A Novel Volume-of-Solid-Based Immersed-Boundary Method for Viscous Flow with a Moving Rigid Boundary

Abstract

The present study adopts a volume-of-solid (VOS)-based immersed-boundary method (IBM) to simulate viscous incompressible flows interacting with moving solids using a numerical model based on the Navier-Stokes equations. The flow equations, with velocity–pressure variables, are discretized by a finite–element method on a nonuniform Cartesian grid, with the solutions obtained using a decoupled numerical scheme. Geometries featuring flexible solid obstacles in the flow are embedded in the Cartesian grid, with special treatments inside the embedded cell to ensure the accuracy of the solutions in the cut cells. In order to satisfy the no-slip condition of the body surface, a volume fraction is estimated to calculate the discretized body force inside the cut cell. More reasonable results for flow problems, including flows past a non-control/control circular cylinder and two cylinders moving against each other, are obtained by the present method. The time histories of drag and lift coefficients, as well as the vortex shedding frequencies, are extensively examined to demonstrate that the proposed method can be suitably combined with the fractional-step algorithm. Moreover, the temporal variations of velocity and vorticity fields are presented to demonstrate the capability of the present formulation in solving flow problems involving complex geometries, and the significance of the solid body forces on the flows.