High Order Immersed Boundary Method for Fluid-Structure Interaction of Viscous Compressible Flowwith a Rigid Body

Abstract

An efficient and versatile immersed boundary method (IBM) for simulating fluid-structure interaction (FSI) of compressible viscous flows with a convex rigid body has been developed. The compressible Navier-Stokes equations are discretized by globally fourth order summationby-parts (SBP) difference operators with built-in stability properties and the classical fourth order explicit Runge-Kutta method. The proposed Cartesian grid-based IBM enforces the solid wall boundary conditions at ghost points. Bilinear interpolation of the flow variables at image points and the solid wall boundary conditions are used to determine the flow variables at three layers of ghost points within the solid body in order to introduce the presence of the body interface in the high order flow computation. FSI of freestream flow at Reynolds number 200 and Mach number 0.25 with an elastically mounted circular cylinder is simulated. The equation of motion of the rigid body is solved by the classical fourth order explicit Runge-Kutta method. The coupling between the fluid and the structure is handled by exchanging the positions, velocities and forces at the fluid-structure interface in each stage. The rate of energy transferred between the fluid and the structure is investigated.