to a very small value, as described above, in order to speed up the calculations.

[0023] In the SPH method, it is preferable to set the time required for one step to be less than the value obtained by dividing the particle diameter by the speed of sound. For example, let's consider the case where the particle diameter is 0.001 (m). In this case, if the speed of sound is 1470 (m / s), the time required for one step is 6.8 × 10⁻⁶. -7 It is approximately (s). On the other hand, if we use a calculated speed of 45 (m / s) for the speed of sound, the time taken for one step is 2.2 × 10⁻⁶. -5 (s) For example, to calculate the time up to 10(s), if the speed of sound is set to 1470(m / s), 14.7 million steps of calculation will be performed. In contrast, if the speed of sound is set to 45(m / s) for calculation purposes, it can be achieved in 450,000 steps of calculation. In this way, speed can be increased by setting a smaller speed of sound for calculation purposes.

[0024] Here, the compressibility of the molten metal 10 due to gravitational acceleration G is approximately 0.5%, so the compressibility of the molten metal 10 can be ignored. The speed of sound is a value that represents the degree of compression of the molten metal 10 due to the driving force given by gravitational acceleration G, but the speed of sound can be determined by assuming that the compressibility of the molten metal 10 due to gravitational acceleration G is a negligible value.

[0025] Furthermore, if the speed of sound is determined as described above, the Mach number, a dimensionless quantity obtained from the ratio of the fluid flow speed to the speed of sound, becomes 0.1, and the effect of compressibility can be ignored in the simulation. However, when the Mach number is greater than approximately 0.3, it becomes difficult to ignore the effect of compressibility. In the case of pressure due to gravitational acceleration G, the compressibility is negligible from the start, and by determining the speed of sound such that the Mach number is such that compressibility is negligible, the accuracy of the simulation can be ensured.

[0026] The provisional acceleration calculation unit 12 uses the speed of sound determined as described above to calculate the provisional acceleration of each particle and the density change amount, which represents the temporal change in the density of the molten metal 10 due to the acceleration, using the SPH method.

[0027] Furthermore, the wall surface of the pressurized wall 22, to which pressure Pe is applied, is also represented by particles. These particles representing the wall surface will be referred to as "wall particles" below. Next, the provisional acceleration calculation unit 12 calculates the provisional acceleration and density change of the wall particles using the conditions of the molten metal 10 particles and wall particles, as well as the calculated acceleration and density change for each particle of the molten metal 10.

[0028] The provisional acceleration calculation unit 12 then outputs the calculated provisional acceleration and density change amounts for the molten metal particles and wall particles to the acceleration calculation unit 16. The provisional acceleration calculation unit 12 also outputs the sound velocity information used to calculate the provisional acceleration using the SPH method to the calculated pressure amount calculation unit 13.

[0029] Here, we will explain in detail how to calculate the acceleration and density changes due to pressurization using the SPH method. Figure 3 is a diagram showing the parameters used in the calculation in the example. The provisional acceleration calculation unit 12 uses the following parameters as shown in Table 101: gravitational acceleration, influence radius (h), liquid density, liquid sound velocity, wall surface area, x-direction component of the wall normal, y-direction component of the wall normal, z-direction component of the wall normal, amount of pressurization from the wall, and wall mass. The x-direction component of the wall normal, the y-direction component of the wall normal, and the z-direction component of the wall normal are, for example, the x-direction, y-direction, and z-direction components shown in Figure 2.

[0030] Figure 4 shows the influence range of a particle. For example, the influence range for particle 102 shown in Figure 4 is set as the distance h, which is the radius of the circle centered on particle 102. In the SPH method, a liquid is represented as a collection of many particles as shown in Figure 4.

[0031] Figure 5 shows the information used to represent particles. Each particle of the molten metal 10 has the information shown as liquid particle data in Table 111 of Figure 5. Specifically, the particles of the molten metal 10 are represented by position x component, position y component, position z component, velocity x component, velocity y component, velocity z component, acceleration x component, acceleration y component, acceleration z component, mass, particle diameter, density, density change, and force. Since wall particles are also represented as particles, they have the same information as the particles of the molten metal 10 as shown in Table 112. Hereafter, this information representing the particles of the molten metal 10 and wall particles will be collectively referred to as "data".

