Frame-invariant sub-grid corrections to the Fictitious Domain Method for the simulation of particulate suspensions in nonlinear flows using OpenFOAM

A particle-scale simulation method for non-Brownian suspensions at low Reynolds numbers is presented, which is well suited to nonlinear flows. It is based on a Fictitious Domain Method supplemented by sub-grid corrections (Gallier et al., 2014 [16]). In the original method, the standard sub-grid corrections involve the underlying suspension linear flow. The conditions required to remove this ambient flow from the sub-grid corrections, while keeping frame indifference, are determined. A sub-grid correction matrix is built for the particle-particle and particle-wall hydrodynamic interactions, such that the mentioned conditions inherently hold. The method is validated against various flows that involve a few particles or a concentrated suspension in linear and nonlinear flows, with various boundary conditions.