A Level-Set Immersed Boundary Method for Incompressible Flows at Subcritical Reynolds Numbers

TL;DR

This paper presents a novel level-set immersed boundary method for simulating flow around two tandem cylinders at subcritical Reynolds numbers, analyzing flow structures and forces for different spacings.

Contribution

It introduces an improved level-set immersed boundary scheme combining a narrow-band conservative level set and ghost-fluid framework for accurate flow simulation.

Findings

Flow structures vary with spacing ratio.

Hydrodynamic forces are quantified at Re=2.2×10^4.

The method accurately captures interface dynamics.

Abstract

In this work, a numerical scheme based on a level-set immersed boundary method is employed for the numerical simulation of the flow around two tandem circular cylinders in the subcritical flow regimes. Three different spacing ratios $\ell/\mathcal{D}$ (where $\ell$ is the center-to-center distance between the two cylinders with $\mathcal{D}$ being the diameter of the cylinders) from $2$ to $4$ is considered. The instantaneous flow structures, pressure distributions and hydrodynamic forces on two tandem cylinders are analyzed at a Reynolds number of $\mathcal{R}\mathfrak{e}=2.2\times 10^4$. The strategy is based on a combination of a narrow-band accurate conservative level set method and ghost-fluid framework. In this strategy, the interface is defined as the isocontour of a hyperbolic tangent function, which is advected by the fluid, and then periodically reshaped to enforce the degraded level set function being a signed distance function using a reinitialization equation based on an improved form. The latter approach takes advantage of a mapping onto a classical distance level set while much better preserving the interface shape.