[0032] Returning to Figure 1, the explanation continues. The provisional acceleration calculation unit 12 calculates the provisional acceleration and density change of each particle in the molten metal 10 using the SPH method, as follows. Here, the particle in question is referred to as the "target particle." The provisional acceleration calculation unit 12 searches for particles that fall within the influence range of the parameters from the data of the target particle in the molten metal 10. Next, the provisional acceleration calculation unit 12 calculates the provisional acceleration and density change of the target particle using the position, velocity, and density of the target particle in the molten metal 10, and the parameters of liquid density, sound velocity, and gravity.

[0033] Next, the provisional acceleration calculation unit 12 calculates the provisional acceleration and density change of the wall particles. Figure 6 is a schematic diagram showing molten metal particles and wall particles. As shown in Figure 6, the wall particles 121 are arranged in a line to represent the wall, while the molten metal 10 particles 122 are arranged irregularly because they are liquid. The provisional acceleration calculation unit 12 uses the data of the particles 122 and wall particles 121 to search for wall particles 121 that are within the influence radius h of the corresponding particle 122. Then, for the wall particles 121 that are within the influence radius h of the corresponding particle, the provisional acceleration calculation unit 12 uses the SPH method with the data of the wall particles 121 to calculate the acceleration and density change given from the wall to the molten metal 10 particles 122. This calculation is the same as the calculation performed for each particle of the molten metal 10.

[0034] Furthermore, after the initial step of the simulation, the provisional acceleration calculation unit 12 calculates the provisional acceleration of each particle of the molten metal 10 using updated information on the position, velocity, and density of each particle of the molten metal 10, as well as the position and velocity of the wall particles. Similarly, the provisional acceleration calculation unit 12 calculates the acceleration given to the particles 122 of the molten metal 10 from the wall using updated information on the position, velocity, and density of each particle of the molten metal 10, as well as the position and velocity of the wall particles.

[0035] Here, the provisional acceleration of each particle of the molten metal 10 calculated by the provisional acceleration calculation unit 12 is an example of the "first acceleration." That is, the provisional acceleration calculation unit 12 calculates the first acceleration of the particles using the SPH method. More specifically, the provisional acceleration calculation unit 12 calculates the first acceleration using the SPH method based on the calculation condition information. Furthermore, the acceleration given to the particles 122 of the molten metal 10 from the wall surface, calculated by the provisional acceleration calculation unit 12, is an example of the "fourth acceleration." That is, the provisional acceleration calculation unit 12 calculates the fourth acceleration of the particles using the SPH method based on the information of the particles of the molten metal 10 and the information of wall surface particles representing the wall surface that pressurizes the fluid. Furthermore, the density change amount of each particle of the molten metal 10 calculated by the provisional acceleration calculation unit 12 is an example of the "first density change amount." That is, the provisional acceleration calculation unit 12 calculates the first density change amount of the particles using the SPH method.

[0036] Also, the Mach number when using 45 (m / s) for calculation as the speed of sound is an example of the "first Mach number". That is, the pseudo-acceleration calculation unit 12 calculates the first acceleration using the first Mach number in the SPH method. Also, for the calculation of 10×(2gh) for calculating 45 (m / s) as the speed of sound 1 / 2 is an example of the "predetermined calculation". That is, the pseudo-acceleration calculation unit 12 uses, as the first Mach number, the Mach number calculated by a predetermined calculation in which the speed of sound for a fluid given a gravitational acceleration is set to a value smaller than the physical property value of the fluid.

