Two-Dimensional Ideal Fluid Dynamics and Flow Around a Circular Cylinder Based on Complex Variable Analysis
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Two-Dimensional Ideal Fluid Dynamics and Flow Around a Circular Cylinder Based on Complex Variable Analysis

Xiaohui Zhong 1*
1 Urumqi Bayi High School International Department
*Corresponding author: 18099115880@outlook.com
Published on 2 October 2025
Journal Cover
TNS Vol.143
ISSN (Print): 2753-8826
ISSN (Online): 2753-8818
ISBN (Print): 978-1-80590-407-6
ISBN (Online): 978-1-80590-408-3
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Abstract

The paper mainly studies how to apply complex variable analysis to practical problems related to a two-dimensional ideal fluid. The author’s purpose is to provide a mathematical and physical method to optimize and facilitate industries related to fluid mechanics, such as oceanography, civil engineering, the aircraft wing manufacturing field, and so on. The main mathematical methodology is complex potential, and the main physical condition is the theorem and definition of the two-dimensional ideal fluid. The result of the study is that the use of complex variable analysis is significantly effective, and the processes of the calculation are much easier for this reason. The calculation process can prove the practicability. In this paper, the author combines mathematical derivation with methods of application, and the author also combines physical definitions and physical properties applied in the paper, clearly demonstrating the method of how complex potential works in practical problems. In conclusion, complex variable analysis can be used in many different fields related to physics, and it can facilitate the development of engineering and reduce the possibility of making mistakes in calculations, making resolutions precise and lowering the cost of the processes.

Keywords:

Two-Dimensional Ideal Fluid, Complex Variable, Complex Potential, Mathematical Physics, Cylinder

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Zhong,X. (2025). Two-Dimensional Ideal Fluid Dynamics and Flow Around a Circular Cylinder Based on Complex Variable Analysis. Theoretical and Natural Science,143,57-69.

References

[1]. Rajeev, S. G. (2009). Geometry of the Motion of Ideal Fluids and Rigid Bodies.

[2]. Perezhgin, P. A., & Dymnikov, V. P. (2017). Modeling of quasi-equilibrium states of a two-dimensional ideal fluid.

[3]. Hairil Anwar, W. S. (2016). Two-dimensional steady flow modeling of ideal fluid in porous medium using finite element method. Journal of Hydrology or related field, Volume (Issue), Page Range.

[4]. Amosova, E. V., & Ozerova, G. P. (2020). Visualization of two-dimensional flows of an ideal fluid by computer technology. Journal Name or Publication, Volume (Issue), Page Range.

[5]. Olver, P. J. (2024). Complex Analysis and Conformal Mapping. Journal Name or Publication, Volume (Issue), Page Range.

[6]. Lacave, C. (2011). Two-dimensional incompressible ideal flow around a small curve. Communications in Partial Differential Equations, 37(4), 690–731.

[7]. Kundu, P. K., & Cohen, I. M. (2007). Fluid Mechanics. Academic Press.

[8]. Wang, Z. (2004). On the methodology of fluid mechanics. Mechanics and Practice, 26(2), 83-84.

[9]. Hildebrand, F. B. (1964). Advanced Calculus for Applications. Prentice-Hall, Inc.

[10]. King, A. C., Billingham, J., & Otto, S. R. (2003). Differential equations: Linear, nonlinear, ordinary, partial.

[11]. Lamb, S. H. (1879). A treatise on the mathematical theory of the motion of fluids. University Press.

[12]. Polya, G., & Latta, G. (1974). Complex variables.

[13]. Munson, B. R., Huebsch, W. W., & Rothmayer, A. P. (2013). Fundamentals of Fluid Mechanics (7th ed.). John Wiley & Sons.

References

[1]. Rajeev, S. G. (2009). Geometry of the Motion of Ideal Fluids and Rigid Bodies.

[2]. Perezhgin, P. A., & Dymnikov, V. P. (2017). Modeling of quasi-equilibrium states of a two-dimensional ideal fluid.

[3]. Hairil Anwar, W. S. (2016). Two-dimensional steady flow modeling of ideal fluid in porous medium using finite element method. Journal of Hydrology or related field, Volume (Issue), Page Range.

[4]. Amosova, E. V., & Ozerova, G. P. (2020). Visualization of two-dimensional flows of an ideal fluid by computer technology. Journal Name or Publication, Volume (Issue), Page Range.

[5]. Olver, P. J. (2024). Complex Analysis and Conformal Mapping. Journal Name or Publication, Volume (Issue), Page Range.

[6]. Lacave, C. (2011). Two-dimensional incompressible ideal flow around a small curve. Communications in Partial Differential Equations, 37(4), 690–731.

[7]. Kundu, P. K., & Cohen, I. M. (2007). Fluid Mechanics. Academic Press.

[8]. Wang, Z. (2004). On the methodology of fluid mechanics. Mechanics and Practice, 26(2), 83-84.

[9]. Hildebrand, F. B. (1964). Advanced Calculus for Applications. Prentice-Hall, Inc.

[10]. King, A. C., Billingham, J., & Otto, S. R. (2003). Differential equations: Linear, nonlinear, ordinary, partial.

[11]. Lamb, S. H. (1879). A treatise on the mathematical theory of the motion of fluids. University Press.

[12]. Polya, G., & Latta, G. (1974). Complex variables.

[13]. Munson, B. R., Huebsch, W. W., & Rothmayer, A. P. (2013). Fundamentals of Fluid Mechanics (7th ed.). John Wiley & Sons.

Cite this article

Zhong,X. (2025). Two-Dimensional Ideal Fluid Dynamics and Flow Around a Circular Cylinder Based on Complex Variable Analysis. Theoretical and Natural Science,143,57-69.

Data availability

The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.

About volume

Volume title: Proceedings of CONF-CIAP 2026 Symposium: International Conference on Atomic Magnetometer and Applications

ISBN: 978-1-80590-407-6(Print) / 978-1-80590-408-3(Online)
Editor: Marwan Omar , Jixi Lu , Mao Ye
Conference website: https://2026.confciap.org/hangzhou.html
Conference date: 30 January 2026
Series: Theoretical and Natural Science
Volume number: Vol.143
ISSN: 2753-8818(Print) / 2753-8826(Online)

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