Abstract
A second order finite-difference numerical method is used to solve the Navier–Stokes equations of incompressible flow, in which the solid body with complex geometry is immersed into the fluid domain with orthogonal Cartesian meshes. To account for influences of the solid body, interactive forces are applied as boundary conditions at Cartesian grid nodes located in the exterior but in the immediate vicinity of the solid body. Fluid flow velocities in these nodes are reconstructed to track and control the deformation of the solid body, in which the local direction normal to the body surface is employed using the level-set function. The capabilities of this method are demonstrated by the application to fish swimming, and the computed behaviors of swimming fish agree well with experimental ones. The results elucidate that the ability of swimming fish to produce more thrust and high efficiency is closely related to the Reynolds number. The single reverse Kármán street tends to appear when both the Strouhal number and tail-beating frequency are small, otherwise the double-row reverse Kármán street appears. The algorithm can capture the geometry of a deformable solid body accurately, and performs well in simulating interactions between fluid flow and the deforming and moving body.
Highlights
In many scientific research and engineering applications, problems of fluid–structure interaction (FSI) are inevitably encountered, such as the aeroelastic response of airplane wings (Gao, Zhang, & Tang, 2016), vibrations of wind turbine blades (Löhner et al, 2015; Mou, He, Zhao, & Chau, 2017), blood flow through heart valves (Zakaria et al, 2017) and flow past swimming fish or flying insects (Shrivastava, Malushte, Agrawal, & Sharma, 2017)
A sharp interface Cartesian-immersed boundaries (IBs) method has been presented to simulate the interactions between fluid flow and a solid body with complex deformed boundaries
The interface of the solid body is treated as a level-set function, and its normal direction is used to reconstruct the velocity of forcing points
Summary
In many scientific research and engineering applications, problems of fluid–structure interaction (FSI) are inevitably encountered, such as the aeroelastic response of airplane wings (Gao, Zhang, & Tang, 2016), vibrations of wind turbine blades (Löhner et al, 2015; Mou, He, Zhao, & Chau, 2017), blood flow through heart valves (Zakaria et al, 2017) and flow past swimming fish or flying insects (Shrivastava, Malushte, Agrawal, & Sharma, 2017) Most of these take place in the fluid domain with complex immersed boundaries (IBs), and these FSI problems present significant challenges to numerical simulations (Akbarian et al, 2018; Ghalandari, Koohshahi, Mohamadian, Shamshirband, & Chau, 2019; Ramezanizadeh, Nazari, Ahmadi, & Chau, 2019) owing to their nonlinear and strongly coupled characteristics (Mhamed & David, 2013; Mosavi, Shamshirband, Salwana, Chau, & Tah, 2019). The velocity reconstruction relies on the normal direction of the solid boundary, which is computed from the level-set function and reinitialization process This algorithm can deal with an arbitrarily solid body with a complex smooth surface, and there is no need to regenerate the mesh when the solid body moves or deforms.
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