[0037] The calculated pressure increase amount calculation unit 13 receives the input of calculation conditions from the calculation condition acquisition unit 11. Also, the calculated pressure increase amount calculation unit 13 receives the input of information on the speed of sound used in the calculation of the pseudo-acceleration by the SPH method from the pseudo-acceleration calculation unit 12. Then, the calculated pressure increase amount calculation unit 13 calculates a calculated pressure increase amount obtained by adding a correction according to the speed of sound used in the calculation of the pseudo-acceleration by the SPH method, that is, a correction according to the speed of sound of the physical property value of the molten metal 10, to the pressure increase amount of the pressure Pe, and outputs the calculated calculated pressure increase amount to the acceleration calculation unit 16.

[0038] Here, a problem when using the same speed of sound as in the case without the pressure Pe in a state where the pressure Pe is applied will be described. When there is no pressure Pe, for example, if the height of the molten metal 10 is h (m) and the gravitational acceleration G is g (m / s 2 )), the speed of sound is Cs_c = 10×(2gh) 1 / 2 and is determined.

[0039] Expressing the density as ρ and the pressure increase amount of the pressure Pe as Pe, the characteristic velocity Vp of the molten metal 10 calculated from the pressure increase of the pressure Pe is Vp = (2Pe / ρ) 1 / 2 and is calculated. The characteristic velocity of the molten metal 10 is a velocity representing the overall velocity of the molten metal 10. That is, when the pressure increase amount of the pressure Pe is 1 M(Pa), the characteristic velocity of the molten metal 10 due to the pressure Pe is 2 1 / 2×100 = approximately 44 (m / s). In this case, the Mach number of the driving force due to the pressurization of pressure Pe and the speed of sound used in the calculation becomes 1.0, and the molten metal 10 is compressed by about 50% due to the effect of the pressurization, making accurate calculation difficult.

[0040] Here, it is possible to perform the SPH method calculation using the sound velocity based on the physical properties of the molten metal 10 as is, but as mentioned above, the number of steps for calculating the position and velocity of the particles increases overall. This results in an increase in the computational load in the simulation, a longer time to complete the simulation, and an increase in cost. Therefore, in this embodiment, the calculated pressure amount calculation unit 13 calculates a calculated pressure amount by adding a correction to the pressure amount Pe based on the sound velocity of the physical properties of the molten metal 10, and this calculated pressure amount is used in the simulation.

[0041] More specifically, the calculated pressure amount calculation unit 13 uses the speed of sound, a physical property of the molten metal 10, to calculate the Mach number resulting from the pressurization of pressure Pe. Then, the calculated pressure amount calculation unit 13 corrects the amount of pressurization Pe so that the calculated Mach number is satisfied for the speed of sound used in the calculation of the provisional acceleration by the SPH method. This corrected Mach number is an example of the "second Mach number".

[0042] For example, if the height of the molten metal 10 is 1 m and the density ρ of the liquid is 1000 kg / m³ 3 ) and the acceleration due to gravity G is 9.8 (m / s²). 2 Next, we will explain the case where the sound velocity Cs of the molten metal 10 is 1470 (m / s). In this case, the sound velocity Cs used to calculate the provisional acceleration by the SPH method is 45 (m / s).

[0043] In this case, when pressure Pe is applied at a pressurization amount of 1 M (Pa), the calculated pressurization amount calculation unit 13 calculates the calculated pressurization amount as follows: The calculated pressurization amount calculation unit 13 calculates the characteristic velocity Vp due to a pressurization amount of 1 M (Pa) by pressure Pe as Vp = (2 × Pe / ρ) = 44.7. Next, the calculated pressurization amount calculation unit 13 calculates the actual Mach number Mc as Mc = Vp / Cs = 0.03. Next, the calculated pressurization amount calculation unit 13 calculates the characteristic velocity Vcp of the molten metal 10 due to the pressurization amount used in the calculation as Vcp = Cs_c × 0.03 = 1.37. Then, the calculated pressurization amount calculation unit 13 calculates the calculated pressurization amount Pec as Pec = ρ / 2 × Vcp 2 It can be calculated as =937.

