Nonlinear free fall of one-dimensional rigid bodies in hyperviscous fluids

Abstract

We consider the free fall of slender rigid bodies in a viscous incompressible fluid. We show that the dimensional reduction (DR), performed by substituting the slender bodies with one-dimensional rigid objects, together with a hyperviscous regularization (HR) of the Navier--Stokes equation for the three-dimensional fluid lead to a well-posed fluid-structure interaction problem. In contrast to what can be achieved within a classical framework, the hyperviscous term permits a sound definition of the viscous force acting on the one-dimensional immersed body. Those results show that the DR/HR procedure can be effectively employed for the mathematical modeling of the free fall problem in the slender-body limit.

arXiv admin note: substantial text overlap with arXiv:1305.0707

References in corpus (1)

• Slender-body theory for viscous flow via dimensional reduction and hyperviscous regularization

Cited by in corpus (1)

• Steady free fall of one-dimensional bodies in a hyperviscous fluid at low Reynolds number