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Numerical simulation of fluid-structure interaction with the volume penalization method. (English) Zbl 1351.76202

Summary: We present a novel scheme for the numerical simulation of fluid-structure interaction problems. It extends the volume penalization method, a member of the family of immersed boundary methods, to take into account flexible obstacles. We show how the introduction of a smoothing layer, physically interpreted as surface roughness, allows for arbitrary motion of the deformable obstacle. The approach is carefully validated and good agreement with various results in the literature is found. A simple one-dimensional solid model is derived, capable of modeling arbitrarily large deformations and imposed motion at the leading edge, as it is required for the simulation of simplified models for insect flight. The model error is shown to be small, while the one-dimensional character of the model features a reasonably easy implementation. The coupled fluid-solid interaction solver is shown not to introduce artificial energy in the numerical coupling, and validated using a widely used benchmark. We conclude with the application of our method to models for insect flight and study the propulsive efficiency of one and two wing sections.

MSC:

76M22 Spectral methods applied to problems in fluid mechanics
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76Z10 Biopropulsion in water and in air

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