KR-20260065385-A - METHOD FOR SOLVING SOLUTION OF POISSON EQUATIONS FOR URBAN FLOW SIMULATION, PROGRAM THEREOF, AND COMPUTING DEVICE EXECUTING THE PROGRAM

Abstract

A method for finding a solution to the Poisson equation for urban wind simulation includes the steps of: a processor receiving dominant wind direction information indicating whether the dominant wind direction of the urban wind is a first wind direction or a second wind direction; the processor performing either a Fast Fourier Transform or a Discrete Cosine Transform to convert spatial domain X-direction information included in a three-dimensional matrix of the Laplace operator of the Poisson equation in the spatial domain into frequency domain X-direction information according to the dominant wind direction information; and the processor performing the other of the Fast Fourier Transform or the Discrete Cosine Transform to convert spatial domain Y-direction information included in the three-dimensional matrix of the Laplace operator into frequency domain Y-direction information according to the dominant wind direction information.

Inventors

• 최정일
• 양민규
• 김정우
• 오근우
• 강지훈

Assignees

• 연세대학교 산학협력단
• 한국과학기술정보연구원

Dates

Publication Date

20260508

Application Date

20241101

Claims (19)

1. In a method for finding the solution to the Poisson equation for urban wind simulation, A step in which a processor receives main wind direction information indicating whether the main wind direction of the urban wind is the first wind direction or the second wind direction; The processor performs either the Fast Fourier Transform or the Discrete Cosine Transform to convert spatial domain X-direction information contained in the three-dimensional matrix of the Laplace operator of the Poisson equation in the spatial domain into frequency domain X-direction information according to the prevailing wind direction information; and The processor comprises the step of performing the other of the Fast Fourier Transform and the Discrete Cosine Transform to convert spatial domain Y-direction information included in the Laplace operator 3D matrix into frequency domain Y-direction information according to the main wind direction information. A method for finding the solution to the Poisson equation for urban wind simulation.
2. In paragraph 1, In the step of performing either the Fast Fourier Transform or the Discrete Cosine Transform, When the above-mentioned main wind direction information represents the first wind direction, the processor performs the Fast Fourier Transform, and When the above main wind direction information represents the above second wind direction, the processor performs the above discrete cosine transform, A method for finding the solution to the Poisson equation for urban wind simulation.
3. In paragraph 2, In the step of performing the other of the above Fast Fourier Transform and the above Discrete Cosine Transform, When the above-mentioned main wind direction information represents the above-mentioned first wind direction, the processor performs the above-mentioned discrete cosine, and When the above main wind direction information represents the above second wind direction, the processor performs the above Fast Fourier Transform, A method for finding the solution to the Poisson equation for urban wind simulation.
4. In paragraph 1, The processor performs either an inverse fast Fourier transform or an inverse discrete cosine transform to convert frequency domain X-direction pressure information included in a pressure information matrix representing the solution of the Poisson equation into spatial domain X-direction pressure information according to the prevailing wind direction information; and The processor further includes the step of performing the other of the inverse fast Fourier transform and the inverse discrete cosine transform to convert the frequency domain Y-direction pressure information included in the pressure information matrix into spatial domain Y-direction pressure information according to the main wind direction information. A method for finding the solution to the Poisson equation for urban wind simulation.
5. In paragraph 4, In the step of performing either the inverse fast Fourier transform or the inverse discrete cosine transform, When the above main wind direction information represents the first wind direction, the processor performs the inverse fast Fourier transform, and When the above main wind direction information represents the above second wind direction, the above inverse discrete cosine transform is performed, A method for finding the solution to the Poisson equation for urban wind simulation.
6. In paragraph 5, In the step of performing the other of the above inverse fast Fourier transform and inverse discrete cosine transform, When the above-mentioned main wind direction information represents the above-mentioned first wind direction, the processor performs the above-mentioned inverse discrete cosine transform, and When the above main wind direction information represents the above second wind direction, the processor performs the above inverse fast Fourier transform, A method for finding the solution to the Poisson equation for urban wind simulation.
7. In paragraph 1, The processor performs either the Fast Fourier Transform or the Discrete Cosine Transform to convert spatial domain X-direction velocity information included in the spatial domain velocity information matrix into frequency domain X-direction velocity information according to the prevailing wind direction information; and The processor further includes the step of performing the other of the Fast Fourier Transform and the Discrete Cosine Transform to convert spatial domain Y-direction velocity information included in the spatial domain velocity information matrix into frequency domain Y-direction velocity information according to the main wind direction information. A method for finding the solution to the Poisson equation for urban wind simulation.
8. In Paragraph 7, When the above-mentioned main wind direction information represents the above-mentioned first wind direction, the processor performs the above-mentioned Fast Fourier Transform to convert the above-mentioned spatial domain X-direction information into the above-mentioned frequency domain X-direction information and to convert the above-mentioned spatial domain X-direction velocity information into the above-mentioned frequency domain X-direction velocity information, and When the above-mentioned main wind direction information represents the above-mentioned second wind direction, the processor performs the discrete cosine transform to convert the above-mentioned spatial domain Y-direction information into the above-mentioned frequency domain Y-direction information and to convert the above-mentioned spatial domain Y-direction velocity information into the above-mentioned frequency domain Y-direction velocity information. A method for finding the solution to the Poisson equation for urban wind simulation.