[0044] In this way, the calculated pressurization amount calculation unit 13 calculates the calculated pressurization amount to be used in the calculation using the fluid's physical properties and pressurization amount included in the calculation condition information. More specifically, the calculated pressurization amount calculation unit 13 calculates the fluid's velocity based on the pressurization amount, and calculates the fluid's Mach number based on the fluid's physical properties, namely the speed of sound and the calculated fluid velocity. Then, the calculated pressurization amount calculation unit 13 corrects the first Mach number based on the calculated Mach number to calculate the second Mach number, and calculates the calculated pressurization amount based on the second Mach number.

[0045] The acceleration calculation unit 16 receives input from the provisional acceleration calculation unit 12 of the provisional acceleration and density change of the particles of the molten metal 10, as well as the acceleration and density change applied to each particle of the molten metal 10 from the wall surface. The acceleration calculation unit 16 also receives input of the calculated pressure amount from the calculated pressure amount calculation unit 13.

[0046] Figure 7 is a diagram illustrating the calculation of the wall surface acceleration. The acceleration calculation unit 16 calculates the acceleration and density change of each particle 122 of the molten metal 10, taking into account the amount of pressure, by adding the acceleration and density change of the particles 122 of the molten metal 10 to the acceleration and density change of the particles 122 of the molten metal 10 that are applied to each particle of the molten metal 10 from the wall surface. In this way, the acceleration calculation unit 16 can calculate the acceleration and density change of each particle of the molten metal 10, taking into account the pressure applied by the wall surface.

[0047] The acceleration of each particle 122 of the molten metal 10 calculated by the acceleration calculation unit 16 is an example of the "second acceleration." That is, the second acceleration is calculated by adding the fourth acceleration to the first acceleration.

[0048] Furthermore, the acceleration calculation unit 16 calculates the force exerted by the wall particles 121 from the acceleration and density change of the wall particles 121, and adds the calculated pressurization amount to calculate the pressurization force P1.

[0049] Next, the acceleration calculation unit 16 calculates the resultant force from the molten metal 10 on the wall surface as follows. The acceleration calculation unit 16 searches for particles 122 that are within the influence radius h of the wall surface particles 121. Then, for the particles 122 that are within the influence radius h of the relevant particles, the acceleration calculation unit 16 calculates the acceleration and density change using the SPH method, using the density, mass, and area of ​​the wall surface, as well as the data of the wall surface particles 121. Furthermore, the acceleration calculation unit 16 calculates the force exerted from the particles 122 of the molten metal 10 on the wall surface particles 121 from the acceleration and density change of the particles 122 of the molten metal 10. In this way, the acceleration calculation unit 16 calculates the force exerted from the particles on the wall surface particles using information on the particles of the molten metal 10 and the information on the distant particles.

[0050] Next, the acceleration calculation unit 16 calculates the resultant force obtained by summing the forces acting on the wall particles 121 from the particles 122, and determines the resultant force P2 from the particles 122 of the molten metal 10. Then, the acceleration calculation unit 16 calculates the acceleration of the wall by dividing the sum of the force P1 due to pressurization and the resultant force P2 from the particles 122 of the molten metal 10 by the mass of the wall.

[0051] Returning to Figure 1, the explanation continues. The acceleration calculation unit 16 calculates the acceleration of the wall particles from the calculated acceleration of the wall surface. The acceleration calculation unit 16 then outputs the acceleration and actual change in each particle of the molten metal 10, as well as the acceleration of each wall particle, to the position velocity update unit 15.

[0052] The acceleration of the wall particles calculated by the acceleration calculation unit 16 is an example of the "third acceleration." That is, the acceleration calculation unit 16 calculates the second acceleration of the particles of the molten metal 10 and the third acceleration of the wall particles representing the wall surface based on the calculated pressure and the first acceleration. More specifically, the acceleration calculation unit 16 calculates the third acceleration based on the calculated pressure and the force applied to the wall particles from each particle of the molten metal 10. Furthermore, the acceleration calculation unit 16 calculates the second density change of the particles of the molten metal 10 and the third density change of the wall particles based on the calculated pressure and the first density change.

