Accuracy of Finite Volume/Staggered Grid Distributed Lagrange Multiplier/Fictitious Domain simulations of particulate flows

Our Distributed Lagrange Multiplier/Fictitious Domain method [1], [2], [3] has been recently implemented with a Finite Volume/Staggered Grid discretization scheme [4] and successfully applied to the settling of a single particle in an unbounded domain. Here we scrutinize the space and time accuracy of the computed solution in a broad range of flow configurations of growing complexity. We suggest a 2nd order interpolation operator to impose the rigid body motion constraint at the particle boundary based on Finite Element cubic quadratic basis functions. This enables us to benefit from the best of both discretization schemes: a fast Finite Volume/Staggered Grid Navier & Stokes solver and a high order Finite Element reconstruction at the particle boundary. The resulting space accuracy of the computed solution is improved without the need to employ any hydrodynamic radius calibration procedure for spherical particles. As a result, the method can also accurately be extended to non-spherical and angular particles. The order of space convergence is between linear and quadratic, depending on the flow configuration, and the magnitude of the error has a tendency to increase with the solid volume fraction, the Reynolds number and the angularity of the particles.