Adaptive Cartesian Immersed Boundary Method for Simulation of Flow over Flexible Geometries

Abstract

A solver for the incompressible Navier–Stokes equations in which solid surfaces are represented using an immersed boundary method is presented. Adaptive Cartesian mesh refinement and coarsening are employed both to resolve immersed boundaries and to dynamically resolve important flow features as they are developing. Dynamically evolving immersed boundaries are tracked using Lagrangian marker points that are governed by direct momentum forcing using either simple force laws or explicitly prescribed motion in a framework that permits simulation of both rigid and flexible lifting surfaces. The adaptive Cartesian immersed boundary method capability presented here is well suited for low Reynolds number flows over flexible lifting surfaces as encountered in modern flapping-wing flyers, flow over complex geometries undergoing large-scale deformations, and vortex-dominated flows. The implementation of both the incompressible Navier–Stokes solver and the immersed boundary method solution algorithm are described in detail, and validation studies are presented that demonstrate the effectiveness of the method for resolving flow over flexible lifting surfaces. Results for several representative test cases are presented, and favorable comparisons are made with published data and with results obtained using a volume of fluid advection scheme in the same solver framework.