Particle-Resolved DNS of heavy and neutrally-buoyant particles with the volume-filtering method

We present a novel computational method for direct numerical simulations of particle-laden with fully-resolved particles (PR-DNS). The method is based on the recently developed Volume-Filtering Immersed Boundary (VFIB) method derived by volume-filtering the transport equations. This approach is mathematically and physically rigorous, in contrast to other PR-DNS methods which rely on ad-hoc numerical schemes to impose no-slip boundary conditions on the surface of particles. With the present PR-DNS based on VFIB, we show that the ratio of filter size to particle diameter acts as a slider that controls the level of fidelity. In the limit where this ratio is very small, a well-resolved PR-DNS is obtained. Conversely, when the ratio of filter size to particle diameter is large, a classic point-particle method is obtained. The discretization of the filtered equations is discussed and compared to other PR-DNS strategies based on direct-forcing immersed boundary methods. Numerical examples with sedimenting resolved spheres show that the method is very robust, stable, and accurate, even with neutrally buoyant particles. The volume-filtering formulations enables multi-resolution simulations where, depending on the local resolution, the particles are represented as resolved spheres or Lagrangian particles.