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A conservative and non-dissipative Eulerian formulation for the simulation of soft solids in fluids. (English) Zbl 1453.74029

Summary: Soft solids in fluids find wide range of applications in science and engineering, especially in the study of biological tissues and membranes. In this study, an Eulerian finite volume approach has been developed to simulate fully resolved incompressible hyperelastic solids immersed in a fluid. We have adopted the recently developed reference-map technique (RMT) by B. Valkov et al. [“Eulerian method for multiphase interactions of soft solid bodies in fluids”, J. Appl. Mech. 82, No. 4, Article No. 040011, 14 p. (2015; doi:10.1115/1.4029765)] and assessed multiple improvements for this approach. These modifications maintain the numerical robustness of the solver and allow the simulations without any artificial viscosity in the solid regions (to stabilize the solver). This has also resulted in eliminating the striations (“wrinkles”) of the fluid-solid interface that was seen before and hence obviates the need for any additional routines to achieve a smooth interface. An approximate projection method has been used to project the velocity field onto a divergence free field. Cost and accuracy improvements of the modifications on the method have also been discussed.

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76D05 Navier-Stokes equations for incompressible viscous fluids
76M12 Finite volume methods applied to problems in fluid mechanics
74S10 Finite volume methods applied to problems in solid mechanics

Software:

IIMPACK
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Full Text: DOI arXiv

References:

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