[0053] The position-velocity update unit 15 receives input from the acceleration calculation unit 16, including the acceleration and density change of each particle of the molten metal 10, as well as the acceleration of each wall particle. Next, the position-velocity update unit 15 calculates and updates the position, velocity, and density of each particle at the next time from the acceleration and density change of each particle of the molten metal 10. The position-velocity update unit 15 also calculates and updates the position and velocity of each wall particle at the next time from the acceleration of each wall particle. After that, the position-velocity update unit 15 outputs information on the position, velocity, and density of each particle of the molten metal 10, as well as the position and velocity of the wall particles at the next time, to the acceleration calculation unit 16 and the output unit 14.

[0054] In other words, the position and velocity update unit 15 updates the position and velocity of the particles and wall particles of the molten metal 10 based on the second acceleration and the third acceleration. The position and velocity update unit 15 also updates the position and velocity of the particles and wall particles of the molten metal 10 based on the second acceleration and the third acceleration, as well as the second density change and the third density change.

[0055] The output unit 14 obtains information from the position-velocity update unit 15 regarding the position, velocity, and density of each particle in the molten metal 10, as well as the position and velocity of the wall particles, for the following time. The output unit 14 then stores the information regarding the position, velocity, and density of each particle in the molten metal 10, as well as the position and velocity of the wall particles, for the following time.

[0056] Subsequently, the output unit 14 generates simulation results using the information on the position, velocity, and density of each particle of the molten metal 10, as well as the position and velocity of the wall particles, and transmits the generated simulation results to the user terminal device 2 for the user to use.

[0057] Figure 8 is a flowchart of the simulation process performed by the simulation device according to the embodiment. Next, the flow of the simulation process performed by the simulation device 1 according to the embodiment will be explained with reference to Figure 8.

[0058] At the start of the calculation, the acceleration calculation unit 16 acquires the calculation conditions to be used for the simulation, which are transmitted from the user terminal device 2 and received by the user via the calculation condition acquisition unit 11. After the calculation has started, the acceleration calculation unit 16 acquires information on the position, velocity, and density of each particle in the molten metal 10, as well as the position and velocity of wall particles, at the following time points from the position and velocity update unit 15 as calculation conditions (step S1).

[0059] The provisional acceleration calculation unit 12 calculates the provisional acceleration and density change of each particle of the molten metal 10 in the absence of pressurization using the SPH method based on the particle data of the molten metal 10 (step S2).

[0060] Next, the provisional acceleration calculation unit 12 searches for wall particles 121 that are within the influence radius h of the molten metal particles 10, using data on the particles and wall particles of the molten metal 10. Then, for the wall particles 121 that are within the influence radius h of the relevant particles, the provisional acceleration calculation unit 12 calculates the provisional acceleration and density change using the SPH method with data on the wall particles 121 (step S3).

[0061] Next, the calculated pressurization amount calculation unit 13 determines whether the calculated pressurization amount has already been calculated (step S4). If the calculated pressurization amount has already been calculated (step S4: affirmative), the simulation process proceeds to step S6.

[0062] In contrast, if the calculated pressurization amount has not been calculated (step S4: negation), the calculated pressurization amount calculation unit 13 calculates the Mach number due to the pressurization of pressure Pe using the sound velocity value of the physical properties of the molten metal 10. Then, the calculated pressurization amount calculation unit 13 corrects the pressurization amount Pe so that the calculated Mach number is satisfied for the sound velocity used in calculating the provisional acceleration by the SPH method, and calculates the calculated pressurization amount (step S5).

