Numerical simulation of fluid forces on moving solid body by the vortex in cell method with volume penalization

Abstract

This study proposes a method for calculating the fluid forces acting on moving solid bodies in flows simulated by the vortex in cell (VIC) method. The body is represented using the volume penalization (VP) method, which introduces the influence of the body on the flow as an external force in the form of a penalization term into the Navier-Stokes equation. The pressure field is computed by solving the Poisson equation, which is derived by taking the divergence of the Navier-Stokes equation. The pressure and viscous stress on the body surface are calculated using a quadratic function along the vector normal to the surface. This study simulates the flow around a cylinder oscillating in still water by the VIC-VP method, and calculates the fluid forces acting on the cylinder using the proposed method. The velocity profiles on four cross-sections at three different time points agree well with the results of a measurement. The in-line force acting on the cylinder also agrees with the existing results computed by a boundary-conforming formulation. These demonstrate the validity of the authors' method for calculating the fluid forces on solid bodies in flows simulated by the VIC-VP method.