A boundary integral equation method for the fluid-solid interaction problem

Yao Sun; Pan Wang; Xinru Lu; Bo Chen; Yao Sun; Pan Wang; Xinru Lu; Bo Chen

doi:10.3934/cam.2023035

Communications in Analysis and Mechanics

2023, Volume 15, Issue 4: 716-742. doi: 10.3934/cam.2023035

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A boundary integral equation method for the fluid-solid interaction problem

College of Science, Civil Aviation University of China, Tianjin, 300300, China

Received: 23 August 2023 Revised: 17 October 2023 Accepted: 18 October 2023 Published: 31 October 2023
35P25, 45A05, 74F10

In this paper, a boundary integral equation method is proposed for the fluid-solid interaction scattering problem, and a high-precision numerical method is developed. More specifically, by introducing the Helmholtz decomposition, the corresponding problem is transformed into a coupled boundary value problem for the Helmholtz equation. Based on the integral equation method, the coupled value problem is reduced to a system of three coupled hypersingular integral equations. Semi-discrete and fully-discrete collocation methods are proposed for the singular integral equations. The presented method is based on trigonometric interpolation and discretized singular operators applied to differentiated interpolation. The convergence of the method is verified by a numerical experiment.
- Fluid-solid interaction problem,
- singular operator,
- boundary integral equation method,
- collocation method
Citation: Yao Sun, Pan Wang, Xinru Lu, Bo Chen. A boundary integral equation method for the fluid-solid interaction problem[J]. Communications in Analysis and Mechanics, 2023, 15(4): 716-742. doi: 10.3934/cam.2023035

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Abstract

In this paper, a boundary integral equation method is proposed for the fluid-solid interaction scattering problem, and a high-precision numerical method is developed. More specifically, by introducing the Helmholtz decomposition, the corresponding problem is transformed into a coupled boundary value problem for the Helmholtz equation. Based on the integral equation method, the coupled value problem is reduced to a system of three coupled hypersingular integral equations. Semi-discrete and fully-discrete collocation methods are proposed for the singular integral equations. The presented method is based on trigonometric interpolation and discretized singular operators applied to differentiated interpolation. The convergence of the method is verified by a numerical experiment.

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