Computational Fluid Dynamics by Takeo Kajishima & Kunihiko Taira

Author:Takeo Kajishima & Kunihiko Taira
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

5.2 Continuous Forcing Approach

The original immersed boundary method was developed to study hemodynamics inside the heart by Peskin [27, 28]. The flow field is represented by a Cartesian grid and the boundary of the immersed body (heart) is represented by a collection of Lagrangian points where boundary forces are introduced to satisfy the no-slip boundary condition, as illustrated in Fig. 5.1. We represent the spatial vector on the Cartesian grid domain as and the spatial vector on the body surface as , which has a surface (boundary) velocity .

Fig. 5.1The continuous forcing approach of the immersed boundary method. The immersed boundary in solid line is represented in the method with a set of Lagrangian points , where boundary force is applied to satisfy the no-slip boundary condition. The shaded boxes around the Lagrangian points depict the support of the discrete delta function over which the boundary force is regularized

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