[0063] The acceleration calculation unit 16 calculates the acceleration and density change of each particle of the molten metal 10, taking into account the amount of pressurization, by adding the acceleration and density change of the wall particles to the acceleration and density change of the particles of the molten metal 10. Furthermore, the acceleration calculation unit 16 calculates the force exerted by the wall particles from the acceleration and density change of the wall particles and adds the calculated amount of pressurization to calculate the force due to the pressurization. Next, the acceleration calculation unit 16 searches for particles within the influence radius h of the relevant particle among the wall particles. Then, for the particles within the influence radius h of the relevant particle, the acceleration calculation unit 16 calculates the acceleration and density change using the SPH method, using the density, mass, and area of ​​the wall, as well as the data of the wall particles. Furthermore, the acceleration calculation unit 16 calculates the force exerted by the particles of the molten metal 10 on the wall particles from the acceleration and density change of the particles of the molten metal 10. Next, the acceleration calculation unit 16 calculates the resultant force from the particles 122 to the wall particles 121 by summing the forces across all wall particles (step S6).

[0064] Next, the acceleration calculation unit 16 calculates the acceleration of the wall particles by adding the force due to the pressurization and the resultant force from the particles of the molten metal 10 to the wall mass (step S7).

[0065] The position-velocity update unit 15 calculates and updates the position, velocity, and density of each particle in the molten metal 10 at the next time, based on the acceleration and density change of each particle. The position-velocity update unit 15 also calculates and updates the position and velocity of each wall particle at the next time, based on the acceleration of each wall particle (step S8).

[0066] Subsequently, the position and velocity update unit 15 determines whether or not to terminate the simulation (step S9). If the simulation is not terminated (step S9: negative), the simulation process returns to step S1. Conversely, if the simulation is terminated (step S9: positive), the simulation device 1 terminates the simulation process.

[0067] In this manner, the simulation device 1 repeatedly performs the calculation of the first acceleration, the calculation of the calculated pressure, the calculation of the second and third accelerations, and the update process based on the updated position and velocity of each particle in the molten metal 10.

[0068] As described above, the simulation apparatus 1 according to this embodiment corrects the amount of pressurization using the sound velocity of the physical properties of the molten metal 10 and the sound velocity for calculation, and performs a simulation using the SPH method by calculating the acceleration and density change of the particles using the corrected amount of pressurization. This makes it possible to perform a simulation that accurately reflects the pressurization conditions while suppressing the increase in the number of steps, and to improve the calculation accuracy of the simulation while maintaining the speed.

[0069] (Hardware configuration) Figure 9 is a hardware configuration diagram of the simulation device. Next, with reference to Figure 9, an example of a hardware configuration for realizing each function of the simulation device 1 will be described.

[0070] As shown in Figure 9, the simulation device 1 includes, for example, a CPU (Central Processing Unit) 91, memory 92, a hard disk 93, and a communication interface 94. The CPU 91 is connected to the memory 92, hard disk 93, and communication interface 94 via a bus.

[0071] The communication interface 94 is an interface for communication between the simulation device 1 and an external device. For example, the communication interface 94 relays communication between the user terminal device 2 and the CPU 91.

[0072] The hard disk 93 is an auxiliary storage device. The hard disk 93 stores various programs, including programs for realizing the functions of the calculation condition acquisition unit 11, provisional acceleration calculation unit 12, calculated pressure amount calculation unit 13, output unit 14, position velocity 15 degree update unit, and acceleration calculation unit 16, as illustrated in Figure 1.

[0073] Memory 92 is the main memory. Memory 92 can be, for example, DRAM (Dynamic Random Access Memory).

[0074] The CPU 91 reads various programs from the hard disk 93, loads them into memory 92, and executes them. As a result, the CPU 91 implements the functions of the calculation condition acquisition unit 11, provisional acceleration calculation unit 12, calculated pressure amount calculation unit 13, output unit 14, position velocity 15 degree update unit, and acceleration calculation unit 16, as illustrated in Figure 2. [Explanation of Symbols]

[0075] 1. Simulation device 2. User terminal device 11 Calculation condition acquisition part 12 Provisional acceleration calculation unit 13. Calculation unit for calculating the amount of pressure 14 Output section 15 Position speed update section 16 Acceleration calculation unit

Claims

1. For each particle representing the fluid pressurized by the wall, The first acceleration of the particle is calculated by the SPH method. Based on the physical properties and pressurization amount of the aforementioned fluid, the calculated pressurization amount to be used in the calculation is determined. Based on the calculated pressurization amount and the first acceleration, the second acceleration of the particle and the third acceleration of the wall particle representing the wall surface are calculated. Based on the second and third accelerations, the positions and velocities of the particles and the wall particles are updated. A simulation program characterized by having a computer perform the processing.

