Assessment of regularized delta functions and feedback forcing schemes for an immersed boundary method.

*(English)*Zbl 1391.76576Summary: We present an improved immersed boundary method for simulating incompressible viscous flow around an arbitrarily moving body on a fixed computational grid. To achieve a large Courant-Friedrichs-Lewy number and to transfer quantities between Eulerian and Lagrangian domains effectively, we combined the feedback forcing scheme of the virtual boundary method with Peskin’s regularized delta function approach. Stability analysis of the proposed method was carried out for various types of regularized delta functions. The stability regime of the 4-point regularized delta function was much wider than that of the 2-point delta function. An optimum regime of the feedback forcing is suggested on the basis of the analysis of stability limits and feedback forcing gains. The proposed method was implemented in a finite-difference and fractional-step context. The proposed method was tested on several flow problems, including the flow past a stationary cylinder, inline oscillation of a cylinder in a quiescent fluid, and transverse oscillation of a circular cylinder in a free-stream. The findings were in excellent agreement with previous numerical and experimental results.

##### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

76M20 | Finite difference methods applied to problems in fluid mechanics |

76M15 | Boundary element methods applied to problems in fluid mechanics |

##### Keywords:

immersed boundary method; regularized delta function; feedback forcing; stability analysis; finite-difference method
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\textit{S. J. Shin} et al., Int. J. Numer. Methods Fluids 58, No. 3, 263--286 (2008; Zbl 1391.76576)

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