解决复杂问题的不同数值技术、建模和仿真

Seng-Phil Hong
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引用次数: 2

摘要

本研究探讨不同数值技术、建模和模拟在解决复杂问题中的表现。研究发现,有限元法是模拟结构在载荷条件下行为的最精确的数值方法,有限差分法是模拟流体流动和传热问题的最有效的数值技术,边界元法是解决涉及奇点的问题的最有效的数值技术,如声学和电磁学中的问题。本研究建立的数学模型能够有效预测系统在不同条件下的行为,误差小于5%。本研究建立的物理模型能够复制系统在不同条件下的行为,误差小于2%。采用多物理场或多尺度模拟可以有效地克服传统数值方法的局限性。本研究结果对数值技术、建模和仿真领域具有重要影响,可用于指导工程师和研究人员针对其具体问题或应用选择最合适的数值技术。
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Different Numerical Techniques, Modeling and Simulation in Solving Complex Problems
This study investigates the performance of different numerical techniques, modeling, and simulation in solving complex problems. The study found that the Finite Element Method was found to be the most precise numerical approach for simulating the behavior of structures under loading conditions, the Finite Difference Method was found to be the most efficient numerical technique for simulating fluid flow and heat transfer problems, and the Boundary Element Method was found to be the most effective numerical technique for solving problems involving singularities, such as those found in acoustics and electromagnetics. The mathematical model established in this research was able to effectively forecast the behaviors of the system under different conditions, with an error of less than 5%. The physical model established in this research was able to replicate the behavior of the system under different conditions, with an error of less than 2%. The employment of multi-physics or multi-scale modeling was found to be effective in overcoming the limitations of traditional numerical techniques. The results of this research have significant effects for the field of numerical techniques, modeling and simulation, and can be used to guide engineers and researchers in choosing the most appropriate numerical technique for their specific problem or application.
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