In order to develop accurate momentum coupling models for particle-laden flow, high-resolution simulations including the no-slip boundary condition at the surface of each particle are required, We have developed a numerical technique using overset grids that is suitable for performing this type of simulation. Here we apply the numerical method to simulations of the Taylor vortex array with a fixed particle. A background cartesian grid resolves the relevant scales away from the particle and enforces the periodic boundary conditions of the Taylor vortex array. The no-slip boundary conditions at the surface of the particle and the smaller flow scales near the particle are resolved by an overset cylindrical grid. We find that the force on the particle is significantly different than the force predicted using a standard drag correlation and estimates of the velocity at the particle location.