A high order sharp immersed method for the simulation of moving bodies interacting with fluid flows

We demonstrate a third order accurate algorithm for solving the incompressible Navier-Stokes equations with moving immersed boundaries. Our approach relies on high-order finite-difference operators applied on a collocated grid, where the immersed geometries are taken into account using a sharp immersed method. This method has been shown to achieve high-order accuracy in space and time for moving immersed bodies. To handle the full Navier-Stokes equations, we present a pressure projection approach that retains high-order convergence of pressure and velocity in the infinity norm. Using an implementation of the algorithm in a 2D Julia code, we show convergence results, solutions to benchmark problems, and performance comparisons with our existing vorticity-velocity flow solver. In addition, we show preliminary results of the algorithm implemented in our in-house HPC solver 'murphy' to generate high-order results of 3D flows with embedded geometries.