Abstract
We evaluate an efficient overset grid method for two-dimensional and three-dimensional particulate flows for small numbers of particles at finite Reynolds number. The rigid particles are discretised using moving overset grids overlaid on a Cartesian background grid. This allows for strongly-enforced boundary conditions and local grid refinement at particle surfaces, thereby accurately capturing the viscous boundary layer at modest computational cost. The incompressible Navier–Stokes equations are solved with a fractional-step scheme which is second-order-accurate in space and time, while the fluid–solid coupling is achieved with a partitioned approach including multiple sub-iterations to increase stability for light, rigid bodies. Through a series of benchmark studies we demonstrate the accuracy and efficiency of this approach compared to other boundary conformal and static grid methods in the literature. In particular, we find that fully resolving boundary layers at particle surfaces is crucial to obtain accurate solutions to many common test cases. With our approach we are able to compute accurate solutions using as little as one third the number of grid points as uniform grid computations in the literature. A detailed convergence study shows a 13-fold decrease in CPU time over a uniform grid test case whilst maintaining comparable solution accuracy.
Highlights
Flows of finite-sized particles in viscous fluids are common to many industrial as well as natural processes, such as primary cementing in the oil and gas industry [1] and blood flow [2]
These include arbitrary Lagrangian–Eulerian (ALE) methods [6,7,8], methods based on level-sets [9,10], fictitious domain methods [11,12,13], embedded boundary methods [14] and immersed boundary methods (IBM) [15,16,17,18,19,20,21,22,23,24,25,26,27]
Assuming this holds true for the 2D equivalent, the above results indicate that the repulsive potential collision model is a poor sub-grid model for low speed impacts
Summary
Flows of finite-sized particles in viscous fluids are common to many industrial as well as natural processes, such as primary cementing in the oil and gas industry [1] and blood flow [2]. Local grid refinement allows boundary layers to be fully resolved without appreciably affecting the total grid point count This is in contrast with general static grid methods where the solver efficiency is offset by the unfavourable scaling associated with uniform grids, making large fully resolved simulations very costly [44]. For these reasons, we evaluate the suitability of the method for fully resolved simulations of incompressible fluid flow with rigid particles.
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