9. In paragraph 8, The step of the processor determining wind and temperature boundary conditions for each side boundary condition into which the urban wind enters within the three-dimensional computational domain for the urban wind simulation as periodic boundary conditions; and The above processor further includes the step of determining the pressure boundary condition for each of the above side boundary conditions as the periodic boundary condition. The above processor uses the Fast Fourier Transform for the periodic boundary conditions, A method for finding the solution to the Poisson equation for urban wind simulation.
10. In paragraph 8, A step in which the processor determines wind and temperature boundary conditions for the inlet boundary condition into which the urban wind enters within the three-dimensional computational domain for the urban wind simulation using an extended synthetic vortex generation method; The step of the processor determining the wind and temperature boundary conditions for the exit boundary conditions where the urban wind flows out in the three-dimensional calculation area as convective boundary conditions; and The above processor further includes the step of determining the pressure boundary conditions for each of the inlet boundary condition and the outlet boundary condition as Neumann boundary conditions. The above processor uses the discrete cosine transform for the above Neumann boundary conditions, A method for finding the solution to the Poisson equation for urban wind simulation.
11. A recording medium storing a program that executes the method for finding the solution to the Poisson equation for urban wind simulation described in claim 1.
12. A memory device storing a program for finding the solution to the Poisson equation for urban wind simulation; and It includes a processor that executes the above program, The above processor is, A step of receiving dominant wind direction information indicating whether the dominant wind direction of the urban wind is the first wind direction or the second wind direction; According to the above-mentioned prevailing wind direction information, a step of performing either the Fast Fourier Transform or the Discrete Cosine Transform to convert spatial domain X-direction information contained in the 3D matrix of the Laplace operator of the Poisson equation in the spatial domain into frequency domain X-direction information; and According to the above-mentioned prevailing wind direction information, the step of performing the other of the above-mentioned Fast Fourier Transform and the above-mentioned Discrete Cosine Transform to convert the spatial domain Y-direction information included in the above-mentioned Laplace operator 3D matrix into frequency domain Y-direction information, Computing device.
13. In Paragraph 12, In the step of performing either the Fast Fourier Transform or the Discrete Cosine Transform, The above processor is, When the above main wind direction information represents the above first wind direction, the above Fast Fourier Transform is performed, and Performing the discrete cosine transform when the above main wind direction information represents the above second wind direction, Computing device.
14. In Paragraph 13, In the step of performing the other of the above Fast Fourier Transform and the above Discrete Cosine Transform, The above processor is, When the above-mentioned dominant wind direction information represents the above-mentioned first wind direction, the above-mentioned discrete cosine is performed, and Performing the Fast Fourier Transform when the above main wind direction information represents the above second wind direction, Computing device.
15. In Clause 12, the above processor, A step of performing either the inverse fast Fourier transform or the inverse discrete cosine transform to convert frequency domain X-direction pressure information included in a pressure information matrix representing the solution of the Poisson equation into spatial domain X-direction pressure information according to the above-mentioned prevailing wind direction information; and A step of further performing the other of the inverse fast Fourier transform and the inverse discrete cosine transform to convert the frequency domain Y-direction pressure information included in the pressure information matrix into spatial domain Y-direction pressure information according to the above-mentioned main wind direction information, Computing device.
16. In paragraph 15, In the step of performing either the inverse fast Fourier transform or the inverse discrete cosine transform, The above processor is, When the above main wind direction information represents the above first wind direction, the above inverse fast Fourier transform is performed, and Performing the inverse discrete cosine transform when the above main wind direction information represents the above second wind direction, Computing device.
17. In Paragraph 16, In the step of performing the other of the above inverse fast Fourier transform and inverse discrete cosine transform, The above processor is, When the above main wind direction information represents the above first wind direction, the above inverse discrete cosine transform is performed, and Performing the inverse fast Fourier transform when the above main wind direction information represents the above second wind direction, Computing device.
18. In Clause 12, the above processor, A step of determining wind and temperature boundary conditions as periodic boundary conditions for each side boundary condition into which the urban wind enters among the three-dimensional computational domain for the urban wind simulation; and Further performing the step of determining the pressure boundary condition for each of the above side boundary conditions as the periodic boundary condition, Using the Fast Fourier Transform for the above periodic boundary conditions, Computing device.
19. In Clause 12, the above processor, A step of determining wind and temperature boundary conditions for the inlet boundary condition where the urban wind enters within the three-dimensional computational domain for the urban wind simulation using an extended synthetic vortex generation method; A step of determining the wind and temperature boundary conditions for the outlet boundary conditions where the urban wind flows out among the above three-dimensional calculation domains as convective boundary conditions; and Further performing the step of determining the pressure boundary conditions for each of the above inlet boundary conditions and the above outlet boundary conditions as Neumann boundary conditions, and Using the discrete cosine transform for the above Neumann boundary conditions, Computing device.

