SPH simulations of flow around a periodic array of cylinders confined in a channel

In this paper, we present a numerical study on the performance of SPH in the case of a very viscous flow of a Newtonian liquid around a linear array of cylinders confined in a channel. This specific flow problem, being characterized by a complex mixing of both shear and extensional behaviour, allows to quantify systematically the accuracy of the standard SPH in, up to now, rarely considered complex geometries. Global accuracy tests based on the estimation of the dimensionless drag force acting on the cylinder as well as the inspection of the local velocity profiles are considered and compared with reference solutions. In agreement with previous findings, the impact of two numerical parameters, namely the smoothing length h and particle spacing Δx, is discussed and found to be crucial for the overall order of convergence of the method. In particular, accurate results can be obtained which are in very good agreement with standard mesh-based methods provided that the number of neighbours is chosen properly. The present results, being based on a detailed convergence analysis in a complex flow problem, justify the applicability of the SPH method to more complex wall-bounded flows upon critical choice of the model parameters and at the same time can serve as a useful benchmark test for further modelling improvement in the field.