A simple immersed-boundary method for solid–fluid interaction in constant- and stratified-density flows

Abstract

The present work reports on the simulation of two- and three-dimensional constant- and stratified-density flows involving fixed or moving objects using an immersed-boundary method. The numerical approach is based on a simple immersed-boundary method in which no explicit Lagrangian marking of the immersed boundary is used. The solid object is defined by a continuous solid volume fraction which is updated thanks to the resolution of the Newton’s equations of motion for the immersed object. As shown on several test cases, this algorithm allows the flow field near the solid boundary to be correctly captured even though the numerical thickness of the transition region separating the fluid from the object is within three computational cells approximately. The full set of governing equations is then used to investigate some fundamental aspects of solid–fluid interaction, including fixed and moving objects in constant and stratified-density flows. In particular, the method is shown to accurately reproduce the steady-streaming patterns observed in the near-region of an oscillating sphere, as well as the so-called Saint Adrew’s cross in the far-field when the sphere oscillates in a rotating stratified fluid. The sedimentation of a particle in a stratified ambient is investigated for particle Reynolds numbers up to O(103) and the effect of stratification and density ratio is addressed. While the present paper only consider fluid–solid interaction for a single object, the present approach can be straightforwardly extended to the case of multiple objects of arbitrary shape moving in a stratified-density flow.