Description

Method for finding a solution of Poisson equations for urban flow simulation, a program for performing said method, and a computing device for performing said program The present invention relates to a method for analyzing the Poisson equation, and more particularly to a method for obtaining the solution to the Poisson equation used in urban flow simulation at high speed and directly using the Fast Fourier Transform (FFT) and the Discrete Cosine Transform (DCT), a program for performing said method, and a computing device for performing said program. In analyzing urban flow or urban wind environments (also known as building wind or skyscraper wind), fluid analysis methods using Computational Fluid Dynamics (CFD) are widely used because they are more economical and accurate compared to observations and wind tunnel experiments; however, they have the disadvantage of requiring a long computation time. The Poisson equation, which must be considered in most computational fluid dynamics (CFD) analyses, is one of the governing equations for analyzing urban wind environments. Traditionally, solutions were converged using iterative methods such as the Jacobi method or the conjugate gradient method, but these methods require a significant amount of computation time. Jacobi methods or conjugate gradient methods, which are based on iterative solutions that take a long time to compute, may have truncation errors in their interpretation. Detailed descriptions of each drawing are provided to help to more fully understand the drawings cited in the detailed description of the present invention. FIG. 1 is a block diagram of a computing device capable of executing a program capable of calculating the solution to the Poisson equation by urban wind simulation according to an embodiment of the present invention. Figure 2 is a conceptual diagram of a three-dimensional computational domain including the prevailing wind direction and non-orthogonal boundary conditions. Figure 3 is a table showing a conversion algorithm used for converting between spatial domain information and frequency domain information according to the type determined by the prevailing wind direction. Figure 4 is a table showing wind and temperature boundary conditions and pressure boundary conditions corresponding to the type determined according to the prevailing wind direction. FIG. 5 is a conceptual diagram for explaining the operation method of the program shown in FIG. 1 when the type determined according to the prevailing wind direction is the first type and the conversion for the X direction is performed first. FIG. 6 is a conceptual diagram to explain the operation method of the program shown in FIG. 1 when the type determined according to the prevailing wind direction is the second type and the conversion for the X direction is performed first. FIG. 7 is a flowchart for explaining the operations of the computing device illustrated in FIG. 1. FIG. 8 is a conceptual diagram to explain the operation method of the program shown in FIG. 1 when the type determined according to the prevailing wind direction is the first type and the conversion for the Y direction is performed first. FIG. 9 is a conceptual diagram to explain the operation method of the program shown in FIG. 1 when the type determined according to the prevailing wind direction is the second type and the conversion for the Y direction is performed first. FIG. 1 is a block diagram of a computing device capable of executing a program capable of calculating the solution to the Poisson equation by urban wind simulation according to an embodiment of the present invention. Referring to FIG. 1, the computing device (100) includes a processor (110) that executes a program (120), an input device (130), and a memory device (140). The computing device (100) may be a PC, a laptop computer, or a server, and may be a computational fluid dynamics (CFD) simulation device that runs software (120) that simulates fluid flow and heat transfer. The processor (110) may be a Central Processing Unit (CPU) or a Graphics Processing Unit (GPU). According to embodiments, when a computing device (100) includes both a CPU and a GPU and each of the CPU and the GPU can execute a program (120), the program (120) of the CPU has an operating priority. The program (120) executed by the processor (110) may be a CDF simulator capable of calculating the solution to the Poisson equation for urban wind simulation to be described in this specification. The program (120) includes a type selection (or determination) program (121) that selects (or determines) one of a plurality of types according to the prevailing wind direction information, a transducer selection program (125) that includes a plurality of transducers (125_1, 125_2, 125_3, and 125_4), and a Poisson equation solving program (127) that finds a solution to the Poisson equation of computational fluid dynamics (CFD) and transmits the found solution to the transducer selection p