Numerical computation of preimage domains for spiral slit regions and simulation of flow around bodies

Kang Wu; Yibin Lu; Kang Wu; Yibin Lu

doi:10.3934/mbe.2023033

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 1: 720-736. doi: 10.3934/mbe.2023033

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Research article

Numerical computation of preimage domains for spiral slit regions and simulation of flow around bodies

Kang Wu ,
Yibin Lu ^,

Faculty of Science, Kunming University of Science and Technology, Kunming, Yunnan 650500, China

Received: 17 August 2022 Revised: 25 September 2022 Accepted: 07 October 2022 Published: 13 October 2022

In this paper, we propose the iterative numerical methods to calculate the conformal preimage domains for the specified logarithmic spiral slit regions and develop the applications of conformal mappings in the simulations of the flow around bodies. Firstly, we postulate that the boundaries of the preimage domains mapped onto logarithmic spiral slits are ellipses. The lengths of the long axes of ellipses and the coordinates of the centers are calculated using our iterative methods. Secondly, each type of the presented iterative method calculates numerical conformal mappings via solving the boundary integral equation with the generalized Neumann kernel. Finally, numerical examples show the convergence and availability of our iterative methods and display the simulations of the flow around the bodies as an application.
- Numerical Conformal Mapping,
- Logarithmic Spiral Slit Region,
- Generalized Neumann Kernel,
- Preimage Domain,
- Flow Around Bodies
Citation: Kang Wu, Yibin Lu. Numerical computation of preimage domains for spiral slit regions and simulation of flow around bodies[J]. Mathematical Biosciences and Engineering, 2023, 20(1): 720-736. doi: 10.3934/mbe.2023033

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Abstract

In this paper, we propose the iterative numerical methods to calculate the conformal preimage domains for the specified logarithmic spiral slit regions and develop the applications of conformal mappings in the simulations of the flow around bodies. Firstly, we postulate that the boundaries of the preimage domains mapped onto logarithmic spiral slits are ellipses. The lengths of the long axes of ellipses and the coordinates of the centers are calculated using our iterative methods. Secondly, each type of the presented iterative method calculates numerical conformal mappings via solving the boundary integral equation with the generalized Neumann kernel. Finally, numerical examples show the convergence and availability of our iterative methods and display the simulations of the flow around the bodies as an application.

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