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

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 $\mathcal{R}\mathfrak{e}=2.2\times 10<sup>4$. 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.