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

Particle settling in yield stress fluids: Limiting time, distance and applications

“…All simulations are run with PeliGRIFF [29,36,37] . In the context of DLM/FD, the particle is discretized with 32 finite volumes over its equivalent diameter.…”

“…As already pointed out above, the whole problem is discretized in space with a classical FV/SG method [27,29] with secondorder schemes both for the diffusive (centered) and advective (TVD/Superbee) fluxes. The DLM/FD method is implemented with a collocation point technique which implies that particles are discretized by a set of points on which the rigid body motion constraint is imposed.…”

“…Since at the discrete level, our solution algorithm is implemented with a Finite Volume/Staggered Grid (FV/SG) scheme [29] , we present the solution algorithm below in a non-variational framework, which also facilitates its reading. Our semi-implicit solution algorithm hence reads:…”

“…They all involve writing the fluid conservation equations over the whole domain (fluid + particles) and solving the problem on a fixed grid. IB and FD force the rigid body motion in the region occupied by the particles with an additional source term in the fluid momentum equation while LB uses modified boundary conditions (see [29] for more detail). LB and IB are generally associated to an explicit time discretization.…”

“…The DLM/FD method is implemented with a collocation point technique which implies that particles are discretized by a set of points on which the rigid body motion constraint is imposed. A second-order interpolation operator is employed to reconstruct the velocity at the particle boundary in order to improve the accuracy of the solution (compared to the classical multi-linear interpolation usually used with FV/SG, see [29] for more detail).…”