2. The calculation process for the first acceleration is as follows: Information on calculation conditions, including the height and physical properties of the fluid, gravity, pressurization amount, and the position and velocity of each particle contained in the fluid, is obtained. The process includes calculating the first acceleration using the SPH method based on the information of the calculation conditions, The calculation process for the calculated pressure amount includes a process of calculating the calculated pressure amount using the physical properties of the fluid and the pressure amount included in the calculation condition information. The simulation program according to feature 1.

3. The calculation process for the second acceleration and the third acceleration is as follows: Based on the information of the aforementioned particles and the information of the wall particles representing the wall surface, the fourth acceleration of the wall particles is calculated by the SPH method. The second acceleration is calculated by adding the fourth acceleration to the first acceleration. Using the information of the aforementioned particles and the information of the aforementioned wall particles, the force exerted by the aforementioned particles on the wall particles is calculated. Based on the calculated pressure and the force applied from the particles to the wall particles, the third acceleration is calculated. The simulation program according to claim 1, characterized by including processing.

4. The calculation process for the first acceleration includes a process for calculating the first acceleration using the first Mach number in the SPH method. The calculation process for the calculated pressure amount is as follows: The velocity of the fluid is calculated based on the amount of pressure, Based on the sound velocity of the fluid's physical properties and the calculated fluid velocity, the Mach number of the fluid is calculated. Based on the Mach number calculated above, the first Mach number is corrected to calculate the second Mach number. Based on the second Mach number, the calculated pressurization amount is calculated. The simulation program according to claim 1, characterized by including processing.

5. The simulation program according to claim 4, characterized in that the calculation process for the first acceleration includes a process in which the Mach number obtained by a predetermined calculation in which the speed of sound is smaller than the physical property value of the fluid, for a fluid given gravitational acceleration, is used as the first Mach number.

6. The simulation program according to claim 1, characterized in that the computer is further instructed to perform the following processes based on the updated position and velocity of the particles: the calculation of the first acceleration, the calculation of the calculated pressurization amount, the calculation of the second acceleration and the third acceleration, and the update process, and repeats these processes.

7. The simulation program according to claim 1, characterized in that the fluid is molten metal that has been injected into a mold and pressurized.

8. The calculation process for the first acceleration includes a process for calculating the first density change, The process for calculating the second acceleration and the third acceleration includes a process for calculating the second density change of the particles and the third density change of the wall particles based on the calculated pressurization amount and the first density change, The update process includes updating the position and velocity of the particles and wall particles based on the second acceleration and the third acceleration, as well as the second density change and the third density change. The simulation program according to feature 1.

9. The simulation device, For each particle representing the fluid pressurized by the wall, The first acceleration of the particle is calculated by the SPH method. Based on the physical properties and pressurization amount of the aforementioned fluid, the calculated pressurization amount to be used in the calculation is determined. Based on the calculated pressurization amount and the first acceleration, the second acceleration of the particle and the third acceleration of the wall particle representing the wall surface are calculated. Based on the second and third accelerations, the positions and velocities of the particles and the wall particles are updated. A simulation method characterized by performing a process.

10. A simulation device that performs simulations for each particle representing a fluid pressurized by a wall surface, A provisional acceleration calculation unit that calculates the first acceleration of the particle by the SPH method, A calculation pressure amount calculation unit calculates the calculated pressure amount used in the calculation based on the physical properties and pressure of the fluid, Based on the calculated pressurization amount and the first acceleration, an acceleration calculation unit is provided which calculates the second acceleration of the particle and the third acceleration of the wall surface particle representing the wall surface. A position and velocity updating unit updates the position and velocity of the particles and the wall particles based on the second and third accelerations. A simulation device characterized by having the following features.

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