SCIENTIA SINICA Physica, Mechanica & Astronomica, Volume 48 , Issue 9 : 094703(2018) https://doi.org/10.1360/SSPMA2018-00191

Recent progress of immersed boundary method and its applications in compressible fluid flow

• ReceivedMay 18, 2018
• AcceptedJun 1, 2018
• PublishedAug 2, 2018
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Abstract

Fluid-structure interaction problems are ubiquitous in nature and engineering applications. Typical examples include leaves waving, flag flapping, insect flight and tail flutter of high speed aircrafts. Accompanied with the development of high performance computers, numerical simulation has been applied to more and more areas and taken as an effective method for fluid–structure interaction problems. The immersed boundary method, first developed by Peskin and based on Cartesian mesh, is one of the methods for handling fluid-structure interaction problems involving complex geometries and large deformations. In this method, the Lagrangian force is spread onto the fluid nodes around the fluid-solid interface, as a forcing source of the Navier-Stokes equations to achieve the boundary conditions at the interface. In the immersed boundary method, it is not necessary to generate body conformal mesh. In addition, mesh movement and regeneration are avoided. Therefore, the efficiency could be higher compared to those methods based on body conformal mesh such as the arbitrary Lagrangian-Eulerian method and the deforming-spatial-domain/stabilized space-time method. Due to its advantages associated mesh generation, the immersed boundary method has recently been extended into compressible fluid-structure interaction problems, and is expected to have more and more significant impact in aeroelasticity and fluid-structure-sound interaction problems especially those involving complex geometries and large deformations. In this review article, we review the basic principle of the immersed boundary method and its recent progress. The applications of the immersed boundary method in compressible flows will be introduced by presenting a few benchmark cases and typical applications, including a flexible plate interacting with shock waves in a shock tube, a flexible plate in a hypersonic flow, acoustics in human phonation, acoustics scattered by a stationary cylinder, and sound generated by a rotating cylinder and a flapping wing in a uniform flow.

Funded by

Australian Research Council Discovery Early Career Researcher Award(DE160101098)

• Figure 1

(Color online) Schematic of immersed boundary method.

• Figure 2

(Color online) The physical and ghost points are tethered together by a virtual spring in the penalty immersed boundary method.

• Figure 3

(Color online) Schematic of a flexible plate interacting with shock waves in a shock tube.

• Figure 4

(Color online) Schlieren pictures from (a) experiments in ref. [39], (b) simulation by penalty immersed boundary method with an interval of 70 $\mu$s in ref. [8], and (c) simulation by sharp-interface immersed boundary method in ref. [21].

• Figure 5

(Color online) Schematic of a plate in a hypersonic flow. The solid line $(OA)$ is the fixed part and the dashed line $(AB)$ is the flexible plate.

• Figure 6

(Color online) Comparison of the time histories of the vertical displacement of the trailing end [8].

• Figure 7

(Color online) Comparison of the schlieren pictures from simulation (a) and experiment (b) [8].

• Figure 8

(Color online) Instantaneous acoustic field, total pressure fluctuation in human phonation [43].

• Figure 9

(Color online) Instantaneous acoustic field scattered by a cylinder.

• Figure 10

(Color online) (a) Time histories of the fluctuation pressure measured at (0, 2). (b) Local magnification.

• Figure 11

(Color online) Instantaneous pressure fluctuation induced by a rotating cylinder (a) and a flapping wing (b) in a uniform flow.

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