A staggered overset grid method for resolved simulation of incompressible flow around moving spheres

An overset grid method for resolved simulation of incompressible (turbulent) flows around moving spherical particles is presented. The Navier-Stokes equations in spherical coordinates are solved on body-fitted spherical polar grids attached to the moving spheres. These grids are overset on a fixed Cartesian background grid, where the Navier-Stokes equations in Cartesian coordinates are solved. The standard second-order staggered finite difference scheme is used on each grid. The velocities and pressures on different grids are coupled by third-order Lagrange interpolations. The method, implemented in the form of a Message Passing Interface parallel program, has been validated for a range of flows around spheres. In a first validation section, the results of simulations of four Stokes flows around a single moving sphere are compared with classical analytical results. The first three cases are the flows due to a translating, an oscillating sphere and a rotating sphere. The numerically produced velocity and pressure fields appear to converge to the corresponding (transient) analytical solutions in the maximum norm. The fourth Stokes case is the flow due to an instantaneously accelerated sphere. For this case, the results are compared with the corresponding numerical solution of the Basset-Boussinesq-Oseen equation. In a second validation section, results of three Navier-Stokes flows around one or more moving spheres are presented. These test configurations are a moving face-centered cubic array of spheres, laminar channel flow with a falling a sphere, and freely moving small spheres in a Taylor-Green flow. Results for the flow with the falling sphere are compared with the results from the literature on immersed boundary methods.